Solar particle radiation storms forecasting and analysis

Malandraki, Olga E.

Crosby, Norma B.

2018

Springer

Solar energetic particles (SEPs) emitted from the Sun are a major space weather hazard motivating the development of predictive capabilities. This book presents the results and findings of the HESPERIA (High Energy Solar Particle Events forecasting and Analysis) project of the EU HORIZON 2020 programme. It discusses the forecasting operational tools developed within the project, and presents progress to SEP research contributed by HESPERIA both from the observational as well as the SEP modelling perspective. Using multi-frequency observational data and simulations HESPERIA investigated the chain of processes from particle acceleration in the corona, particle transport in the magnetically complex corona and interplanetary space, to the detection near 1 AU. The book also elaborates on the unique software that has been constructed for inverting observations of relativistic SEPs to physical parameters that can be compared with spac
e-borne measurements at lower energies. Introductory and pedagogical material included in the book make it accessible to students at graduate level and will be useful as background material for Space Physics and Space Weather courses with emphasis on Solar Energetic Particle Event Forecasting and Analysis.

This book is published with open access under a CC BY 4.0 license.

Physics

Natural disasters

Atmospheric physics

English

978-3-319-60051-2

978-3-319-60050-5

Astrophysics and Space Science Library 444

Olga E. Malandraki
Norma B. Crosby
Editors

Solar Particle
Radiation Storms
Forecasting
and Analysis
The HESPERIA HORIZON 2020 Project
and Beyond

Solar Particle Radiation Storms Forecasting
and Analysis

Astrophysics and Space Science Library
EDITORIAL BOARD
Chairman
W. B. BURTON, National Radio Astronomy Observatory, Charlottesville,
Virginia, U.S.A. (bburton@nrao.edu); University of Leiden, The Netherlands
(burton@strw.leidenuniv.nl)
F. BERTOLA, University of Padua, Italy
C. J. CESARSKY, Commission for Atomic Energy, Saclay, France
P. EHRENFREUND, Leiden University, The Netherlands
O. ENGVOLD, University of Oslo, Norway
E. P. J. VAN DEN HEUVEL, University of Amsterdam, The Netherlands
V. M. KASPI, McGill University, Montreal, Canada
J. M. E. KUIJPERS, University of Nijmegen, The Netherlands
H. VAN DER LAAN, University of Utrecht, The Netherlands
P. G. MURDIN, Institute of Astronomy, Cambridge, UK
B. V. SOMOV, Astronomical Institute, Moscow State University, Russia
R. A. SUNYAEV, Max Planck Institute for Astrophysics, Garching, Germany

More information about this series at http://www.springer.com/series/5664

Olga E. Malandraki • Norma B. Crosby
Editors

Solar Particle Radiation
Storms Forecasting
and Analysis
The HESPERIA HORIZON 2020 Project
and Beyond

Editors
Olga E. Malandraki
National Observatory of Athens
IAASARS
Athens, Greece

Norma B. Crosby
Space Physics Division - Space Weather
Royal Belgian Institute for Space Aeronomy
Brussels, Belgium

ISSN 0067-0057
ISSN 2214-7985 (electronic)
Astrophysics and Space Science Library
ISBN 978-3-319-60050-5
ISBN 978-3-319-60051-2 (eBook)
DOI 10.1007/978-3-319-60051-2
Library of Congress Control Number: 2017957900
© The Editor(s) (if applicable) and The Author(s) 2018. This book is an open access publication.
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Preface

Ranging in energy from tens of keV to a few GeV solar energetic particles (SEPs)
are an important contributor to the characterization of the space environment.
Emitted from the Sun they are associated with solar flares and shock waves driven
by coronal mass ejections (CMEs). SEP radiation storms may last from a period of
hours to days or even weeks and have a large range of energy spectrum profiles.
These events pose a threat to modern technology relying on spacecraft and humans
in space as they are a serious radiation hazard. Though our understanding of
the underlying physics behind the generation mechanism of SEP events and their
propagation from the Sun to Earth has improved during the last decades, to be able
to successfully predict a SEP event is still not a straightforward process.
The motivation behind the 2-year HESPERIA (High Energy Solar Particle Events
forecasting and Analysis) project of the EU HORIZON 2020 programme, successfully completed in April 2017, was indeed to further our scientific understanding and
prediction capability of high-energy SEP events by building new forecasting tools
while exploiting novel as well as already existing datasets. HESPERIA, led by the
National Observatory of Athens, with Project Coordinator Dr. Olga E. Malandraki,
was a consortium of nine European teams that also collaborated during the project
with a number of institutes and individuals from the international community.
The complementary expertise of the teams made it possible to achieve the main
objectives of the HESPERIA project:
• To develop two novel real-time SEP forecasting systems based upon proven
concepts.
• To develop SEP forecasting tools searching for electromagnetic proxies of the
gamma-ray emission in order to predict large SEP events.
• To perform systematic exploitation of novel high-energy gamma-ray observations of the FERMI mission together with in situ SEP measurements near 1 AU.
• To provide for the first time publicly available software to invert neutron monitor
observations of relativistic SEPs to physical parameters that can be compared
with space-borne measurements at lower energies.

v

vi

Preface

• To perform examination of currently unexploited tools (e.g. radio emission).
• To design recommendations for future SEP forecasting systems.
This book reviews our current understanding of SEP physics and presents the
results of the HESPERIA project. In Chap. 1 the book provides a historical overview
on how SEPs were discovered back in the 1940s and how our understanding has
increased and evolved since then. Current state of the art based on the unique
measurements analysed in the three-dimensional heliosphere and the key SEP
questions that remain to be answered in view of the future missions Solar Orbiter
and Parker Solar Probe that will explore the solar corona and inner heliosphere are
also presented. This is followed by an introduction to why SEPs are studied in the
first place describing the risks that SEP events pose on technology and human health.
Chapters 2 through 6 serve as background material covering solar activity related to
SEP events such as solar flares and coronal mass ejections, particle acceleration
mechanisms, and transport of particles through the interplanetary medium, Earth’s
magnetosphere and atmosphere. Furthermore, ground-based neutron monitors are
described. The last four chapters of the book are dedicated to and present the main
results of the HESPERIA project. This includes the two real-time HESPERIA SEP
forecasting tools that were developed, relativistic SEP related gamma-ray and radio
data comparison studies, modelling of SEP events associated with gamma-rays and
the inversion methodology for neutron monitor observations that infers the release
timescales of relativistic SEPs at or near the Sun.
With emphasis on SEP forecasting and data analysis, this book can both serve as
a reference book and be used for space physics and space weather courses addressed
to graduate and advanced undergraduate students. We hope the reader of this book
will find the world of SEP events just as fascinating as we do ourselves.
Olga E. Malandraki
Norma B. Crosby

Acknowledgements

The HESPERIA project has received funding from the European Union’s Horizon
2020 research and innovation programme under grant agreement No 637324. The
authors thank the EU for this support making it possible to further our knowledge
in solar energetic particle research and forecasting, as well as write this book.
The authors of Chaps. 4, 9 and 10 acknowledge the use of ERNE data from
the Space Research Laboratory of the University of Turku and of the SEPEM
Reference Data Set version 2.00, European Space Agency (2016). They thank the
ACE/EPAM, SWEPAM and MAG instrument teams and the ACE Science Center
for providing the ACE data. They acknowledge the use of publicly available data
products from WIND/SWE and 3DP, GOES13/HEPAD and the CME catalogues
from SoHO/LASCO and STEREO/COR1. SoHO is a project of international
cooperation between ESA and NASA. They acknowledge also the use of the
Harvard-Smithsonian Interplanetary shock Database maintained by M. L. Stevens
and J. C. Kasper and of the Heliospheric Shock Database, generated and maintained
at the University of Helsinki.
Rolf Bütikofer thanks Erwin Flückiger and Claudine Frieden for their suggestions and assistance in writing Chaps. 5 and 6. This work was supported by
the Swiss State Secretariat for Education, Research and Innovation (SERI) under
the contract number 15.0233 and by the International Foundation High Altitude
Research Stations Jungfraujoch and Gornergrat.
The authors of Chap. 7 thank the National Oceanic Atmospheric Administration
(NOAA) for providing GOES data files which were used to calibrate and evaluate the HESPERIA UMASEP-500 tool. They acknowledge the NMDB database
(www.nmdb.eu) funded under the European Union’s FP7 programme (contract No.
213007). They also acknowledge Dr. Juan Rodriguez from NOAA for his support
on the estimation of >500 MeV integral proton flux and expert advice on the
GOES/HEPAD data.
The authors of Chap. 8 acknowledge STEREO/HET/LET/SEPT, ACE/EPAM,
ACE/SIS, GOES/HEPAD, WIND/3DP and SoHO/ERNE/EPHIN teams as well
as the SEPServer team for the availability of the energetic particle data. The
STEREO/SEPT and the SoHO/EPHIN projects are supported under grant
vii

viii

Acknowledgements

50OC1702 by the Federal Ministry of Economics and Technology on the basis
of a decision by the German Bundestag. Gerald H. Share and Ronald J. Murphy
(Department of Astronomy, University of Maryland, College Park MD 20742
and National Observatory of Athens; Naval Research Laboratory, Washington DC
20375) are acknowledged for making Fermi/LAT data available to the project
prior to their publication. Specifically, the authors of Chap. 9 thank G. Share for
providing the data on interacting proton spectra derived from the Fermi/LAT ”-ray
observations.
Alexandr Afanasiev and Rami Vainio acknowledge the financial support of
the Academy of Finland (project 267186) and the computing resources of the
Finnish Grid and Cloud Infrastructure maintained by CSC—IT Centre for Science
Ltd. (Espoo, Finland) and co-funded by the Academy of Finland and 13 Finnish
research institutions. The team of the University of Barcelona has been also partially
supported by the Spanish Ministerio de Economía, Industria y Competitividad,
under the project AYA2013-42614-P and MDM-2014-0369 of ICCUB (Unidad
de Excelencia ‘María de Maeztu’). Computational support was provided by the
Consorci de Serveis Universtiaris de Catalunya (CSUC).
Alexis P. Rouillard (external collaborator of the HESPERIA project) acknowledges support from the plasma physics data center (Centre de Données de la
Physique des Plasmas; CDPP; http://cdpp.eu/), the Virtual Solar Observatory
(VSO; http://sdac.virtualsolar.org), the Multi Experiment Data & Operation Center
(MEDOC; https://idoc.ias.u-psud.fr/MEDOC), the French space agency (Centre
National des Etudes Spatiales; CNES; https://cnes.fr/fr) and the space weather
team in Toulouse (Solar-Terrestrial Observations and Modelling Service; STORMS;
https://stormsweb.irap.omp.eu/). This includes the data mining tools AMDA (http://
amda.cdpp.eu/) and the propagation tool (http://propagationtool.cdpp.eu). He also
acknowledges financial support from the HELCATS project under the FP7 EU
contract number 606692. The STEREO SECCHI data are produced by a consortium
of RAL (UK), NRL (USA), LMSAL (USA), GSFC (USA), MPS (Germany), CSL
(Belgium), IOTA (France) and IAS (France).
The authors thank Springer for their interest in the HESPERIA project and the
opportunity for the publication of its results.

Contents

1

Solar Energetic Particles and Space Weather: Science
and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Olga E. Malandraki and Norma B. Crosby

1

2

Eruptive Activity Related to Solar Energetic Particle Events . . . . . . . . .
Karl-Ludwig Klein

27

3

Particle Acceleration Mechanisms . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Rami Vainio and Alexandr Afanasiev

45

4

Charged Particle Transport in the Interplanetary Medium . . . . . . . . . . .
Angels Aran, Neus Agueda, Alexandr Afanasiev, and Blai Sanahuja

63

5

Cosmic Ray Particle Transport in the Earth’s Magnetosphere . . . . . . .
R. Bütikofer

79

6

Ground-Based Measurements of Energetic Particles
by Neutron Monitors .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
R. Bütikofer

95

7

HESPERIA Forecasting Tools: Real-Time and Post-Event . . . . . . . . . . . 113
Marlon Núñez, Karl-Ludwig Klein, Bernd Heber,
Olga E. Malandraki, Pietro Zucca, Johannes Labrens,
Pedro Reyes-Santiago, Patrick Kuehl, and Evgenios Pavlos

8

X-Ray, Radio and SEP Observations of Relativistic
Gamma-Ray Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 133
Karl-Ludwig Klein, Kostas Tziotziou, Pietro Zucca, Eino Valtonen,
Nicole Vilmer, Olga E. Malandraki, Clarisse Hamadache,
Bernd Heber, and Jürgen Kiener

9

Modelling of Shock-Accelerated Gamma-Ray Events. . . . . . . . . . . . . . . . . . 157
Alexandr Afanasiev, Angels Aran, Rami Vainio, Alexis Rouillard,
Pietro Zucca, David Lario, Suvi Barcewicz, Robert Siipola,
Jens Pomoell, Blai Sanahuja, and Olga E. Malandraki
ix

x

Contents

10 Inversion Methodology of Ground Level Enhancements . . . . . . . . . . . . . . 179
B. Heber, N. Agueda, R. Bütikofer, D. Galsdorf, K. Herbst, P. Kühl,
J. Labrenz, and R. Vainio
Index . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 201

List of Abbreviations

ACE
AEPE
AIA
AMS
AU
AWT
CDAW
CGRO
CME
CORONAS
CIR
CSA
CS
DSA
DSP
EGRET
EPAM
EPD
EPHIN
ESA
ESP
FAR
GBM
GCR
GLE
GME
GOES
GSE
HCS
HEPAD

Advanced Composition Explorer
Atypical Energetic Particle Event
Atmospheric Imaging Assembly
Alpha Magnetic Spectrometer
Astronomical Unit
Average Warning Time
Coordinated Data Analysis Workshops
Compton Gamma-Ray Observatory
Coronal Mass Ejection
Complex Orbital near-Earth Observations of Solar Activity
Corotating Interaction Region
Coronal Shock Acceleration
Current Sheet
Diffusive Shock Acceleration
Downstream Propagation
Energetic Gamma Ray Experiment Telescope
Electron, Proton, and Alpha Monitor
Energetic Particle Detector
Electron Proton Helium Instrument
European Space Agency
Energetic Storm Particle
False Alarm Ratio
Gamma-ray Burst Monitor
Galactic Cosmic Rays
Ground Level Enhancement
Goddard Medium Energy
Geostationary Operational Environmental Satellites
Geocentric Solar Ecliptic
Heliospheric Current Sheet
High Energy Proton and Alpha Detector

xi

xii

HESPERIA
ICME
IMF
IMP
INTEGRAL
ISIS
ISS
L1
LAT
LMA
MED
MHD
NASA
NGDC
NNLS
NOAA
NoRP
NM
PAD
PAMELA
PFSS
POD
QLT
PROBA
REleASE
RHESSI
RICH
RSTN
SaP
SCR
SDA
SDO
SEP
SEPEM
SMM
SOHO
SolO
SSD
STEREO
SWAP

List of Abbreviations

High Energy Solar Particle Events forecasting and Analysis
Interplanetary Coronal Mass Ejection
Interplanetary Magnetic Field
International Monitoring Platform
INTErnational Gamma-Ray Astrophysics Laboratory
Integrated Science Investigation of the Sun
International Space Station
first Lagrangian point
Large Area Telescope
Levenberg-Marquardt algorithm
Medium Energy Detector
MagnetoHydroDynamics
National Aeronautics and Space Administration
National Geophysical Data Center
Non-Negative Least Squares
National Oceanic and Atmospheric Administration
Nobeyama Radio Polarimeters
Neutron Monitor
Pitch Angle Distribution
Payload for Antimatter Matter Exploration and Light-nuclei
Astrophysics
Potential Field Source Surface
Probability of Detection
Quasi-Linear Theory
Project for On-Board Autonomy
Relativistic Electron Alert System for Exploration
Ramaty High Energy Solar Spectroscopic Imager
Ring Imaging CHerenkov
Radio Solar Telescope Network
Shock and Particle
Solar Cosmic Rays
Shock Drift Acceleration
Solar Dynamics Observatory
Solar Energetic Particle
Solar Energetic Particle Environment Modelling
Solar Maximum Mission
SOlar and Heliospheric Observatory
Solar Orbiter
Solid State Detector
Solar Terrestrial Relations Observatory
Sun Watcher using Active pixel system detector and image
Processing

List of Abbreviations

SXR
UMASEP
WCP
WL

Soft X-Ray
University of MAlaga Solar particle Event Predictor
Well-Connected Prediction model
White Light

xiii

Chapter 1

Solar Energetic Particles and Space Weather:
Science and Applications
Olga E. Malandraki and Norma B. Crosby

Abstract This chapter provides an overview on solar energetic particles (SEPs)
and their association to space weather, both from the scientific as well as from
the applications perspective. A historical overview is presented on how SEPs were
discovered in the 1940s and how our understanding has increased and evolved
since then. Current state-of-the-art based on unique measurements obtained in the
3-dimensional heliosphere (e.g. by the Ulysses, ACE, STEREO spacecraft) and
their analysis is also presented. Key open questions on SEP research expected
to be answered in view of future missions that will explore the solar corona and
inner heliosphere are highlighted. This is followed by an introduction to why SEPs
are studied, describing the risks that SEP events pose on technology and human
health. Mitigation strategies for solar radiation storms as well as examples of current
SEP forecasting systems are reviewed, in context of the two novel real-time SEP
forecasting tools developed within the EU H2020 HESPERIA project.

1.1 Science
1.1.1 Historical Perspective of Solar Energetic Particle (SEP)
Events
It is widely accepted that protons, electrons, and heavier nuclei such as He-Fe are
accelerated from a few keV up to GeV energies in at least two distinct locations,
namely the solar flare and the coronal mass ejection (CME)-driven interplanetary
(IP) shock. The particles observed in IP space and near Earth are commonly referred
to as solar energetic particles (SEPs). Those accelerated at flares are known as

O.E. Malandraki ()
National Observatory of Athens, IAASARS, Athens, Greece
e-mail: omaland@noa.gr
N.B. Crosby
Royal Belgian Institute for Space Aeronomy, Brussels, Belgium
e-mail: Norma.Crosby@aeronomie.be
© The Author(s) 2018
O.E. Malandraki, N.B. Crosby (eds.), Solar Particle Radiation Storms Forecasting
and Analysis, The HESPERIA HORIZON 2020 Project and Beyond, Astrophysics
and Space Science Library 444, DOI 10.1007/978-3-319-60051-2_1

1

2

O.E. Malandraki and N.B. Crosby
3600
3400
3200

Nucleonic Component for U.S.S. Arneb pile
(Welington Harbor) Counts per min

3000
2800
2600
2400
2200
2000
1800
1600
1400
1200
1000
800
600
400
200
0
0300

0400

0500

0600

0700

0800

Hours – Univeral Time

Fig. 1.1 Early observation of a solar energetic particle event (Reproduced from Meyer et al.
1956, permission for reuse from publisher American Physical Society for both print and electronic
publication)

impulsive SEP events, particle populations accelerated by near-Sun CME-shocks
are termed as gradual SEP events, and those associated with CME shocks observed
near Earth are known as energetic storm particle (ESP) events (Desai and Giacalone
2016).
The first SEP event observations extending up to GeV energies were made with
ground-based ionization chambers and neutron monitors in the mid 1940s (Forbush
1946). One early event is shown in Fig. 1.1. Until the mid-1990s the so-called ‘solar
flare myth’ scenario was prevalent, in which large solar flares were considered to
be the primary cause of major energetic particle events observed at 1 AU (Gosling
1993). However, Wild et al. (1963) had reviewed radio observations and on the basis
of the slow-drifting type II bursts observed in close association with the SEP events,
proposed an alternative view for the particle acceleration at magnetohydrodynamic
shock waves, typically accompanying the flares.
By the end of the 1990s a two-class paradigm of SEP events (see Fig. 1.2)
had been generally accepted (e.g. Reames 1999). The flare-related impulsive events
lasted a few hours and were typically observed when the observer was magnetically
connected to the flare site, were electron-rich and associated with type III radio
bursts. These events also had 3 He/4 He ratios enhanced by factors 103 –104 , enhanced
Fe/O ratios by a factor of 10 over the nominal coronal values, and Fe ionization
states of up to 2. On the other hand, the gradual events lasted several days, had
larger fluences, and were attributed to be a result of diffusive acceleration at CMEdriven coronal and IP shocks. They were proton-rich, had average Fe/O ratios of
0.1 and Fe ionization states of 14 and were associated with type II radio bursts (e.g.
Cliver 2000; Reames 2013).

1 Solar Energetic Particles and Space Weather: Science and Applications

3

Fig. 1.2 The two-class paradigm of SEP events is presented (a) the gradual SEP events occur as
a result of diffusive acceleration at CME-driven coronal and IP shocks and populate interplanetary
magnetic field (IMF) lines over a large longitudinal extent (b) the impulsive SEP events which
are produced by solar flares and which populate only those IMF lines well-connected to the flare
site. Comparison of intensity-time profiles of electrons and protons in ‘pure’, (c) gradual and (d)
impulsive SEP events. The gradual event is a disappearing—filament event with a CME but no
impulsive flare. The impulsive events come from a series of flares with no CMEs (Reproduced
from Desai and Giacalone 2016, permission for reuse from publisher Springer for both print and
electronic publication)

Since then, observations have indicated that there are ‘hybrid’ or mixed event
cases, where both mechanisms appear to contribute, with one accelerating mechanism operating in the flare while the other operates at the CME-driven shock
(Kallenrode 2003). Such hybrid events may result from the re-acceleration of
remnant flare suprathermals by shock waves (Mason et al. 1999; Desai et al. 2006) or
from the interaction of CMEs (Gopalswamy et al. 2002). It is noteworthy however,
that based on large enhancements in the Fe/O during the initial phases of two
large SEP events observed by Wind and Ulysses when the two spacecraft (s/c)
were separated by 60ı in longitude (Tylka et al. 2013) argued that the initial Fe/O
enhancements cannot be cited as evidence for a direct flare component, but instead

4

O.E. Malandraki and N.B. Crosby

Fig. 1.3 Proton spectra of the SEP events of April 1998 (green, Tylka et al. 2000) and September
1989 (blue, Lovell et al. 1998) are compared. In yellow the hazardous portion of the spectrum
during the April 1998 event is highlighted. The region of additional hazardous radiation from the
September 1989 event is shaded red (Reproduced from Reames 2013, permission for reuse from
publisher Springer for both print and electronic publication)

they are better understood as a transport effect, driven by the different mass-tocharge ratios of Fe and O.
High-energy protons in the largest SEP events can pose significant radiation
hazards for astronauts and technological systems in space, particularly beyond
the Earth’s protective magnetic field (National Research Council (NCR) 2008;
Cucinotta et al. 2010; Xapsos et al. 2012) (see Sect. 1.2 for more details).
Protons of 150 MeV are considered as ‘hard’ radiation since they are very
difficult to shield against. Essentially most of the radiation risk of humans in space
from SEPs is due to proton intense fluxes of above 50 MeV, i.e. ‘soft’ radiation, the
energy at which protons begin to penetrate spacesuits and s/c housing. Figure 1.3
compares the proton energy spectra for two large SEP events, presenting typical
knee energies of soft and hard radiation SEP events. The most important factor in
the radiation dose and depth of penetration of the ions is the location of the energy
spectral knee. In yellow in Fig. 1.3, the hazardous part of the spectrum for the
April 1998 event is shown, whereas the red shaded area denotes the region of the
additional hazardous radiation from the September 1989 event. In the April 1998
event the spectrum rolls over much more steeply at high energies, whereas in the
September 1989 event the spectral knee occurred between 200 and 300 MeV.
Events with higher roll-over energies have significantly higher proton intensities
above 100 MeV and can constitute a severe radiation hazard to astronauts (Reames
2013). In fact during the September 1989 event, even an astronaut behind 10 g cm2
of material would receive a dose of 40 mSv. The annual dose limit for a radiation
worker in the United States is 20 mSv (Zeitlin et al. 2013; Kerr 2013). In each solar

1 Solar Energetic Particles and Space Weather: Science and Applications

5

Sun

5

10
10

3

10

1

W53°

10

Shock

5

E45°

Shock

3

10

101

10–1

10–1

CME

10–3

10

10–5

105
6

7

82Mar

8

E01°

9 10 11 12 13
10

–3

10–5
Shock

3

1–4 Mev
7–13 Mev
22–27 Mev

25 26 27 28 29 30 31
82Dec

1

83Jan

101
10–1
10

–3

10–5
9

10 11 12 13 14 15 16

78Nov

Fig. 1.4 Typical intensity–time profiles of 1–30 MeV protons for gradual SEP events observed at
three different solar longitudes relative to the parent solar event. Dashed lines indicate the passage
of shocks (Reproduced from Reames 2013, permission for reuse from publisher Springer for both
print and electronic publication)

cycle several events of this intensity occur, thus, knowledge of the spectral knee
energies is essential.

1.1.2 Large Gradual SEP Events
Early multi-spacecraft SEP observations revealed that 1–30 MeV proton timeintensity profiles in large gradual SEP events observed in the ecliptic plane at 1
AU are organized in terms of the longitude of the observer with respect to the
traveling CME-driven shock and can be understood if the strongest acceleration
occurs near the ‘nose’ of a CME-driven shock radially expanding outward from the
Sun (see Fig. 1.4, Reames 2013; Cane et al. 1988; Cane and Lario 2006).1 Figure
1.4 shows proton intensity profiles of several SEP events observed by the IMP-8 s/c
as a function of longitude of the parent solar event. For observers at solar longitudes
to the east of the source, the intensities have rapid rises peaking relatively earlier
during the event when there is magnetic connection to the nose of the CME-shock
1

When observing images of the Sun east and west are reversed.

6

O.E. Malandraki and N.B. Crosby
20 MeV

2 MeV
104
Wind - LASCO
103

Protons/(cm2 sr s MeV)

102

Helios - SOLWIND
j - V4.36
r=0.616

LS fit:
j - V4.83
r=0.718

101
100
10–1
10–2
10–3
10–4
100

200

400 600

1000 2000 100
200
CME speed (km/s)

400 600

1000

2000

Fig. 1.5 Peak proton intensity in SEP events at 2 and 20 MeV as a function of CME speed. The
different symbols denote two combinations of SEP instruments (Wind, Helios) and coronagraphs
(LASCO, SOLWIND). Linear least-squares fits as well as the corresponding correlation coefficients are shown for each proton energy (Reproduced from Kahler 2001, permission for reuse
from publisher John Wiley and Sons for both print and electronic publication)

near the Sun. Gradual decreasing intensities are observed subsequently, as the shock
moves outward and the s/c becomes magnetically connected to the eastern flanks of
the shock. For sources near the central meridian the proton intensities peak when the
nose of the shock itself arrives at the s/c location. Observers located to the west of the
source observe slowly rising intensities that peak after the local passage of the shock.
Comparison between the SEP and the CME or IP shock properties have shown no
evidence of a clear correlation. In Fig. 1.5 (Kahler 2001) it is shown that CMEs with
similar speeds are associated with a significant spread (3–4 orders of magnitude)
in the peak proton intensities at 2 and 20 MeV of the associated SEPs at 1 AU.
This study subsequently constituted the basis for comparison of a more recent
multi-spacecraft study by (Rouillard et al. 2012) in which shock speeds could be
measured where the shock intersected the field lines to each s/c in the heliosphere
(see Sect. 1.1.4). Using a large number of SEP events, Kahler (2013a) examined
the SEP-CME relationship calculating three different SEP event timescales: the
onset time from CME launch to the 20 MeV SEP onset time, the rise time from

1 Solar Energetic Particles and Space Weather: Science and Applications

7

SEP onset to half the peak intensity and the duration of the SEP intensity above
half the peak value. Comparison of these timescales with the CME properties such
as speed, acceleration, width and location confirmed that faster (and wider) CMEs
drive shocks, and accelerated SEPs over longer periods of time produce SEP events
with longer timescales and larger fluences.
A flatter size distribution of SEP events relative to that of flare soft X-ray (SXR)
events has been previously reported, with the power-law characterizing SEP size
being significantly flatter than that of the SXR flux (e.g. Hudson 1978; Belov
et al. 2007; Cliver et al. 2012). Cliver et al. (2012) have shown that this difference
is primarily due to the fact that flares associated with large gradual SEP events
are an energetic subset of all flares also characteristically accompanied by fast
(>1000 km/s) CMEs that drive coronal/IP shock waves. They also concluded that
the difference of 0.15 between the slopes of the SEP event distributions and
SEP SXR flares is consistent with the observed variation of SEP event peak flux
with SXR peak flux. Kahler (2013b) presented arguments against using scaling
laws for the description of the relationship between the size distributions of SXR
flares and SEP events. They suggested an alternative explanation for flatter SEP
power-law distributions in terms of the recent model of fractal-diffusive selforganized criticality proposed by Aschwanden (2012), providing evidence against
a close physical connection of flares with SEP production. Trottet et al. (2015),
although based on a limited SEP event sample, have recently studied the statistical
relationships between SEP peak intensities of deka-MeV and near-relativistic
electrons and characteristic parameters of CME and solar flares: the CME speed
as well as the peak flux and fluence of SXR emission and the fluence of microwave
emission. Via a partial correlation analysis they showed that the CME speed and
SXR fluence are the only parameters that significantly affect the SEP intensity and
concluded that both flare acceleration and CME shock acceleration contribute to the
deka-MeV proton and near-relativistic electron populations in large SEP events.
Above a few tens of MeV per nucleon, large gradual SEP events are highly
variable in their spectral characteristics and elemental composition. As an example,
Fig. 1.6 (left) shows the event-integrated Fe/C ratio as a function of energy for
the SEP events of April 21, 2002 and August 24, 2002 (Tylka et al. 2005). Both
events were associated with flares nearly identical in terms of their sizes and solar
locations (W80), as well as with CMEs with similar speeds of 2000 km/s,
however, there were remarkable differences observed in their associated heavy ion
spectral behaviour. To explain these differences, Cane et al. (2003) and Cane et
al. (2006) proposed a direct flare particle component above 10 MeV/nuc and
that large SEP events are a mixture of flare-accelerated and shock-accelerated
populations. According to this scenario, well-connected western hemisphere events
are dominated by flare-accelerated particles above 10 MeV/nuc, causing the
significant increase of Fe/O, and could also account for the increasing energy
dependence of the Fe/O ratios observed e.g. during the August 24, 2002 event. On
the other hand the CME shock during the April 21, 2002 event is strong enough
to accelerate >10 MeV/nucleon particles at 1 AU and lead to the observed Fe/O
decrease with increasing energy.

8

O.E. Malandraki and N.B. Crosby

Fig. 1.6 The left panel shows a comparison of the energy dependence of the event-integrated Fe/C
for the two SEP events of 21 April 2002 (blue) and 24 August 2002 (red) which are otherwise
similar in their properties (Tylka et al. 2005). The right panel shows hypothetical spectra of the
suprathermal seed populations for shock-accelerated SEPs, comprising both solar wind and flareaccelerated ions. Different injection thresholds will yield different abundance ratios (Reproduced
from Reames 2013, permission for reuse from publisher Springer for both print and electronic
publication)

Fig. 1.7 (left) The 90 large SEP events defined as events with >12 MeV/nucleon Fe fluences > 0.1/(cm2 sr) from 1998 to 2005. Days with high fluence only occur when the density of
pre-existing suprathermal Fe was >0.3 Dm3 . (right) Histogram of daily averaged suprathermal Fe
densities for all days from March 1998 to December 2005 (Reproduced from Mewaldt et al. 2012a,
permission for reuse from publisher AIP Publishing LLC for both print and electronic publication)

Re-acceleration of remnant flare suprathermals or from accompanying flares has
been another plausible idea to account for the observed elemental composition
variability in SEP events. Mewaldt et al. (2012a) examined the dependence of
SEP fluences on suprathermal seed-particle densities. In Fig. 1.7 (left) the Fe
fluence in 90 large SEP events is compared with the pre-existing number density
of suprathermal Fe at 1 AU 1 day before the occurrence of the SEP event. They

1 Solar Energetic Particles and Space Weather: Science and Applications

9

found that the maximum Fe daily-average SEP fluences measured by ACE/SIS
are apparently limited by the pre-existing suprathermal number density. In Fig. 1.7
(right) it is shown that the suprathermal Fe densities are significantly greater before
the occurrence of these large SEP events with respect to all other days, strongly
suggesting that the large fluences of Fe in SEP events only occurred when there was
a pre-existing high density of suprathermal Fe. According to these authors remnant
flare suprathermal ions, as well as suprathermal material accelerated at previous
CME shocks, existed in the heliosphere and served as seed particles subsequently
re-accelerated by the CME shock that produced the large CME event (Mason et al.
1999; Desai et al. 2006).
An alternative scenario that (Tylka et al. 2005) proposed is that the observed
variability in the energy dependence of the Fe/O ratio could be due to the interplay
of two factors namely the evolution in the shock-normal angle as the shock moves
outward from the Sun and a compound seed population, typically comprising at
least suprathermals from the corona (or solar wind) and flare suprathermals. In
this scenario, (Fig. 1.6, right), since the quasi-perpendicular (Q-Perp) shock needs
higher injection energy, it may only effectively accelerate impulsive suprathermals
originating from the flare acceleration process to high energy, producing the Fe-rich
events. On the other hand, since quasi-parallel (Q-Par) shocks have lower injection
thresholds they can accelerate the ambient solar wind (or coronal suprathermal ions)
producing the Fe-poor events at higher energies. Tylka and Lee (2006) formalized
the ideas put forward by Tylka et al. (2005) in an analytical model which above
1 MeV/nucleon the Tylka and Lee (2006) model reproduced key features of the
SEP variability observed in terms of the energy dependence of Fe/O, the 3 He/4 He
ratio and the mean ionic charge state of Fe. Schwadron et al. (2015) further improved
the model of coronal shock acceleration. In the left panel of Fig. 1.8, the injection
energy of shock-accelerated particles is shown as a function of ™Bn for a range of the
perpendicular to parallel diffusion coefficient ratios, whereas in the right panel, the
time profiles of the shock or compression radial position (top panel) and ™Bn (bottom

Fig. 1.8 Left panel: the injection energy of shock-accelerated particles as a function of ™Bn for a
range of the perpendicular and parallel diffusion coefficient ratio. Right panel: Time profiles of the
shock radial position ™Bn relative to 01:28:57 in the simulation time (see text) (© AAS. Reproduced
with permission from Schwadron et al. 2015)

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O.E. Malandraki and N.B. Crosby

Fig. 1.9 Energy dependence of (Fe/O)n predicted by the Tylka and Lee (2006) model shown
for different values of the parameter R, which reflects the relative strengths of the remnant flare
and coronal source contributions at a parallel shock, where seed ions from both populations are
injected with equal efficiency (Reproduced from Reames 2013, permission for reuse from publisher
Springer for both print and electronic publication)

panel) relative to 01:28:57 in the simulation time are shown. Apparently as the
shock moves outward, ™Bn decreases, and the geometry of the shock would change
from Q-Perp to Q-Par. Schwadron et al. (2015) noted that the CME expansion and
acceleration in the low corona may naturally give rise to rapid particle acceleration
and broken power-law distributions in large SEP events. Figure 1.9 shows the results

1 Solar Energetic Particles and Space Weather: Science and Applications

11

of the (Tylka and Lee 2006) model for the case in which the injection of coronal seed
ions at Q-Perp shocks is suppressed. The energy dependence of the normalized Fe/O
ratio i.e. (Fe/O)n is shown for different values of the impulsive suprathermal fraction
R in the seed population. In the Q-Par shock event (Fe/O)n 1 at lower energies
(E < 2 MeV/nucleon), while (Fe/O)n monotonically decreases with increasing E.
In contrast, in the Q-Perp shock (Fe/O)n is between 1 and 8 at lower energies,
depending on the impulsive suprathermal fractions. With increasing energy the
normalized ratio exhibits a complex variation e.g. approaching a plateau or reaching
a minimum and further increasing afterwards. Tylka et al. (2005) hence assumed that
the high-energy Fe/O ratio could be used as a crude proxy for shock geometry, with
Fe-poor and Fe-rich events corresponding to Q-Par and Q-Perp shock geometries,
respectively.
It should be noted that these explanations have not taken into account the IP
transport effect, which could further distort the Fe/O ratio that emerged from the
CME-shock acceleration process (e.g. Tylka et al. 2013). Recently, (Tan et al. 2017)
examined 29 large SEP events with peak proton intensity Jpp (>60 MeV) > 1 pfu
during solar cycle 23. The emphasis of their examination was put on a joint analysis
of the Ne/O and Fe/O data in the 3–40 MeV/nucleon energy range as covered
by the Wind/LEMT and ACE/SIS sensors in order to differentiate between the
Fe-poor and Fe-rich events at higher energies that emerged from the CME-driven
shock acceleration process, after correcting the IP transport effect. One of the main
findings of this work is presented in Fig. 1.10 in which the plot of the source plasma
temperature T as very recently reported by Reames (2016) versus the normalized
Ne/O ratio i.e. (Ne/O)n at E D 30 MeV/nucleon is shown. T is well correlated
with (Ne/O)n with the linear correlation coefficient (CC) D 0.82. Therefore, the
(Ne/O)n value at high energies should be a proxy of the injection energy in the shock
acceleration process, and hence the shock ™Bn according to the models of Tylka and
Lee (2006) and Schwadron et al. (2015).

1.1.3 Ground Level Enhancement (GLE) Events
Ground Level Enhancement (GLE) events form a particular case of high-energy SEP
events associated with GeV protons. These events pose severe radiation hazards
to astronauts and technological assets in space and disrupt airline communications
(Shea and Smart 2012). GLEs are nowadays measured with better coverage from
space than at ground level, including 80 MeV/amu to 3 GeV/amu H and He
spectra (Adriani et al. 2011), onsets (Reames 2009a, b), energy spectral shapes
and abundances (Mewaldt et al. 2012b), electrons (Kahler 2007, 2012; Tan et al.
2013) and general properties (Gopalswamy et al. 2012). Rouillard et al. (2016)
recently studied the link between an expanding coronal shock and the energetic
particles measured near Earth during the GLE of 17 May 2012. The analysis showed
that the GLE event occurred inside a clear magnetic cloud (see e.g. Malandraki et
al. 2002). Using a new technique developed to triangulate the three-dimensional

12

O.E. Malandraki and N.B. Crosby

Fig. 1.10 Source plasma temperature T very recently reported by Reames (2016) is plotted vs. the
Ne/O/0.157 (30 MeV/nucleon) value for the large Fe-poor (red) and Fe-rich (blue) events during
solar cycle 23. The dashed line is the least-square fitting result for all the collected events as listed
in Table 2 of Tan et al. (2017) (Reproduced from Tan et al. 2017)

(3D) expansion of the shock forming in the corona it was found that the highest
Mach number (MFM ) values appear near the coronal neutral line within a few
minutes of the CME onset. This neutral line is usually associated with the source
of the heliospheric current sheet (HCS) and plasma sheet. It was shown that the
release time of GeV particles occurs when the coronal shock becomes super-critical
(MFM > 3).

1.1.4 Multi-Spacecraft Observations of SEP Events
In this section the differences in the SEP event characteristics as observed from
different vantage points in the heliosphere are discussed. Figure 1.11 shows as an
example the 1 March 1979 SEP event observed by three different s/c. Helios 1
encounters the event near central meridian and observes a peak in the 3–6 MeV
proton intensity near the shock passage time. The intensities at the other s/c, after
reaching a peak, begin to track closely those seen at Helios 1 after they enter the socalled ‘reservoir’ region (see also McKibben 1972; Roelof et al. 1992) in which the
intensities and energy spectra are nearly identical. These results indicate that only a
small number of particles can leak out of the reservoir. Observations have provided
strong evidence for the location of magnetic ‘barriers’ in space beyond 1 AU and

1 Solar Energetic Particles and Space Weather: Science and Applications

13

Fig. 1.11 The top left panel shows the intensity time-profiles for protons in the 1 March 1979
event at 3 s/c. ‘S’ denotes the time of shock passage at each s/c. The top right panel shows energy
spectra in the ‘reservoir’ region behind the shock at time ‘R’. The lower panel shows the s/c
trajectories through a sketch of the CME (Reproduced from Reames 2013, permission for reuse
from publisher Springer for both print and electronic publication)

their role in determining the decay phase of SEP events and the establishment and
maintenance of particle reservoirs in the heliosphere (Roelof et al. 1992, 2012a, b;
Sarris and Malandraki 2003; Tan et al. 2012). Reames et al. (1996) also considered
that the decay phase of the SEP events consists of particles propagating between
the converging magnetic field near the Sun and a moving shell of strong scattering
formed downstream of the distant traveling shocks. After formation, the reservoir
slowly dissipates as a result of the nominal diffusion, convection, adiabatic cooling,
and drift mechanisms that govern the propagation of SEPs.
The Ulysses European Space Agency (ESA)/National Aeronautics and Space
Administration (NASA) mission provided unprecedented observations of the 3D
heliosphere inside 5 AU. Comparison of simultaneous SEP observations near
the ecliptic plane with the Ulysses observations at high latitudes showed that
most events that produce large high-energy (>20 MeV) proton and near-relativistic

14

O.E. Malandraki and N.B. Crosby

electron flux increases near Earth also produce flux increases at high latitudes,
regardless of the longitudinal, latitudinal and radial separation between the s/c,
although with somewhat lower maximum intensities and slower rise at Ulysses
(McKibben et al. 2003; Lario and Pick 2008; Malandraki et al. 2009). Particle
anisotropies during SEP events at high latitudes are typically directed outward from
the Sun and aligned with the local magnetic field (McKibben et al. 2003; Malandraki
et al. 2009).
The observed field-aligned anisotropies, with components perpendicular to the
local magnetic field that are essentially zero, indicate that there is no net flow of
particles across the local magnetic field. The Ulysses observations revealed the 3D
nature of the reservoir effects in the heliosphere. Dalla et al. (2003) concluded that
the presence of a shock is not necessary for creating the near-equality observed at
Ulysses and near Earth decay phases, but that these observations are better explained
by diffusion across the interplanetary magnetic field (IMF).
More recently, combined observations by the twin STEREO s/c as well as nearEarth observatories revealed the wide longitudinal spreads of large gradual SEP
events in the heliosphere and even strongly questioned the constraint of a narrow
spread for 3 He-rich events (Wiedenbeck et al. 2013). A combination of physical
processes appears to cause the large longitudinal spread of high-energy particles.
Dresing et al. (2014) concluded that both an extended source region at the Sun
and perpendicular transport in the IP medium are involved for most of the widespread events under study. The studies (Rouillard et al. 2011, 2012) found that
the delayed SEP release times at STEREO and L1 are consistent with either the
time required for the CME shock to reach field lines connected to the s/c or with
the time required (30–40 min) for the CME to perturb the corona over a wide
range of longitudes. Observations by Gómez-Herrero et al. (2015) indicated that
higher SEP fluxes, harder SEP spectra and direct injections of SEPs onto wellconnected IMF lines are associated with lateral expansions of CME-driven shocks
in the low corona, and may therefore be responsible for the rapid longitudinal spread
as observed at vastly distributed s/c in many SEP events. Other factors that may also
play a role in distributing SEP events longitudinally include the large-scale IMF
configuration inside interplanetary CMEs (ICMEs) (e.g. Kahler and Vourlidas 2013)
and the relative strength of the CME shock, which depends on the local Alfvén
speed, rather than the actual speed of the CME (e.g. Gopalswamy et al. 2014).

1.1.5 Particle Acceleration
Recently, important progress has occurred, both from the theoretical and the
observational perspective in the research of small-scale magnetic islands in the
solar wind and their role in particle acceleration. Khabarova et al. (2015) presented
observations that show the occurrence of small-scale magnetic islands and related
plasma energization in the vicinity of the HCS. They found evidence that magnetic
islands experience dynamical merging in the solar wind and that increases of

1 Solar Energetic Particles and Space Weather: Science and Applications

15

energetic particle fluxes in the keV–MeV range are found to coincide with the
presence of magnetic islands confined by strong current sheets (CSs). Moreover,
the interaction of ICMEs with the HCS can lead to significant particle acceleration
due to plasma confinement. Their observations confirmed the rippled structure
of the HCS and since such a structure confines plasma, it makes possible the
strong energization of particles trapped inside small-scale magnetic islands. They
concluded that although initial particle acceleration due to magnetic reconnection
at the HCS may be insufficient to obtain high energies, the presence of magnetic
islands inside the ripples of the HCS or between two CSs with a strong guide field
offers the possibility of re-accelerating particles in the ways discussed theoretically
by Zank et al. (2014) and le Roux et al. (2015a).
Khabarova et al. (2016) further explored the role of the heliospheric magnetic
field configurations and conditions that favor the generation and confinement of
small-scale magnetic islands associated with the so-called atypical energetic particle
events (AEPEs) in the solar wind. Some AEPEs have been found not to align
with standard particle acceleration mechanisms, such as flare-related or simple
diffusive shock acceleration processes related to ICMEs and corotating interaction
regions (CIRs). They provided more observations fully supporting the idea and
the theory of particle energization by small-scale-flux-rope dynamics previously
developed by Zank et al. (2014, 2015a, b) and le Roux et al. (2015a, b). If the
particles are pre-accelerated to keV energies via classical mechanisms, they may
be additionally accelerated up to 1–1.5 MeV inside magnetically confined cavities
of various origins. Khabarova et al. (2016) showed that particle acceleration inside
magnetic cavities may explain puzzling AEPEs occurring far beyond IP shocks,
within ICMEs, before approaching CIRs, as well as between CIRs. SEP transport
processes are described in detail in Chap. 4 of this volume (see also Desai and
Giacalone (2016) which includes a review on this topic).

1.1.6 Key Open Questions and Future Missions
Solar Orbiter (SolO) is a unique ESA/NASA joint mission conceived to unveil
the Sun-heliosphere connection (Mueller et al. 2013), expected to be launched in
2019. The orbital configuration includes a close perihelion, high inclination intervals
allowing the observation of the solar polar regions and quasi-co-rotation periods.
One of the top-level science questions is “How do solar eruptions produce energetic
particle radiation that fills the heliosphere?” which can be broken down into three
inter-related key topics: What are the seed populations for energetic particles? How
and where are energetic particles accelerated at the Sun? How are energetic particles
released from their sources and distributed in space and time?
The Energetic Particle Detector (EPD) instrument suite onboard SolO (Principal
Investigator: Prof. J. Rodríguez-Pacheco, Spain) will measure energetic electrons,
protons and ions, operating at partly overlapping energy ranges covering from a few
keV to 450 MeV/nucleon. The EPD sensors will measure the composition, spectra

16

O.E. Malandraki and N.B. Crosby

and anisotropies of energetic particles with sufficient temporal, spectral, angular and
mass resolution to achieve the mission goals (Gómez-Herrero et al. 2016). Energetic
particles escaping from the acceleration sites propagate through the turbulent IMF.
Previous observations by the Helios s/c have shown that SEP events near the Sun
are much less affected by IP transport effects compared to 1 AU observations. As
the s/c moves further away from the Sun, scattering and diffusion processes become
more important and multiple injections closely spaced in time cannot be resolved
(Wibberenz and Cane 2006). Thus, SolO observations close to the perihelion will
be crucial to unveil SEP injection, acceleration, release and transport processes,
in view of the ongoing debate about the SEP acceleration sites, disentangling the
acceleration at CME-driven shocks and at reconnection sites in solar flares (e.g.
Malandraki et al. 2006).
NASA’s Solar Probe Plus mission, recently re-named to Parker Solar Probe
to honour pioneering physicist Prof. Eugene Parker, will fly within nine solar
radii of the Sun’s surface and is scheduled to be launched in July 2018. The
two Energetic Particle Instruments (EPI) of the Integrated Science Investigation of
the Sun (ISIS) (Principal Investigator: Prof. D. J. McComas, USA) will measure
lower (EPI-Lo) and higher (EPI-Hi) energy particles. EPI-Lo will measure ions and
ion composition from 20 keV/nucleon–15 MeV total energy and electrons from
25–1000 keV. EPI-Hi measures ions from 1–200 MeV/nucleon and electrons
from 0.5–6 MeV. The unique ISIS observations will allow the exploration of the
mechanisms of energetic particles dynamics, including their (1) Origin: defining
the seed populations and physical conditions necessary for energetic particle
acceleration; (2) Acceleration: determining the role of shocks, reconnection, waves
and turbulence in accelerating energetic particles; (3) Transport: revealing how
energetic particles propagate from the corona out into the heliosphere (McComas
et al. 2016).
It is evident that the next decade is expected to revolutionize our understanding
of SEP acceleration and transport, by means of state-of-the-art sensors on board
these two upcoming missions providing unique and unprecedented measurements
for the exploration of the solar corona and inner heliosphere. Synergies between
the two missions are of particular relevance, since both missions have overlapping
timelines and the Parker Solar Probe perihelion, reaching up to 9 solar radii, will
permit simultaneous in-situ observations at the SEP acceleration region close to
the Sun and at larger radial distances, with continuous remote sensing coverage
provided by SolO and near-Earth s/c. Radial alignments between the two s/c will
enable the observations of plasma ‘entities’ from the same solar source region
at progressive radial distances as well as the study of energetic particle radial
gradients. Furthermore, other useful configurations for the optimization of the
science return are alignments along the same IMF line allowing the observation of
SEPs originating at the same acceleration site by two or more s/c located at different
radial distances. SEP event observations by multiple s/c located at widely separated
points in the heliosphere, both in longitude and in latitude, will be valuable for the
investigation of the spatial distribution of SEPs and the unraveling of the physical

1 Solar Energetic Particles and Space Weather: Science and Applications

17

mechanisms responsible for producing wide-spread SEP events (see e.g. Sect. 1.1.4)
(Gómez-Herrero et al. 2016).

1.2 Applications
1.2.1 Why Study SEP Events?
It has become apparent during the last decades that SEP events pose important
challenges for modern society. Due to their unpredictability, specifically for those
that reach relativistic velocities (high energies) and peak values in very short time
scales, they are of concern. SEPs ranging from protons to heavy ions up to iron
have been found to have impacts on space systems (s/c, instruments, electronic
components, solar arrays, : : : ), avionics and living organisms (e.g. Feynman and
Gabriel 2000; Jiggens et al. 2014). It has even been suggested that systems with
very high safety and reliability requirements (e.g. in the nuclear power industry)
may need to take account of superstorm ground level radiation on microelectronic
devices within the system.
In the case of nuclear power a Carrington event may not be a sufficient case since relevant
timescales for risk assessment may be as long as 10,000 years.
(Paul Cannon (Cannon et al. 2013))

In the following some of the most important and common SEP induced effects
are presented, as well as mitigation strategies currently being relied on.

1.2.2 SEP Effects on Technology
Developments in technology such as miniaturization has no doubt benefited space
industry, but at the same time technical equipment has increasingly become more
vulnerable to the space environment. On a lesser scale the well-known “snow”
effect, resulting from the increase in high energy protons during intense SEP events
is sometimes seen on coronagraphic images, as shown in Fig. 1.12, obscuring the
image of the CME itself. However, in some instances SEP induced effects may be of
such a nature that they can result in long-term damage. Missions that target the inner
solar system are especially vulnerable to high-energy charged particles (DiGregorio
2008).
Table 1.1 presents a summary of SEP induced effects observed onboard s/c and
aircraft. It is clearly shown how both the energy and species of the particles being
considered is an important factor for evaluating their potential effect. Particle flux
intensities at lower energies are important for effects such as solar cell degradation,
whereas nuclear interactions are associated with particle flux intensities at higher

18

O.E. Malandraki and N.B. Crosby

Fig. 1.12 The snowstorm
effect observed on the
LASCO/SoHO coronagraph
on 28 Oct. 2003. Image:
ESA/NASA—
SOHO/LASCO

Table 1.1 Particle effects on technology observed as a function of the particle energy range
Energy range
Protons <10 MeV
Protons >10 MeV
Protons >50 MeV and
Ions >10 MeV
nucleon1

Effects
Material and solar cell effects over time as a result of cumulated
dose (e.g. solar cell degradation)
Nuclear interactions (e.g., sensor background noise, ionization,
displacement damage)
Nuclear interactions (e.g., single event effects in electronics onboard
satellites, as well as aircraft)

energies. Single-event effects (SEEs) are classified as either non-destructive or
destructive:
• Single Event Upsets: Occurs in logical circuits and is defined as a bit switching
from an initial logical state to an opposite logical state.
• Single Event Latchup: Results in a high operating current, above device specifications, and must be cleared by a power reset.
• Single Event Gate Rupture: Occurs in powerful transistors and is manifested by
an increase in gate leakage current
• Single Event Burnout: A condition that can cause device destruction due to a
high current state in a power transistor.
For s/c mission planning and operations SEP events are considered. In regard
to launch operations the SEP environment is also a decisive factor whether to give
the go ahead to launch or not for several reasons. Launch vehicles and s/c reaching
sufficiently high geomagnetic latitudes could for example see an increase in SEE
rates at times of significant SEP events. On the other hand, optical instruments are
also vulnerable to SEPs and induced sensor interference can disrupt the operation
of star trackers and put critical s/c manoeuvres at risk.

1 Solar Energetic Particles and Space Weather: Science and Applications

19

Under normal space weather conditions Earth’s magnetosphere acts as a shield
and protects us from charged particles and magnetic clouds. Nevertheless at times
SEPs may have sufficient energies to “break” through this shield and enter the
ionosphere; SEPs have easier access to the polar regions near Earth’s magnetic poles
than at the equator due to the “open” magnetic field lines. The cutoff latitude is a
function of a particle’s momentum per unit charge and is referred to as its rigidity
(see Chap. 5). Variations in SEP access to latitudes can occur on time scales of an
hour or less in response to changes in the solar wind dynamic pressure and IMF
(Kress et al. 2010). For this reason high inclination LEO satellites can at times be
vulnerable to SEPs, as well as the International Space Station that has an orbital
inclination of 51.64ı.
SEP events can also effect signal propagation between Earth and satellites. Polar
cap absorption (PCA) events result from intense ionisation of the D-layer of the
polar ionosphere by strong (>10 MeV) SEP events. Due mainly to protons with
energy in the range of 1–100 MeV (corresponds to an altitude between 30 and
80 km) the increased ionisation absorbs radio waves in the HF and VHF bands,
resulting in problems for communications (degraded radio propagation through the
polar regions) and navigation position errors with the importance being a function
of the individual SEP event.
Despite the relative steepness of SEP energy spectra, the small percentage
of protons accelerating up to high energies (>500 MeV) still pose considerable
problems. These high-energy SEP events such as the September 1989 SEP event
(Fig. 1.3) are often associated with GLE events and can result in secondary radiation
caused by particles interacting with s/c shielding and other material. This results in
the production of particles such as lower energetic protons, neutrons, and pions that
in some cases may be more of an obstacle for the s/c designer than the primary SEPs
themselves. While the former can induce SEEs, secondary particle background can
have more profound effects on sensitive space-borne instrumentation.
Technology onboard commercial airline operations can also be affected by SEP
events including avionics (electronic systems), communications and GPS navigation
systems (Jones et al. 2005). Specifically ultra-long-haul “over-the-pole” routes and
high-latitude flights are susceptible to these SEP induced effects.

1.2.3 SEPs and Human Health Effects
In addition to being a threat to technology, SEP events are also an important risk to
human health. Since the Apollo missions to Earth’s Moon in the 1970s human space
exploration has mainly been focused on low-Earth orbit altitudes (e.g. Space Shuttle,
International Space Station) and suborbital flights. Outside Earth’s magnetosphere
SEP events have for the most part been a concern for robotic flight missions up
until now. During the last decades the vision for space exploration has changed as
space agencies and private companies are contemplating sending humans to Mars
and asteroids, and as the population on Earth increases colonizing such targets and
pursuing deep space exploration will only become more and more attractive. The

20

O.E. Malandraki and N.B. Crosby

downside is that human interplanetary exploration will expose astronauts not only to
the galactic cosmic ray background but at times also to increased levels of radiation
during SEP events and this may indeed be the most important obstacle to overcome.
The field of radiation biology concerns how the radiation environment of space
affects cells. Radiation effects on astronauts are sub-classed into two categories:
1. Deterministic (early) Effects: Due to exposure to a large dose of radiation for a
limited time (ranges from hair loss, nausea, acute sickness, death)
2. Stochastic (late) Effects: Due to random radiation-induced changes at the
deoxyribonucleic acid (DNA) molecule level (cancer).
As already mentioned in Sect. 1.1.1 protons with high energies (>30 MeV)
are a health risk for astronauts. For this reason protons with energies >10 MeV
are continuously monitored and taken into account when planning extra-vehicular
activities.
In those instances SEP events reach aviation altitudes they become also a concern
for human health as the radiation dose received can increase. This specifically
applies to high-latitude flights (>50ı N) and polar routes (>78ıN). For commercial
aviation this can be a risk for frequent flyers and particularly for aircrew. Effective
pilot training programs as well as monitoring, measuring, and regulatory measures
in regard to radiation exposure risks for both human tissue and avionics are
recognized by a broad community (Tobiska et al. 2015).

1.2.4 Mitigating the Effects of SEPs
The SEP radiation environment is assessed when designing s/c, for s/c mission
planning and operations, and when human spaceflight is involved. How does one
best go about protecting assets in space and on the ground from the effects of
SEP events? For this purpose post-event analysis “hazard assessment” is performed
after an anomaly occurs (is recorded). Furthermore, mitigation procedures are put in
place before launch (e.g. s/c shielding, redundancy onboard) and during operations
SEP forecasting takes place.

1.2.4.1 Hazard Assessment
Analyzing s/c anomalies (hazard assessment) is one way to infer whether an
observed anomaly was due to technical or human error, or whether it was a
direct consequence of space environment conditions. In Fig. 1.13 it is clearly seen
that there was an increase in the number of SEUs in the Ramdisk onboard the
LEO Algerian Alsat-1 satellite during three SEP events (29/10/2003: 790 SEUs,
20/01/2005: 774 SEUs, 13/12/2006: 303 SEUs). Figure 1.14 illustrates that the SEU
rate is directly a function of the SEP energy spectrum; the flatter the spectrum the
higher the number of SEUs (Bentoutou and Bensikaddour 2015).

1 Solar Energetic Particles and Space Weather: Science and Applications

21

Fig. 1.13 The daily SEU rate observed on the Alsat-1 Ramdisk during the previous solar cycle
(Reproduced from Bentoutou and Bensikaddour 2015, permission for reuse from publisher
Elsevier for both print and electronic publication)

Fig. 1.14 SEU rate (purple bars) with proton energy spectrum composition (>30 MeV, >50 MeV,
>100 MeV integral flux) when significant SEP events were observed (28–30/10/2003, 17–
18/01/2005, 20–21/01/2005, 7–8/12/2006, 13/12/2006) (Reproduced from Bentoutou and Bensikaddour 2015, permission for reuse from publisher Elsevier for both print and electronic
publication)

22

O.E. Malandraki and N.B. Crosby

Information obtained from hazard assessment can provide useful input for both
engineering (mitigation) and scientific approaches (forecasting), and establish a
one-to-one correction between space environment conditions and technical failures.
However, s/c operators are sometimes reluctant in providing anomaly data due to
confidentiality issues specifically when the anomaly is an important one (e.g. loss
of s/c); this makes it sometimes difficult to assess whether a failure was due to the
space environment or not. To complement hazard assessment one therefore relies on
efficient mitigation strategies such as s/c shielding and forecasting techniques.

1.2.4.2 Mitigation Procedures
The classical engineering approach is based on passive shielding that can protect
the crew and hardware (exterior and interior) of the s/c and understanding how the
space environment interacts with the shielding. For this reason SEP energy spectra
are used as input in engineering tools when computing induced effects such as the
dose encountered on technology and humans during SEP events. The shape of the
spectrum is important as worst-case scenarios are application dependent, meaning
that the flux intensity at lower energies are important for material and solar cell
effects. At the other end of the energy spectrum, flux intensities at higher energies
are more important for nuclear interactions (e.g., background noise, single event
upsets).
Aluminium is generally the material used when building most s/c shielding
structures and this type of shielding protects against SEP proton events for the most
part (Wilson et al. 1997). However, the higher the particle energy, for example in
the case of extreme events, the thicker the shielding material necessary to stop the
primary particles. This not only implies the possibility of secondary radiation but
also higher costs. For these reasons SEP event forecasting is also relied upon to
mitigate against SEP events. Currently, short-term SEP event forecasting systems
are based on:
• theoretical understanding (e.g. physical models),
• remote sensing of phenomena such as solar flares, CMEs and active regions
• space-based in-situ observations at L1 (shock arrival, energetic storm particles)
and GEO
• historical data
• ground-based observations (e.g. radio, neutron monitors).
and can roughly be divided in two categories:
(a) Physics-based numerical models (e.g. Earth-Moon-Mars Radiation Environment Module (EMMREM) (Schwadron 2010), Predictions of radiation from
REleASE, EMMREM and Data Incorporating CRaTER, COSTEP and other
SEP measurements (PREDICCS) (Schwadron 2012), Solar Energetic Particle
MODel (SEPMOD) (Luhmann et al. 2010), SOLar Particle ENgineering Code
(SOLPENCO) (Aran et al. 2006), and SOLPENCO2 (provides SEP modelling

1 Solar Energetic Particles and Space Weather: Science and Applications

23

away from 1 AU to the SEP statistical model of the SEPEM project (Crosby et
al. 2015)))
(b) Empirical models (e.g. University of Malaga Solar Energetic Particle
(UMASEP) system (Núñez 2011), Relativistic Electron Alert System for
Exploration (REleASE) (Posner 2007), Proton Prediction System (PPS) (Kahler
et al. 2007), PROTONS system (Balch 2008), GLE Alert Plus (Kuwabara et
al. 2006; Souvatzoglou et al. 2014) and Laurenza’s approach (Laurenza et al.
2009))
In some cases forecasting systems rely on methods from both categories such as
the SEPForecast tool built under the EU FP7 COMESEP project (263252) (Crosby
et al. 2012), (http://www.comesep.eu/alert/).
The EU H2020 HESPERIA project (637324) developed two novel real-time SEP
forecasting tools based on the UMASEP and REleASE proven concepts:
• The HESPERIA UMASEP-500 tool makes real-time predictions of the occurrence of GLE events, from the analysis of SXR and differential proton flux
measured by the GOES satellite network.
• The HESPERIA REleASE tool generates expected proton flux alerts at two
energy ranges (15.8–39.8 MeV and 28.2–50.1 MeV) making use of relativistic
electrons (v > 0.9 c) provided by the Electron Proton Helium Instrument (EPHIN)
on SOHO and near-relativistic (v < 0.8 c) electron measurements from the
Electron Proton Alpha Monitor (EPAM) aboard the Advanced Composition
Explorer (ACE).
Both of these new tools are operational through the project’s website (https://
www.hesperia.astro.noa.gr/) and described in detail in Chap. 7 of this volume.
Acknowledgements Olga E. Malandraki has been partly supported by the International Space
Science Institute (ISSI) in the framework of International Team 504 entitled “Current Sheets,
Turbulence, Structures and Particle Acceleration in the Heliosphere”.

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Chapter 2

Eruptive Activity Related to Solar Energetic
Particle Events
Karl-Ludwig Klein

Abstract Solar energetic particle events are associated with solar activity, especially flares and coronal mass ejections (CMEs). In this chapter a basic introduction
is presented to the nature of flares and CMEs. Since both are manifestations of
evolving magnetic fields in the solar corona, the chapter starts with a qualitative
description of the magnetic structuring and electrodynamic coupling of the solar
atmosphere. Flares and the radiative manifestations of energetic particles, i.e.
bremsstrahlung, gyrosynchrotron and collective plasma emission of electrons, and
nuclear gamma-ray emission are briefly presented. Observational evidence on the
particle acceleration region in flares is given, as well as a very elementary qualitative
overview of acceleration processes. Then CMEs, their origin and their association
with shock waves are discussed, and related particle acceleration processes are
briefly described.

2.1 Introduction
Solar energetic particle events are associated with transient solar activity, especially
with flares and coronal mass ejections (CMEs). The understanding of how and
when the sun ejects enhanced fluxes of protons, ions and electrons, sometimes
up to relativistic energies, needs insight into these basic eruptive processes. In
this chapter an elementary introduction is presented. Particle acceleration requires
transient electric fields. They are produced in relation with magnetic reconnection
and turbulence, and in large-scale shock waves driven by CMEs. Since flares
and CMEs often occur together, it is not easy to identify which of the candidate
acceleration processes is at work. They may all act together, but provide particles of
different energies.

K.-L. Klein ()
LESIA-Observatoire de Paris, CNRS, 92190 Meudon, France
PSL Research University, Universités P & M. Curie, Paris-Diderot, Meudon, France
e-mail: ludwig.klein@obspm.fr
© The Author(s) 2018
O.E. Malandraki, N.B. Crosby (eds.), Solar Particle Radiation Storms Forecasting
and Analysis, The HESPERIA HORIZON 2020 Project and Beyond, Astrophysics
and Space Science Library 444, DOI 10.1007/978-3-319-60051-2_2

27

28

K.-L. Klein

The chapter starts with a brief overview of the magnetic structuring of the outer
solar atmosphere (Sect. 2.2). Flares and accelerated particle signatures related to
them in the solar atmosphere are introduced in Sect. 2.3, together with the radiative
processes that make these particles observable at gamma-ray, hard X-ray and radio
wavelengths. CMEs, shock waves and the related particle acceleration processes are
addressed in Sect. 2.4. Because of the introductory nature of this chapter, references
are rather to review papers than to the original literature.

2.2 The Scene
The solar corona is a hot plasma with an average ion temperature T ' 1:5  106 K.
The mean energy of the particles in this plasma, to the extent that it can be described
by a Maxwellian distribution, is kT ' 160 eV, where k is Boltzmann’s constant.
A remarkable and significant feature revealed by eclipse observations (Fig. 2.1a)
is the non-spherical shape of the corona. In an eclipse image one sees especially light
from the photosphere, which is Thomson-scattered by free electrons in the corona.
The morphology of the corona hence shows the electron density integrated along the
line of sight. The image demonstrates that gravity is not the only force that comes
into play. The electron concentrations shown by the bright localized structures are
confined by magnetic fields. This is also shown by the EUV multi-wavelength image
from the Solar Dynamics Observatory in Fig. 2.1b: this emission is a mixture of
bremsstrahlung and spectral lines emitted mostly at MK-temperatures. The bright
structures (active regions) visualize coronal magnetic field lines connected to the
underlying atmosphere and the solar interior. They overlie regions with strong
magnetic fields in the photosphere, often including sunspots.

Fig. 2.1 The solar corona during a total eclipse in visible light (a; courtesy C. Viladrich) and as
seen in EUV (b; courtesy of NASA/SDO and the AIA, EVE, and HMI science teams)

2 Eruptive Activity Related to Solar Energetic Particle Events

29

The localized magnetic fields in active regions are the emerged parts of a global
solar magnetic field. The plume-like structures pointing to the lower left and upper
right in the eclipse image show clearly that such a global magnetic field exists.
In and below the photosphere this field is subject to the motions of the plasma,
such as the convective motions revealed by granulation and super granulation
in the photosphere. These motions shuffle field lines around in the photosphere,
concentrate them into magnetic flux tubes with a strong magnetic field that is
surrounded by regions with no or weak magnetic field. As the kinetic and dynamic
pressure of the plasma decrease with increasing altitude, the magnetic field fills
the entire space in the corona, and dominates the dynamics of the low corona. The
confinement of the plasma there creates the structures shown in Fig. 2.1.
The plasma motions in the photosphere and below inject energy into the magnetic
field, which is transported by field-aligned electric currents to the overlying
corona, and may be temporarily stored there (Forbes 2010). As a result of this
electrodynamic coupling with the photosphere and the convection zone, the corona
undergoes dynamical evolution on different scales of time and energy, ranging from
coronal heating to large eruptive events, the manifestations of which are flares
and CMEs. They often occur together. In the following these combined events are
referred to as eruptive events. When a flare is not accompanied by a CME, it is often
called a confined flare.

2.3 Solar Flares: Energy Release and Radiative Signatures
of Charged Particle Acceleration
From the observational viewpoint a solar flare is defined as a temporary brightening
across the electromagnetic spectrum. Radio and X-ray signatures observed during
a major flare are shown in Fig. 2.2. No spatial resolution is involved. The shape of
the light curve depends strongly on the nature of the emitting particle population:
the relatively slow and smooth time evolution in soft X-rays (top panel) comes from
the heating to T > 107 K of a coronal volume located in an active region. The
emission evolves relatively slowly, on minute time scales, due to the thermal inertia
of the coronal plasma. H˛ emission (not shown here) comes from a cooler plasma
volume in the chromosphere and displays also a smooth overall evolution. Hard Xrays (second panel from top) and microwaves, on the other hand, are mostly emitted
by non-thermal electron populations, that is electrons accelerated to energies of tens
of keV or sometimes several MeV. These are much higher than average energies
in the pre-eruptive corona (100–200 eV) or even in the hot flare plasma (a few
keV). Emission from non-thermal electrons is usually spiky, in particular during
the impulsive flare phase of the flare, which is the rise phase of the soft X-ray time
profile. The spikiness most probably reveals the fragmentation of the acceleration
process.

K.-L. Klein

counts s–1

GOES flux

30
10–3
10–4

1.6 keV
3.1 keV

10–5
10–6
10–7
600
400
200
100–150 keV

0

610 MHz

sfu

10

12

1010

432 MHz

108

410 MHz

106

327 MHz

104

236 MHz

102

164 MHz

100
2000
1500
1000

frequency [MHz]

500
400

300

200

100
hhmm
2003 Nov 03

0950

0955

1000

Fig. 2.2 Dynamic spectrum and single-frequency records of a complex hard X-ray and radio burst
on 2003 Nov 3 (Dauphin et al. 2006). From top to bottom: (1) Time histories in two soft X-ray
channels (GOES), (2) in one hard X-ray channel (RHESSI), (3) at six individual radio frequencies
(Trieste at 610 MHz, Nançay Radioheliograph at the other frequencies), (4) dynamic spectrum
from 2000 to 500 MHz (Zurich) and 400 to 40 MHz (Potsdam). Shading from black (background)
to white (bright emission). Horizontal white bands are frequency ranges where no observation is
possible because of terrestrial emitters. Credit: Dauphin et al., A&A 455, 339, 2006, reproduced
with permission ©ESO

2 Eruptive Activity Related to Solar Energetic Particle Events

31

Soft X-rays are routinely observed since 1975 by the Geostationary Operational
Environmental Satellites (GOES) operated by NOAA (USA). Because of their
general availability they replaced H˛ observations from ground as the standard
indicator of solar flares. The reference for the importance of a solar flare is the
peak soft X-ray flux in the 0.1–0.8 nm channel of GOES (also referred to as the
1–8 Angstrom channel): bursts with peak flux n  10m are referred to as class X
(m D 4), M (m D 5), C (m D 6) etc. for classes B and A, followed by a
multiplier n of the order of magnitude. A flare of class X3.5 has a peak flux in the
0.1–0.8 nm band of 3:5  104 W m2 .

2.3.1 Emission Processes
Emission in different spectral ranges is produced by different mechanisms in
different regions of the atmosphere: microwaves (1 GHz—some tens of GHz)
are gyrosynchrotron radiation, while hard X-rays are bremsstrahlung of energetic
electrons with ambient protons and ions. In the event shown in Fig. 2.2 a first hard
X-ray burst (second panel from top, photon energies 100–150 keV) occurs during
the impulsive phase of the flare. After its decay minor fluctuations persist. They
are followed by a new rise near 09:57 UT. The single-frequency records at radio
frequencies between 610 and 164 MHz show some similarities with the hard Xrays, especially the initial impulsive phase emission and (down to 236 MHz) the new
rise near 09:57 UT. But the brightest emission at these frequencies has no obvious
counterpart in the hard X-ray time profile. This emission comes from higher in the
solar atmosphere than the X-rays. In fact the radio spectrum is rather complex, as
shown by the dynamic spectrogram in the bottom panel. Broadband features like
the late rise near 09:57 UT are clearly visible, but are a relatively faint background
emission. The broadband nature points to the gyrosynchrotron mechanism as the
basic process. The brightest emissions are very strongly structured in frequency and
time. They reveal a variety of different radiation processes, which involve micro
instabilities of the plasma that are far from being completely understood. These
emissions are collectively referred to as “plasma emission”.

2.3.1.1 Bremsstrahlung
Free electrons travelling through a background of ions are deflected by the Coulomb
force. This change of momentum and energy is balanced by the emission of a
photon. The long range of the Coulomb force implies that the electron’s motion
is dominated by multiple interactions at long distance within the Debye sphere.
Each individual interaction creates only a small deflection, corresponding to the
emission of a photon with small momentum and energy, at radio wavelengths. Close
encounters are rare, but each one creates an individual strong deflection, associated
with the emission of a high-energy (X-ray or gamma-ray) photon.

32

K.-L. Klein

Since bremsstrahlung is a collisional process, the volume emissivity depends on
the product of the electron number density and the ion number density, or rather
on the sum of this product over protons and all ion species in the plasma. If the
impacting electrons are non-thermal, with density ne , the emissivity is proportional
to the product with the ambient ion density, ne ni . In a thermal plasma, since ne  ni ,
the emissivity is  n2e . Thermal bremsstrahlung produces the radio emission of the
quiet solar atmosphere and also a weak microwave emission in bursts. However,
much higher intensities can be reached at radio frequency by other processes.
Bremsstrahlung of non-thermal electrons produces the hard X-ray emission of solar
flares (Tandberg-Hanssen and Emslie 1988). Because of its dependence on the
ambient ion density, the emission comes from dense layers of the solar atmosphere,
mostly the chromosphere.

2.3.1.2 Gyrosynchrotron Radiation
The smooth broadband emission of moderate flux density in Fig. 2.2 is ascribed
to gyrosynchrotron radiation by mildly relativistic electrons (energies from about
100 keV to a few MeV). This mechanism is the generally adopted interpretation of
the microwave spectrum of solar flares, implying magnetic fields of some hundreds
of gauss in the low corona, and may on occasion extend to much lower frequencies.
The radiation is produced by electrons gyrating in magnetic fields. Thermal
electrons in the corona, which have rather low energy, may emit at low harmonics
of the electron cyclotron frequency
c D

1 eB
;
2 me

(2.1)

where e is the electric charge, me the mass of the electron, B the magnetic field
intensity. In magnetic fields of order 1000 G D 0:1 T the cyclotron frequency is in
the GHz range. As long as the energy of the emitting electron is low, an observer
in the plane of the cyclotron motion will see an electric field that varies nearly
sinusoidally in the course of time, corresponding to a frequency spectrum that shows
a signal at the cyclotron frequency and its low harmonics. For a relativistic electron
with speed  the fundamental frequency of the emission
p is the electron cyclotron
frequency divided by the Lorentz factor  D 1= 1  .=c/2 . Its radiation is
strongly beamed in the direction of motion. The observer looking at a single gyrating
electron will perceive a flash each time the velocity vector of the electron is along the
line of sight, and will record a succession of sharp pulses. The frequency spectrum
contains numerous lines at harmonics of the relativistic cyclotron frequency. In
practice these lines are broadened, and the spectrum is a continuum. For a highly
relativistic electron ( >> 1; synchrotron radiation) with pitch angle ˛ the emitted

2 Eruptive Activity Related to Solar Energetic Particle Events

33

spectrum extends from the cyclotron frequency up to the critical frequency
c D

3 2
 ce sin ˛ :
2

(2.2)

The emission is referred to as gyrosynchrotron in the case of mildly relativistic
electrons as observed in solar flares.

2.3.1.3 Plasma Emission from Electron Beams
The radio spectrum of Fig. 2.2 shows a wealth of structure at decimetre-metre waves
(1000–40 MHz), which contrast with the smooth evolution of the gyrosynchrotron
spectrum. For instance, a cluster of narrow-band features is seen between 200 and
400 MHz in the time interval 09:50–09:53. A structured band of emission drifts
from about 500 MHz (09:51–09:53) down to 200 MHz (09:53–09:56). The clear
spectral structure with narrow bandwidth as compared to the central frequency
(=  1) and the high flux density are typical of collective or coherent emission
processes, where a perturbation of the plasma makes the entire electron population
radiate at the characteristic frequencies of the plasma. In the solar corona the
plasma frequency is the relevant frequency, because it is higher than the cyclotron
frequency.
Most often plasma emission arises from some micro-instability due to deviations
of the electron distribution function from isotropy. We outline this mechanism for
a type III burst from a magnetic field-aligned electron beam: when a beam of fieldaligned fast electrons is superposed on a Maxwellian, a positive slope arises over
some velocity range in the distribution function measured along the magnetic field.
The electrons in the beam interact with plasma waves with phase speeds in the range
where the distribution function has a positive slope. These are Langmuir waves. If
there is more energy in electrons slightly above the phase velocity than in electrons
that are slower, waves are excited at the expense of the kinetic energy of the electron
beam. Electrons are removed from the beam and transferred to lower speeds so
that the beam distribution is flattened to a plateau. The instability ceases when the
distribution function has no longer a positive slope. Actual measurements of such
distribution functions in space are shown in Ergun et al (1998). A recent review is
Sinclair Reid and Ratcliffe (2014).
The Langmuir waves cannot escape from the corona, but can transfer their energy
to electromagnetic waves, for instance through coupling with other waves: lowfrequency waves like ion sound waves or high-frequency waves, especially other
Langmuir waves. The transfer of energy between waves can occur provided the three
waves satisfy parametric conditions, which can be formulated like the conservation
of energy (h) and momentum in quantum mechanics. Energy conservation implies
that the frequency of the resulting wave must be the sum of the frequencies of the
interacting waves. The frequency of Langmuir waves L is close to the electron
plasma frequency. The frequency EM of an electromagnetic wave generated through

34

K.-L. Klein

the coupling process with an ion-sound wave (frequency lf ) is EM D L C lf '
L ' pe . Coupling of two Langmuir waves yields EM D L C L0 ' 2pe . The
electromagnetic wave is hence generated near the electron plasma frequency or
its harmonic. Depending on which process prevails, the resulting electromagnetic
emission is referred to as “fundamental” or “harmonic”. Both may occur together,
or one of the two modes may prevail.
The dependence of the plasma frequency on the ambient electron density creates
the typical frequency behaviour of type III bursts: as the electron beam proceeds
to increasing altitude, hence to lower ambient electron density, the frequency of
the emission decreases. The result is a short burst that drifts from high to low
frequencies. In a hydrostatic atmosphere the frequency drift rate is directly related to
the speed of the exciter along the density gradient. Relatively fast drifts in type III
bursts are related to a fast exciter, namely an electron beam. The slowly drifting
type II bursts are ascribed to a slower exciter, namely a shock wave. An example is
the burst between 09:53 and 09:55 in the 200–400 MHz range of Fig. 2.2.

2.3.1.4 Gamma-Rays from Accelerated Protons and Ions
So far only electron-related radiative diagnostics were addressed. This is a real bias,
since observational signatures of non-thermal protons and ions are more difficult to
obtain in the solar atmosphere. These particles emit at gamma-ray wavelengths.
Prominent nuclear lines are produced when accelerated protons or ions with
energies in the range 1–100 MeV/nucleon bombard the low solar atmosphere. The
nuclei of the ambient medium are excited to high energies, and subsequently relax
by emitting the gamma-ray photons. If the impacting high-energy particle is a proton
and the target a heavy ion, the target does not move significantly, and the emitted
gamma-ray line is narrow. If an accelerated ion hits a target proton or helium,
it continues its motion and emits a Doppler-shifted line, which is considerably
broadened by the angular distribution of the ions.
The most widely observed nuclear line is the neutron capture line near h D
2:2 MeV. When protons with energies exceeding about 30 MeV interact with other
nuclei, neutrons are released, initially with high energy. When thermalised after
some tens of seconds, they can be captured by ambient protons to form a deuterium
nucleus. Its binding energy is released via emission of a photon at 2.223 MeV. At
still higher energies, above 300 MeV/nucleon, nuclear interactions of protons and
helium nuclei with ambient protons create pions, which decay rapidly. Pion-decay
positrons eventually annihilate with electrons. Neutral pions decay into photons
and create a specific emission feature at h > 60 MeV, which in solar gammaray spectra shows up as a high-energy bump on top of the decaying spectrum of
electron bremsstrahlung. A recent review of solar gamma-ray emission is given by
Vilmer et al. (2011). Pion decay gamma-ray emission from relativistic protons will
be addressed in more detail in Chap. 8.

2 Eruptive Activity Related to Solar Energetic Particle Events

35

2.3.2 Where Are Electrons Accelerated in Solar Flares?
Images of flares in hard X-rays show frequently configurations that look like
magnetic loops with a particle acceleration region near or above the top. In the
RHESSI image of the 2005 Jan 20 flare (Fig. 2.3a) the red contours outline a thermal
X-ray source at temperatures above 107 K, which traces the upper part of a coronal
loop. The blue contours are the sources of hard X-ray emission from non-thermal
electrons precipitated into the chromospheric footpoints. The two elongated grey
bands onto which the footpoints project are flare ribbons seen in UV. They outline
regions of the chromosphere heated by energy deposition during the flare. This
source morphology is generally interpreted as a signature of energy release near
or above the loop top, which heats the plasma in the coronal loop and accelerates
electrons. They escape from the primary acceleration site as magnetic field-aligned
beams. Because of their high energy they interact very little with the low-density
coronal plasma and precipitate into the dense chromosphere at the base of the
loop. They lose their energy instantaneously through collisions with this dense
environment, while simultaneously emitting a small amount as hard X-rays. The
RHESSI image is a snapshot: during the impulsive phase of the event the hard X-ray
sources occur in an irregular temporal succession at neighbouring places on the UV
ribbons. A standard cartoon scenario as in Fig. 2.3b locates the energy release above
the loop top, probably related to magnetic reconnection. The upward field lines
may be part of a plasmoid that is ejected upward or they may be open to the high
corona. The energy release may equally well be related to magnetic reconnection

a

b

320
300

Y (arcsecs)

280
260
240
220
200

12–15 keV
250–500 keV
image: TRACE 1600A

180
780

800

820

840

860

880

900

920

X (arcsecs)

Fig. 2.3 (a) Contours of hard X-ray emission in two spectral bands (RHESSI) superposed on
a negative TRACE image of chromospheric flare ribbons in UV (Krucker et al. 2008). Credit:
Krucker et al., Astrophys. J. 678, L63 (2008). ©AAS. Reproduced with permission. (b) Cartoon
scenario of particle populations and related electromagnetic emissions during a flare. From Klein
and Dalla (2017)

36

K.-L. Klein

with another closed magnetic structure. A more detailed discussion of hard X-ray
source morphology and its interpretation can be found in Holman et al. (2011).
Radio emission of electron beams, such as type III bursts, is another key observation to identify the electron acceleration. In some flares Aschwanden and coworkers
were able to identify radio emissions from bidirectional electron beams, with
downward-directed beams at high frequency (high ambient electron density) and
upward directed beams at low frequency. The authors concluded that these beams
came from a common acceleration region where the electron plasma frequency
had the value corresponding to the frequency from where the oppositely drifting
radio bursts emanate. They derived an ambient density of about .1–10/  109 cm3 .
From the timing of peaks at different hard X-ray energies they concluded that the
acceleration region is placed at a typical altitude of about 1.5 times the half-length
of the magnetic loop above the photosphere (see Sects. 3.3 and 3.6 of Aschwanden
2002). This corresponds to cartoon scenarios such as Fig. 2.3b.
It is not clear if protons and ions are accelerated in the same regions as electrons.
A close connection between relativistic electrons (above 300 keV) and protons
above 30 MeV is suggested by the observed correlation of the peak fluxes of
their respective bremsstrahlung and nuclear line emissions (Shih et al. 2009). But
differences become visible in the detailed time evolution (Kiener et al. 2006), and
the source locations are in general not identical (see review in Vilmer et al. 2011).
While models exist to explain different acceleration regions of these particle species,
for instance in terms of resonances with different types of waves, the observations
provide a number of challenges which show that our understanding is far from
complete.

2.3.3 A Qualitative View of Acceleration Processes
An electric field is needed to accelerate charged particles. This is simply because
only the electric component of the Lorentz force F D q.E C v  B/ is able to change
the energy, dW
dt D vF D qvE. Since the solar corona is a highly conducting medium
in most parts (comparable to copper), no static electric field can be maintained
along the ambient magnetic field. Peculiar configurations where transient magneticfield-aligned electric fields can exist are current sheets and shock waves. We cannot
measure electric fields in the corona, only infer them from the plasma motions.
In the cartoon scenario of Fig. 2.3b, where a reconnection region is depicted
by oppositely directed magnetic fields, the most elementary electric field is the
motional E D V  B induced by the inflow of plasma into the reconnecting
current sheet. A test particle exposed to this field will E  B-drift into the current
sheet. In the region where the magnetic field is near zero, the particle decouples
from the magnetic field. Protons propagate along the induced electric field, while
electrons propagate opposite to it. Both particle species are hence accelerated. The
stationary situation shows the principle, but is unlikely to be encountered in the
solar corona. Current sheets are expected to fragment into magnetic islands. They

2 Eruptive Activity Related to Solar Energetic Particle Events

37

correspond to parallel electric currents that attract each other, so that the magnetic
islands formed during the fragmentation coalesce. Charged particles are trapped in
a highly dynamical medium between coalescing magnetic islands and gain more
energy (Cargill et al. 2012).
Reconnection jets are another ingredient of magnetic reconnection that can lead
to particle acceleration. They evacuate the plasma from the reconnection region.
The jets may generate shock waves when impinging on the underlying magnetic
structures, or waves (turbulence) in the ambient plasma. Different particle species
interact with different types of waves. This may explain preferential acceleration of
some particle species, as observed in those SEP events where the 3 He abundance
is enhanced by several orders of magnitude with respect to the quiet solar corona.
Acceleration processes at shock waves and in turbulent plasmas are discussed in
more detail in Chap. 3.

2.4 What Is a Coronal Mass Ejection?
The observational definition of a coronal mass ejection (CME) is an extended
outward travelling feature in white-light coronographic images. This means that the
visible manifestation is the outward motion of plasma. Phenomenologically many
CMEs have a three-part structure in coronographic images as shown in Fig. 2.4: an
outer bright region, which is understood to be mainly composed of plasma swept up
from the ambient corona by the outward propagating piston, a dark cavity, which is
low-density material in the ejected magnetic structure, and a bright core consisting
of filament material. This basic structure of the CME is created by the magnetic
field. A CME is hence the ejection of a large-scale coronal magnetic structure
together with the confined plasma.
Fig. 2.4 Coronographic
image of a CME in white
light, from Riley et al. (2008).
Credit: Riley et al.,
Astrophys. J. 672, 1221
(2008). ©AAS. Reproduced
with permission

38

K.-L. Klein

The time-height diagram constructed from tracking the front of the white-light
feature through the field of view of the coronograph shows CMEs that travel at
constant speed in the field of view, while others accelerate or decelerate. The fastest
part is in general the outward-moving apex of the CME, but in some events fast
lateral expansion is also observed. Outward speeds observed by SoHO/LASCO
since 1996 range from a poorly defined lower limit of some tens of km s1 to
a maximum of 3400 km s1 (Gopalswamy 2009). The CME leaves the Sun and
travels through the heliosphere. The physical process behind this phenomenology is
a large-scale instability of coronal magnetic structures. A recent review on CMEs is
Chen (2011).

2.4.1 CME Magnetic Structure and Eruption
The magnetic structure outlined by the dark CME cavity (Fig. 2.4) looks like a
closed two-dimensional magnetic field. More detailed studies suggest it is the
projection of a three-dimensional magnetic flux rope, where the magnetic field lines
are helices wound around the confined plasma. Such a flux rope is sketched in
Fig. 2.5a. The blue-green loop-like structure is the plasma in the flux rope, the blue
and black field lines indicate the helicoidal magnetic field in and around the flux
rope. The Lorentz force on this configuration is directed upward, since the magnetic
field lines are more densely packed below the flux rope than above. The upward
Lorentz force, sometimes called “hoop force”, is balanced in equilibrium by the
downward-directed Lorentz force exerted by the surrounding coronal magnetic field,
whose field lines are plotted in orange. An excess upward force can be generated
for instance by the torsion of one foot of the flux rope and its magnetic field, due
to the plasma motions in the photosphere. When this happens, the excess magnetic
pressure below the flux rope is enhanced—the flux rope is lifted by the Lorentz force
(Fig. 2.5b), ambient coronal plasma and the embedded magnetic field are convected
from both sides towards the region where it was located before, and oppositely
directed magnetic fields can reconnect. This is illustrated in Fig. 2.5b, c for two field
lines, with the reconnection happening in a limited region schematically indicated
by the yellow symbol of an explosion. New magnetic field is then added to the flux
rope (the upper part of the field line drawn in red colour), and new magnetic loops
form in the low corona. These reconnected loops appear as arcades in EUV images.
Their formation may continue over several hours.
A 2D projection of this situation is depicted in Fig. 2.5d, together with the
consequences of the magnetic reconnection: charged particles accelerated in transient electric fields around the reconnection region, and electromagnetic emissions
excited directly or indirectly by these particles in different regions of the erupting configuration. Hard X-rays and gamma-rays are generated respectively by
electrons and ions in the dense low atmosphere. Radio emission is generated
by energetic electrons in different regions, including the dilute plasma in higher
atmospheric layers. Typical radio signatures of electrons accelerated during flux

2 Eruptive Activity Related to Solar Energetic Particle Events

39

Fig. 2.5 Cartoon scenario of the magnetic field configuration around a magnetic flux rope in the
solar corona (a), and of its evolution during the liftoff of a coronal mass ejection (CME; b, c). The
white and grey-shaded areas indicate opposite magnetic polarities in the photosphere, separated
by the grey line, where the vertical photospheric magnetic field is zero. Figure (d) shows a twodimensional projection of (c)

rope eruptions are broadband continua like the one created by gyrosynchrotron
emission in the bottom panel of Fig. 2.2, or similar features created by plasma
emission from trapped electrons. Since the electrons are simultaneously present in
a range of ambient electron densities, plasma emission occurs at a corresponding

40

K.-L. Klein

range of frequencies, i.e. over a broad spectral band. These emissions are called
type IV bursts.

2.4.2 Shock Waves and Particle Acceleration at CMEs
A characteristic signature of the corona observed in EUV in the aftermath of a
CME liftoff is the arcade of loops, which is thought to form as the magnetically
stressed corona reconnects. The progress of the reconnection process is depicted in
the cartoons of Fig. 2.5, where a loop formed in the course of reconnection is plotted
in red. Both reconnection and turbulence in the aftermath of the CME are able to
accelerate particles in a similar way as during the impulsive phase of solar flares.
Because of the outward movement of the CME, the relevant processes occur higher
up than during the impulsive flare phase, and less particles get access to the low
solar atmosphere. All processes involving collisions with the ambient plasma, such
as electron bremsstrahlung or nuclear line radiation, are less efficient. The main
evidence on particle acceleration in the aftermath of a CME is a long-lasting type
IV burst at frequencies below about 1 GHz.
Fast CMEs are likely to exceed the Alfvén speed and the fast magnetosonic speed
of the coronal plasma, and to drive shock waves. Such shock waves are observed
in situ in the heliosphere, and can be inferred in the corona from type II bursts
at radio frequencies, for instance between 09:51 and 09:55 in the 500–100 MHz
range in Fig. 2.2. Shock waves have also been inferred from UV spectroscopy in
the corona (Mancuso 2011). The associated shocks usually have moderate Mach
numbers: model-dependent interpretations of the radio spectra of type II bursts give
MA D 1:2–2:9 (Vršnak et al. 2002). But modelling of stereoscopic white-light
observations (Rouillard et al. 2016) shows that higher Mach numbers can be found
in localized regions of some CMEs.
Particle acceleration at coronal shock waves is discussed in Chap. 3. Two broad
categories of processes are commonly distinguished: shock drift acceleration occurs
predominantly in quasi-perpendicular shock regions, where the normal on the
shock front and the upstream magnetic field include a large angle. In the shockdrift acceleration process particles gain energy from the convective electric field
E D V  B in the shock frame, where V is the inflow speed of the plasma, B
the upstream magnetic field in the rest frame of the shock. In the upstream region,
electrons and ions E  B-drift towards the shock front. Because the magnetic field
is compressed by the oblique shock, the particles undergo a gradient drift along
the shock front. This drift is directed along the electric field for positively charged
particles, and opposite to the electric field for negatively charged particles. Hence
electrons, protons and ions gain energy. Depending on the energy and pitch angle
before the first encounter with the shock, the energy gained from the drift along
the convection electric field may be such that the particle is again injected into the
upstream medium and may escape. Besides a gradient drift, a particle also undergoes
a curvature drift while its guiding centre travels along the magnetic field, which is

2 Eruptive Activity Related to Solar Energetic Particle Events

41

curved in the shock transition. In a planar fast shock, the angle between a field line
and the shock normal is larger downstream than upstream, and the curvature drift
is opposite to the gradient drift. The curvature drift hence leads to energy losses.
But the drift speed decreases as the shock becomes more oblique, so that in quasiperpendicular shocks the gradient drift, and hence the energy gain, dominates.
In work on shock-acceleration of SEPs the acceleration process most often
invoked is diffusive shock acceleration. When ions are reflected at shock waves
and stream into the upstream region, they acquire a beam-like distribution and
are therefore likely to generate waves, parallel-propagating Alfvén waves as well
as obliquely propagating fast magnetosonic waves. When these waves grow to
sufficient amplitudes, they can scatter subsequent ions back to the shock. Since the
shock propagates faster than these waves, ions find themselves confined between
approaching scattering centers downstream and upstream, and gain energy by
bouncing back and forth through the shock front, until they eventually escape.
In order to interact with the waves, the particles must be able to escape into the
upstream medium after the initial reflection. This means that they must stream away
from the shock front at a minimum speed V= cos Bn , where V is the speed of the
shock as above, and Bn the angle between the shock normal and the upstream
magnetic field vector. Since this speed is the smaller, the smaller Bn , diffusive shock
acceleration is expected to work best at quasi-parallel shocks.

2.5 Summary and Conclusion
Charged particles may be accelerated during flares and CMEs to energies largely
above the mean energy in the corona. The energy transferred to the particles is drawn
from plasma flows in the photosphere and below, transported to the corona along
magnetic field lines, and stored in the coronal field. The release involves magnetic
reconnection or the loss of equilibrium of large-scale magnetic structures, leading
to CMEs.
Particle acceleration processes related to magnetic reconnection, turbulence
and shock waves are all supported by observations of electromagnetic emissions
and SEPs. The evolution of the coronal magnetic field is usually described by
magnetohydrodynamics, and the accelerated particles as test particles. High fluxes
of non-thermal particles may, however, develop sufficient pressure and energy to
back-react on the magnetic field configuration, invalidating the MHD and test
particle hypotheses. This is especially expected in large solar events, where the
energetic particles contain a substantial amount of the energy released during the
flare or the CME (Emslie et al. 2005; Mewaldt et al. 2005). We are therefore far
from a complete understanding of how particle acceleration proceeds.
In the present author’s opinion it is not possible to identify an acceleration
process that is a priori more plausible than others. In astrophysical settings like
supernovae, shock waves produced in the course of a gravitational instability are
widely considered as a privileged process to explain energetic particle populations.

42

K.-L. Klein

Shock waves in the solar corona are always the result of plasma processes that
are themselves conducive to particle acceleration. The preference for shock waves
as particle accelerators is not justified under these conditions. Constraints from
observations remain essential to understand how particle acceleration is related to
the different manifestations of eruptive solar activity, and which physical processes
are at work.
Acknowledgements The author is grateful to the HESPERIA consortium for many interesting
discussions, and to J. Kiener for his comments on the manuscript.

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Sinclair Reid, H.A., Ratcliffe, H.: Res. Astron. Astrophys. 14, 773 (2014). doi:10.1088/16744527/14/7/003

2 Eruptive Activity Related to Solar Energetic Particle Events

43

Tandberg-Hanssen, E., Emslie, A.G.: The Physics of Solar Flares. Cambridge University Press,
Cambridge/New York (1988)
Vilmer, N., MacKinnon, A.L., Hurford, G.J.: Space Sci. Rev. 159, 167 (2011). doi:10.1007/s11214010-9728-x
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Open Access This chapter is licensed under the terms of the Creative Commons Attribution
4.0 International License http://creativecommons.org/licenses/by/4.0/), which permits use, sharing,
adaptation, distribution and reproduction in any medium or format, as long as you give appropriate
credit to the original author(s) and the source, provide a link to the Creative Commons license and
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Commons license, unless indicated otherwise in a credit line to the material. If material is not
included in the chapter’s Creative Commons license and your intended use is not permitted by
statutory regulation or exceeds the permitted use, you will need to obtain permission directly from
the copyright holder.

Chapter 3

Particle Acceleration Mechanisms
Rami Vainio and Alexandr Afanasiev

Abstract This chapter provides a short tutorial review on particle acceleration
in dynamic electromagnetic fields under scenarios relevant to the problem of
particle acceleration in the solar corona and solar wind during solar eruptions. It
concentrates on fundamental aspects of the acceleration process and refrains from
presenting detailed modeling of the specific conditions in solar eruptive plasmas. All
particle acceleration mechanisms (in the solar corona) are related to electric fields
that can persist in the highly conductive plasma: either electrostatic (or potential)
or inductive related to temporally variable magnetic fields through Faraday’s law.
Mechanisms involving both kinds of fields are included in the tutorial.

3.1 Introduction
Solar energetic particles (SEPs) are accelerated in flares and coronal mass ejections
(CMEs) (see Chap. 2 and references therein). In this chapter, we will give a tutorial
review of particle acceleration mechanisms in solar eruptions. The aim is not to give
a comprehensive review of the original literature but rather give the reader an idea
of what are the main ideas that could explain the acceleration of ions and electrons
to the relativistic energies, we observe to be produced in the SEP events. For recent
reviews on SEPs we direct the reader to Desai and Giacalone (2016) and Reames
(2017).
SEPs are accelerated in the electromagnetic fields related to the dynamics of the
solar corona and solar wind during solar eruptions. In quasi-static fields of the quiettime solar corona, strong electric fields would not exist and particle acceleration
beyond quasi-thermal energies (up to keV) would seldom occur. However, solar
eruptions are manifestations of very non-thermal conditions favorable for particle
acceleration.
Magnetic reconnection is by definition a process, which requires electric fields
to be present in the system. As discussed in Chap. 2 the plasma advected towards

R. Vainio () • A. Afanasiev
Department of Physics and Astronomy, University of Turku, Turku, Finland
e-mail: rami.vainio@utu.fi; alexandr.afanasiev@utu.fi
© The Author(s) 2018
O.E. Malandraki, N.B. Crosby (eds.), Solar Particle Radiation Storms Forecasting
and Analysis, The HESPERIA HORIZON 2020 Project and Beyond, Astrophysics
and Space Science Library 444, DOI 10.1007/978-3-319-60051-2_3

45

46

R. Vainio and A. Afanasiev

a current sheet with a frozen-in magnetic field will be associated with a convective
electric field, which can accelerate particles. The situation is most likely a dynamic
one, where induced electric fields with closed field lines will be generated by
temporally varying magnetic fields. As discussed in Sect. 3.2.1, this can lead to very
efficient conditions for particle acceleration. Reconnection outflows from the corona
towards the Sun may generate collapsing loop systems, which can also act as particle
accelerators. In addition to direct acceleration by large scale fields, reconnection jets
in flares can also be turbulent regions. These can give rise to stochastic acceleration
in the plasma (see Sect. 3.2.5). Even shock acceleration (Sect. 3.2.3) could in
principle occur in reconnection regions, since the super-Alfvénic reconnection jets
can be terminated by dense plasma or strong magnetic fields impeding their flow.
Flares are commonly thought of as being the source of (at least) the impulsive SEP
events (Reames 2017). These events show peculiar abundance ratios of ions difficult
to explain in terms of non-selective acceleration processes, as shock acceleration.
Presently the abundances are probably best explained by stochastic acceleration
(Petrosian 2012).
Especially the gradual SEP events are undoubtedly related to CMEs. Mostly,
but not exclusively, because of the morphology of the time-intensity profiles of the
MeV and deka-MeV protons, showing clear organization based on the magnetic
connectivity of the observer to the CME, the bow shock driven by the fast
magnetized eruption has been identified as the prime candidate for accelerating
the ions in SEP gradual events (Desai and Giacalone 2016; Reames 2017). There
is a large amount of evidence that CME-driven shocks accelerate protons up to
some tens of MeVs, but the case becomes more open at energies approaching and
exceeding 100 MeV. Theoretical modeling (see, e.g., Chap. 9), however, suggests
that CME-driven shocks are able to accelerate ions also to relativistic energies.
For electrons, strong correlation between the observed flux properties of dekaMeV protons and MeV electrons (see, e.g., Chap. 7) could point towards shock
acceleration as well, but the theoretical foundations of electron acceleration by
shocks are not on such solid basis as for ions, mainly because electrons resonate with
plasma fluctuations at much lower scales than protons (see Sect. 3.2.2). The main
shock acceleration mechanisms are, however, able to accelerate electrons as well. In
addition to shock acceleration, the CME downstream region hosts regions of strong
plasma compression and turbulence. Such regions may accelerate particles via the
compressional acceleration mechanism (Sect. 3.2.4) and stochastically (Sect. 3.2.5),
respectively. Note also, that coronal magnetic restructuring (outside the flaring
active region) behind the CME may also lead to particle acceleration via many of
the same mechanisms.

3.2 Acceleration Mechanisms
Particle acceleration in solar plasmas requires electric fields and the ability of
particles to propagate along them, since the energy gain rate produced by the

3 Particle Acceleration Mechanisms

47

P D qv  E. Here q, v, and W are the charge,
Lorentz force, q.E C v  B/, is W
the velocity and the kinetic energy of the particle and E and B are the electric and
the magnetic field. Electric fields can be derived from the scalar and vector potential
of the electromagnetic field:
E D r 

@A
;
@t

(3.1)

and the magnetic field from the vector potential B D r  A. Particles can move in
the direction of the electric field in several possible ways. In the following, we will
discuss the different possibilities briefly.

3.2.1 Large-Scale Electric Field Acceleration
We will first discuss electric fields in large scales, meaning that the field changes
over scales that are large compared to the gyroradii of the accelerated particles. In
the simplest case, the electric field has a component parallel to the magnetic field,
along which ions and electrons can move without being affected by the magnetic
field. Large-scale, static parallel electric fields are, however, not easy to set up
in dilute coronal plasmas, since in the near absence of collisions, electrons can
usually move very quickly along the magnetic field and build up charge separation
to counter any accelerating parallel electric field. In the presence of magnetic
field inhomogeneities, however, gradient and curvature drifts can move ions and
electrons in the direction perpendicular to the field. This may lead to particles
gaining energy, if there is an electric field along the direction of the drift motion.
This is the basis of several shock-acceleration mechanisms to be discussed in
Sect. 3.2.3.
Magnetic reconnection is perhaps the most obvious plasma process to set up
large-scale electric fields. Some models consider static electric fields accelerating
particles near magnetic nulls, where particles can propagate along the electric field
unimpeded (Litvinenko 1996). This, however, is not the only way to set up a large
scale electric field that particles can utilize effectively to get accelerated.
Choosing to work in the Coulomb cauge (r  A D 0), the electric fields due to
charge separation are all described by the scalar potential and, thus,
r2 D 

q
:

0

(3.2)

Therefore, the part of the electric field related to the vector potential contains
inductive fields related to the time derivative of the magnetic field via Faraday’s law.
These electric fields are then described by fields lines that are either closed loops or
extend to the boundaries of the system. Electric fields induced by the temporally
variable magnetic field (or vector potential) can sometimes lead to very efficient
acceleration of particles. Let us illustrate this with an example.

48

R. Vainio and A. Afanasiev

Consider

B D B0

yex  xey
C 0 tez
r0


DrA



yex  xey
x2 C y2
0 t C
A D B0 
ez ;
2
2r0
0 J D r  B D 

r AD0

2B0
ez
r0

(3.3)

(3.4)
(3.5)

This magnetic configuration is represented by a helical magnetic field, where the
axial field increases linearly with time and the poloidal field (driven by a constant
axial current) is constant (see Fig. 3.1).
The axial magnetic field is generated by a poloidal external current flying at
some radial distance, e.g., r D r0 , increasing linearly with time. We neglect the
displacement current so the time evolution of the axial field (and external current)
has to be slow in the sense that r0 0  c. With these assumptions, the induced
electric field is
E C r D 

yi  xj
@A
D 0 B0
D 12 r0 0 Bp :
@t
2

(3.6)

Clearly, the induced electric field is in the direction of the poloidal magnetic field
and, therefore, particles propagating along the field lines will be accelerated along
the field, ions in one direction and electrons in the other. The axial field, however,
will make sure that electrons and ions will also propagate along the axial direction,

Fig. 3.1 Electromagnetic fields in the simple model. The magnetic field (left) is a helix, where
the axial field (Bz ) is linearly increasing with time and the poloidal field (Bp ) is driven by a
homogeneous axial current. The poloidal electric field Ep (right) is induced by the time-dependent
axial magnetic field and it is in the same direction as the poloidal magnetic field. Charge separation
caused by the particles accelerated by Ep along the magnetic field lines will produce an oppositely
directed axial electric field. This would eventually turn the electric field perpendicular to the
magnetic field if charge separation is let to build up in the plasma

3 Particle Acceleration Mechanisms

49

in the opposite directions. Thus, charge separation will be set up. It produces a
potential field in the axial and radial direction, which combined to the induced field
could produce a total electric field perpendicular to the magnetic field. The condition
would be
EB D

)

r2 zB0
2r0 t

r 2 0 2
@
0
B0  B0 0 t
2r0
@z
) r  

rzB0
r 2 B0
er 
ez
r0 t
2r0 t

(3.7)

However, it is clear that this field can be approached only after a finite time (as it
diverges at t ! 0). Thus, during a limited amount of time, the induced electric field
can accelerate particles very efficiently.
We notice also that particles could be accelerated by the induced electric field
even without the poloidal magnetic field in the system. If only the axial magnetic
field is present, particles will perform gyro-motion around it. The contour integral
of the Lorentz force along one circular Larmor orbit,
I
W? D

qE  dl;

(3.8)

L

is in the left-handed [right-handed] sense around the magnetic field B D B.t/ ez for
q > 0 [q < 0]. Taking the integral in the right-handed sense (denoted below by the
minus sign after L) gives
I

Z

W? D jqj
Z

E  dl D jqj
L

D jqj
AL

.r  E/  .ez dS/
AL

@B
@B
 .ez dS/ D jqjrL2
@t
@t

(3.9)

Since the Larmor radius is rL D v?
L =2, where
L D 2 m=jqjB is the particle
gyrotime, and  and m its Lorentz factor and mass, respectively, we have
v? p? D W? D jqj
)

v?
L  mv? @B
2 jqjB @t

pP ?
1 p?
1 @B
D 12 0 ;
D
D
p?
p ?
L
2B @t

(3.10)
1

which describes the betatron acceleration process. Clearly, p? D p?0 e 2 0 t gives the
perpendicular particle momentum in terms of its initial value p?0 at t D 0.

50

R. Vainio and A. Afanasiev

3.2.2 Resonant Wave Acceleration
As discussed above, generating electric fields with quasi-static components along
the magnetic field is not easy. Instead of large scale fields, the fields can also be
at the gyromotion scale, and such fields can be carried by various plasma waves.
At first sight, if the electric field is fluctuating, it is quasi-periodically pointing in
opposite directions and the time integral of the acceleration would seem to vanish
in most cases. In this case, however, it is possible for the particle to be in resonance
with the wave’s electric field: if the period of particle motion agrees with the period
of the wave, the phase of the wave at the location of the particle can be constant,
leading to a constant accelerating electric field felt by the particle.
This process can be illustrated with a simple linearized model. Consider the
electric field of a circularly polarized wave propagating along the mean magnetic
field taken to be constant and along the z axis. Thus,
E1 D E1 Œex cos.kz  !t/  ey sin.kz  !t/;

(3.11)

and the phase speed of the wave is V D !=k. The electric and magnetic fields of
the wave are related via Faraday’s law, i.e.,
ˇ
ˇ
ˇ ex ey ez ˇ
ˇ
ˇ
@E1y
@B1
@E1x
D r  E1 D  ˇˇ @x @y @z ˇˇ D ex
 ey
@t
@z
@z
ˇE E 0 ˇ
1x 1y
D kE1 Œex sin.kz  !t/  ey cos.kz  !t/
k
E1 Œex cos.kz  !t/ C ey sin.kz  !t/
!
!
) E1 D  B1 D V B1 ;
k

) B1 D

(3.12)
(3.13)
(3.14)

i.e., the magnetic field is circularly polarized, as well. In case the phase speed is
less than the speed of light, we can always make a boost along the z axis to a
coordinate system where the wave frequency is zero. In this frame the wave electric
field vanishes and the charged particles interacting with the wave conserve their
energy. In the laboratory frame the change in the particle energy is, thus, obtained
through
W D  V p0 0 ;

(3.15)

where  D .1  V2 =c2 /1=2 , 0 and p0 are the pitch-angle cosine and the (constant)
momentum magnitude of the particle in the wave frame, and X represents the

3 Particle Acceleration Mechanisms

51

change in the quantity X. The equations of motion in the wave frame (omitting the
primes) can be written as
P D

B1 p
1  2 ˝0 cos.' C kz/
B0

'P D ˝0 C


B1
˝0 sin.' C kz/
p
B0 1  2

zP D v;

(3.16)
(3.17)
(3.18)

where ' is the phase angle measured around the z axis and ˝0 D qB0 = m is
the particle’s relativistic (signed) gyro-frequency. Now, assuming that the magnetic
amplitude of the wave is small compared to the mean magnetic field, B1  B0 , we
can approximate the phase angle evolution by ' D '0  ˝0 t. Substituting that to
the equation for  shows a resonance (a constant right-hand side) at kz  ˝0 t D 0
) kv D ˝0 ;

(3.19)

which is the cyclotron resonance condition between charged particles and electromagnetic waves propagating parallel to the mean magnetic field, written in
the rest-frame of the wave. Transforming back to the laboratory frame gives the
resonance condition as
!  kv D ˝0 ;

(3.20)

where negative (positive) frequencies denote left-handed (right-handed) polarization. The circular polarization of the wave has to match the handedness of the
particle motion in the guiding-centre rest-frame (where v D 0), so ions (electrons)
resonate with left-hand (right-hand) polarized waves in that frame. The waveparticle resonance is sketched for protons and cold-plasma waves in Fig. 3.2. We
can see that low-energy protons (with jvj . 2VA ) can only resonate with counterpropagating left-handed waves (Vainio 2000).
Approximating the left-handed dispersion curve with a straight line at ˝0 <
! < 0 simplifies the picture so that the phase speed of the resonant wave is constant.
Thus, the relevant wave-frame, where the proton would conserve its energy, is
propagating at speed ˙VA along the background field and protons with positive
[negative] parallel speed resonate with waves with !=kk D VA [!=kk D CVA ].
Thus, their position in .vk ; v? / velocity plane is constrained on semicircles centered
at vk D ˙VA . Starting from low speeds, v0  VA , wave-frame pitch-angle
scattering leads to an increase of perpendicular velocity of protons, as depicted
in Fig. 3.3. If the extent of the initial distribution in the parallel direction is v0 ,
then the extent of the final distribution in the perpendicular direction would be

52

R. Vainio and A. Afanasiev

Fig. 3.2 Cyclotron resonance of protons with parallel propagating cold-plasma waves. The
resonance condition, Eq. (3.19), is depicted with the black line for a proton with positive parallel
speed v. The green and the red curves give the dispersion relations of parallel-propagating coldplasma waves with negative frequencies denoting the left-handed Alfvén–ion-cyclotron waves and
positive frequencies the right-handed fast-MHD–whistler waves. The red (green) line gives the
wave with positive (negative) phase speed !=kk . The red (green) dashed lines depict the lowfrequency approximation to the dispersion relation, i.e., the Alfvén waves with positive (negative)
phase speed, !=kk D ˙VA . The wave-particle resonances are found where the black line crosses
the dispersion curves

Fig. 3.3 The resonant-wave acceleration process. Particles are scattered off electromagnetic waves
propagating in the medium at phase speeds ˙V , here approximated with ˙VA . Scattering is
elastic in the wave frame, which leads to particles conserving their kinetic energies in that frame.
If waves have left-handed polarization, low-energy ions resonate with them when propagating in
the opposite direction (in the plasma frame) than the wave. Particles initially in the grey region
inside the blue semi-circle will be scattered by the waves to fill the intersection of the green and
red sectors, centered at vk D VA and vk D CVA , respectively

q

.VA C v0 /2  VA2 D
parallel energies is

q

2VA v0 C v02 and the ratio of final perpendicular and initial

W?;max
v 2 C 2VA v0
2VA
D 0
D1C
;
2
Wk;0
v0
v0

(3.21)

3 Particle Acceleration Mechanisms

53

so obviously the mechanism alone cannot accelerate ions to very high energies. This
mechanism is, however, the basis of the cyclotron heating models of the solar corona
(Isenberg 2001).
The resonant wave-acceleration process in solar flares is thought to be responsible for the preferential acceleration of minor ions. The dispersion relations of
the waves in a multi-species plasma are not as simple as in Fig. 3.2, but contain
additional resonances (jkk j ! 1) with thermal He4 ions at cyclotron frequency
half of protons, ˝˛ D 12 ˝p . Ions with cyclotron frequencies differing from that of
protons and alpha particles are much more efficiently accelerated than protons and
alphas in such plasmas. We will come back to this in Sect. 3.2.5.

3.2.3 Shock Acceleration
Shocks can accelerate particles in various ways. The three most commonly studied
mechanisms are shock drift acceleration (SDA), shock surfing acceleration and
diffusive shock acceleration (DSA).
SDA occurs, when a particle interacts once with a quasi-perpendicular shock
front (Fig. 3.4, panels a and b) (Sarris and Van Allen 1974). The particle drifts (due
to the motional electric field, E D u1  B1 ) with the upstream bulk speed u1x
toward the shock wave. When the ion [electron] hits the shock front, it feels the
stronger downstream magnetic field, meaning that its Larmor radius is smaller than
in the upstream field, and that its guiding center shifts parallel [anti-parallel] to
the electric field. Thus, the particle is accelerated. During their interaction with
the shock the particles, at least in an averaged sense, conserve their first adiabatic
invariant, p2? =B. For a perpendicular shock, we then get
s
p21
p22
B2
D
) p2 D p1
;
(3.22)
B2
B1
B1

A

B
E

E

Fig. 3.4 Shock drift acceleration and shock surfing. An energetic charged particle is convected to
a quasi-perpendicular shock from upstream by the electric-field drift. In the shock front, due to
magnetic field gradient in the front, (a) ions drift parallel and (b) electrons drift anti-parallel to the
electric field and, thus, gain energy. Panel (c) depicts an ion surfing on the shock due to multiple
reflections by the cross-shock potential electric field. (Panels (a) and (b) from Koskinen 2011)

54

R. Vainio and A. Afanasiev

p
so the particle momentum in the downstream region, p2 , is approximately B2 =B1
times the particle momentum in the upstream region, p1 . The total gain in energy
is, therefore, not very significant, but may explain the so-called shock spike events
observed during nearly perpendicular interplanetary shocks crossing the spacecraft.
SDA operates in oblique shocks as well, but slightly modified. It is most advantageous to transform to the so-called de Hoffmann–Teller frame, where the flow and
the magnetic field are parallel throughout the shock and the motional electric field
vanishes. This transformation from the upstream plasma frame is along the magnetic
field at speed u1 D u1x = cos ‚Bn away from the shock in the upstream region.
Here ‚Bn is the shock normal angle. Now, particles incident on the shock from the
upstream side with high-enough pitch-angle, i.e., with 1 2 > B1 =B2 , cannot enter
the downstream side of the shock while conserving their adiabatic invariant and,
thus, are reflected back to the upstream region. This reflection process, when viewed
in the upstream plasma frame, give the reflected particle a parallel momentum
addition of the same order as transmission in the quasi-perpendicular shock.
Shock surfing (Fig. 3.4, panel c) is related to SDA in the sense that the
accelerating electric field is the same, the motional electric field. However, the
drift motion along the field is related to the upstream-directed cross-shock potential
electric field, caused by charge separation at the shock front (Shapiro and Üçer
2003). The cross-shock potential electric field can specularly reflect ions incident
on the shock and enable their acceleration in the direction of the motional electric
field. The specular reflections can occur multiple times at a grazing angle. This leads
to ion trajectories surfing on the shock front in the direction of the electric field.
The maximum energy gained in the process depends on the thickness of the shock
and can be estimated to reach the MeV range at interplanetary shocks, if the shock
thickness is as low as an electron skin depth (Koskinen 2011). Note that electrons
will not be accelerated in this simple type of model, which has a monotonic potential
(and, thus, unidirectional field) inside the shock front.
One encounter with the shock does not typically lead to a very substantial gain of
energy. If, however, particles can interact with the shock many times, acceleration
becomes more efficient. Shock surfing is not the only way this can happen.
Particles can interact with magnetic irregularities in the plasma flow, and this can
change the particle’s propagation direction relative to the shock front enabling
several encounters with the shock. Since particle transport under such conditions is
described by diffusion relative to the local plasma flow, this acceleration mechanism
is called diffusive shock acceleration (DSA) (Drury 1983; Lee 1983).
DSA can be best understood by considering shock waves propagating parallel to
the magnetic field. There, as the particle crosses the shock front, its velocity vector
does not change, because the magnetic field is not compressed. When the particle is
moving relative to the plasma under the influence of frozen in magnetic turbulence,
providing scattering centers,1 it conserves its energy in the local plasma frame while

1

For simplicity, the turbulence in the vicinity of the shock is often assumed to be magnetostatic,
but the DSA theory can be formulated assuming that the scattering centers are propagating Alfvén
waves. This simply modifies the velocities of the scattering centers.

3 Particle Acceleration Mechanisms

55

v
3

1

2

u2

v||

u1

Fig. 3.5 Diffusive shock acceleration. An energetic charged particle scatters off magnetic irregularities frozen in to the local plasma flow. The numbered points depict successive crossings of the
shock front, where the speed of the scattering centers changes. Because points with odd numbers
must have vk > 0 and points with even numbers must have vk < 0, the shock crossings lead to a
systematic gain of energy W D 12 mv 2 . (From: Koskinen 2011)

simultaneously scattering in pitch angle. Upstream [downstream] particles are, thus,
staying on semicircles in velocity space, centered at .vk ; v? / D .u1Œ2 ; 0/. Due to
pitch-angle scattering, energetic (v 0 > u) particles can propagate in either direction
relative to the shock. When the flow at the shock is compressed (i.e., u2 < u1 ),
particles crossing the shock many times gain speed systematically as shown in
Fig. 3.5.
When particle speeds are much larger than the fluid speeds, v  u, particle
distributions become almost isotropic as a result of the scattering process. This
enables one to calculate the energy spectrum of accelerated particles resulting from
DSA. After n shock crossings, the mean particle momentum is
9
8
n
<4 X
u1  u2 =
h pn i D p0 exp
;
:3
vj ;
jD1

(3.23)

where p0  mu1 is the injection momentum. The probability of a particle of
performing at least n crossings of the shock is
9
8


n
< X
u2 =
h pn i 3u2 =.u1 u2 /
D
:
Pn D exp 4
:
v ;
p0
jD1 j

(3.24)

By combing these, the integral momentum spectrum can be given as

N. p > h pn i/ D N0

h pn i
p0

3=.r1/

;

(3.25)

56

R. Vainio and A. Afanasiev

where N0 is the total number of particles injected to the acceleration process and
r D u1 =u2 is the compression ratio of the shock. Thus, shock-accelerated particles
have a power-law differential momentum spectrum
dN
3N0
D
dp
r1



p0
p

.rC2/=.r1/
(3.26)

with spectral index  D d ln N=d ln p D .r C 2/=.r  1/ solely determined by
the compression ratio of the shock. While the calculation above was presented for
parallel shocks, the final result applies for oblique shocks as well.
The spectral index is actually determined by the shock’s compression ratio only
if MA  1. If the Mach number of the shock is of the order unity, the magnetic
scattering centers in the flow (which are actually magnetohydrodynamic waves or
turbulence and not static) are no longer static magnetic fluctuations. Instead, they
have non-negligible phase speeds V  VA relative to the flow. Recall that the
scattering is elastic in the frame of the propagating magnetic structure, where the
electric field of the fluctuation vanishes. Taking these considerations into account
when determining the scattering-center compression ratio of the shock (Vainio and
Schlickeiser 1999), one gets
D

rsc C 2
I
rsc  1

with

rsc D

u1x C V1 M!1 u1x
!
D r:
u2x C V2
u2x

(3.27)

In slow-mode shocks, the scattering centers (Alfvén waves) always have larger
phase speeds than fluid speeds. Thus, the scattering centers do not converge in slow
shocks under many circumstances. In such cases, DSA is not operating at the shock.
Upstream of fast-mode shocks, particles can generate their own scattering centers
by streaming instabilities of the Alfvén waves (Lee 1983; Afanasiev et al. 2015).
This can be figured out most easily by looking at particle scattering in the upstream
plasma frame. Particles conserve their energies in the frame co-moving with the
MHD waves, because in that frame, the wave has no electric field (since ıB has
no time dependence there, as discussed above). Thus, particle energy in the plasma
frame is
W D W 0 ˙ VA1 p0k ;

(3.28)

where the signs denote waves propagating forward (CVA1 ) and backward (VA1 )
relative to the flow. Particles entering the upstream region from downstream have
p0k =W 0 < .u1 ˙ VA1 / < 0. Scatterings make the particles isotropic in the wave
frame, so as a result of scatterings in the upstream region, p0k increases. Thus,
particle energy in the plasma frame increases (decreases) in scatterings off forward
(backward) MHD waves in the upstream region. Since the total energy of particles
and waves has to remain constant in the plasma frame, this means that the energy
density of backward waves increases and forward waves decreases.

3 Particle Acceleration Mechanisms

57

Finally, one should note that the power-law spectrum does not extend to infinite
energies, but experiences a cut-off at some high energy determined by the age and
the size of the system. Obviously, if there is limited time
available to accelerate
the particles, they cannot be accelerated beyond energies determined by pP  p=
,
where pP is the momentum gain rate related to the scattering rates and flow velocities
in the system. Likewise, when the particle’s diffusion length, =u1 , becomes of the
order of the system size, the particle can not be accelerated any further, as it will
not be confined to the vicinity of the shock anymore but may escape from the
system. Here,  D 13 v is the spatial diffusion coefficient and  is the scattering
mean free path, which cannot be smaller than the Larmor radius of the particle. In
an inhomogeneous magnetic field, such as the coronal field, particles also need to
be confined by turbulence near the shock strong enough to avoid the escape by
adiabatic focusing (Vainio et al. 2014). This leads to yet another condition that
=L < u1 , where L D B=.@B=@s/ is the focusing length, i.e., the scale height of
the magnetic field intensity. This represents the relevant system size in the coronal
medium.

3.2.4 Compressional Acceleration and Collapsing
Magnetic Traps
DSA operates because of the convergence of the flow of scattering centers at the
shock. The acceleration rate of an isotropic population of particles in a converging
flow is given by pP D  13 pr  u, where u is the scattering center velocity.
Compressional acceleration can, therefore, work also in presence of compressions
(r  u < 0) of non-shock type. If the diffusion length of the particles, =u, is much
longer than the gradient scale of the flow, L  u=jr  uj, then the compression
acts on the particles as a shock, i.e., the resulting spectrum is practically the same
as in the case of DSA (Jokipii and Giacalone 2007). In the opposite case,  
u2 =jr  uj, the compression will accelerate the particle distribution adiabatically.
Because their diffusion length is very small, particles are primarily advected through
the compression and all particles regardless of their initial momentum will gain the
same factor in momentum.
Let us illustrate this with a simple example. Assume that scattering centers are
frozen-in in the plasma flow. Thus, r  u is given by the hydrodynamic conservation
of mass as
r uD

1 d
;
dt

(3.29)

where is the density of the plasma parcel being advected at velocity u. Thus,
pP
p3
P
D  13 r  u D
)
D constant;
p
3


(3.30)

58

R. Vainio and A. Afanasiev

which is consistent with the adiabatic equation of state for a monoatomic gas, i.e.,
T 2=3 D constant at non-relativistic energies.
Similar to compressional acceleration, particles can be accelerated adiabatically
if they are confined to a collapsing magnetic trap (see Borissov et al. 2016 and
references therein). A simple example is a shrinking magnetic bottle, consisting
of two magnetic mirrors in the ends, e.g., a contracting coronal loop. Particles
mirroring in the ends of the trap would get accelerated, as in the rest frame of the
center of the trap (the loop apex in the simple example), the mirrors in the two ends
of the trap would be approaching each other. The acceleration
rate is obtained from
H
the conservation of the second adiabatic invariant, pk dsk D 2jpkjs D constant,
where the integral is along the magnetic field lines from one end of the trap to the
other and back, and s is the length of the trap along the field. Decreasing s has to be
compensated by increasing jpk j and the parallel momentum will increase at rate
djpk j
sP
D jpk j
dt
s

(3.31)

As a magnetic bottle cannot trap particles residing in the loss-cone of the weaker
magnetic mirror, this mechanism would appear at first sight to be limited to rather
modest gains of momentum. However, if the magnetic field inside the trap is simultaneously increasing the betatron effect will increase the perpendicular momentum
and help the particles stay trapped. The details of the magnetic configuration and its
evolution will determine the acceleration efficiency of a collapsing magnetic trap.

3.2.5 Stochastic Acceleration
DSA, compressional acceleration, and collapsing traps are all examples of so-called
first-order Fermi acceleration, where particles gain momentum systematically and
proportionally to the speed of a moving magnetic structure. Stochastic acceleration,
or second-order Fermi acceleration, is a process, where particles gain or lose
energy (with a positive net energy gain) by interacting simultaneously with plasma
disturbances with different phase speeds in the laboratory frame (Miller 1998).
For example, if a high-energy proton is propagating in a medium with counterpropagating Alfvén waves, it can simultaneously scatter off waves propagating in
both directions (Fig. 3.6, left panel). As the scatterings conserve the energy of the
proton in each wave frame, the scatterings off one wave produce energy change
along different characteristics in the .vk ; v? / plane than the scatterings off the other
mode. This leads to random walk of the particle in the .vk ; v? / plane, which can
be described by momentum diffusion. In this process the net momentum gain rate
is proportional to the second power of the wave speed. (Hence, second-order Fermi
acceleration.)

3 Particle Acceleration Mechanisms

59

Fig. 3.6 The left panel shows the resonance plot for a multi-species plasma with protons and alpha
particles as the major ion species. The wave modes with positive (negative) phase speeds are plotted
with green (red) curves. The grey shaded regions are those where resonances with thermal ions
will damp the wave power efficiently. Cyclotron waves have two branches with resonances with
alpha particles and protons, respectively. The lines depict the resonance conditions for energetic
protons (jvj  VA ) and thermal minor ions. The right panel shows the possible velocity-space
trajectories of protons in a plasma with counter propagating Alfvén waves, only. The red (green)
semicircles are trajectories of particles interacting with Alfvén waves with positive (negative) phase
speeds. The red (green) region depicts the velocities at which resonances with and Alfvén waves
with positive (negative) phase speeds are not possible. Outside these regions, protons can always
resonate with waves propagating in both directions leading to random walk in velocity space, i.e.,
momentum diffusion

The situation is illustrated in Fig. 3.6, right panel, where energetic protons can
interact with two Alfvén waves propagating in opposite directions, when the proton
velocity is situated in the region jvk j & 2VA . Scatterings off waves with positive
(negative) phase speed will result in motion along the red (green) semi-circles
showing that the particle energy in the plasma frame can change in a random
fashion, i.e., increase or decrease. As this diffusive process spreads the distribution
of protons in energy, the net effect will be acceleration. This is an example of
stochastic acceleration, but other types of waves as well as randomly moving
coherent structures interacting with the particles can lead to a similar situation of
particles diffusing in momentum when interacting with the structures.
Figure 3.6, left panel also shows the resonant interaction of low-energy minor
ions (3 He and iron) with higher-frequency left-handed wave modes. The figure
shows that while thermal protons and alpha particles would typically resonate
with heavily damped wave modes (and their resonant wave acceleration should,
therefore, be somewhat inefficient), minor ions not only resonate with much less
damped waves but also simultaneously with several waves propagating at different
phase speeds. Especially 3 He can be very efficiently accelerated stochastically
in this process, starting already from thermal energies. Stochastic acceleration

60

R. Vainio and A. Afanasiev

process, therefore, has the power to explain the peculiar abundances (strong increase
in 3 He and heavy ion abundances over protons and alphas) observed in impulsive
events (cf. Chap. 2). Note that stochastic acceleration may also occur in the turbulent
sheath regions of coronal shocks and help to explain the observed double-power-law
spectral form often observed in large gradual SEP events (Afanasiev et al. 2014).

3.3 Concluding Remarks
The basic acceleration mechanisms at play in erupting coronal plasmas accelerating
particles to the highest energies have been described. By making several simplifications the aim has been to convey the principles of the most important SEP
acceleration mechanisms, fostering efforts to create realistic and comprehensive
models of solar eruptions also from the particle acceleration aspect. The models
should involve realistic descriptions of both the macroscopic and microscopic fields
in the plasma, as electric fields of practically all scales from the kinetic to the global
may contribute to the acceleration of particles in solar eruptions.

References
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Afanasiev, A., Battarbee, M., Vainio, R.: Astron. Astrophys. 584, 81 (2015). doi:10.1051/00046361/201526750
Borissov, A., Neukirch, T., Threlfall, J.: Solar Phys. 291, 1385 (2016). doi:10.1007/s11207-0160915-0
Desai, M., Giacalone, J.: Living Rev. Sol. Phys. 13, 3 (2016). doi:10.1007/s41116-016-0002-5
Drury, L’O.C.: Rep. Progr. Phys. 46, 973 (1983). doi:10.1088/0034-4885/46/8/002
Isenberg, P.A.: J. Geophys. Res. 106, 29249 (2001). doi:10.1029/2001JA000176
Jokipii, J.R., Giacalone, J.: Astrophys. J. 660, 336 (2007). doi:10.1086/513064
Koskinen, H.: Shocks and Shock Acceleration. In: Physics of Space Storms, pp. 279–298. Springer,
Heidelberg (2011)
Litvinenko, Y.E.: Astrophys. J. 462, 997 (1996). doi:10.1086/177213
Lee, M.A.: J. Geophys. Res. 88, 6109 (1983). doi:10.1029/JA088iA08p06109
Miller, J.A.: Space Sci. Rev. 86, 79 (1998)
Petrosian, V.: Space Sci. Rev. 173, 535 (2012). doi:10.1007/s11214-012-9900-6
Reames, D.V.: Solar Energetic Particles – A Modern Primer on Understanding Sources, Acceleration and Propagation. Lecture Notes in Physics, vol. 932, 127 pp. Springer, Cham (2017)
Sarris, E.T., Van Allen, J.A.: J. Geophys. Res. 79, 4157 (1974). doi:10.1029/JA079i028p04157
Shapiro, V.D., Üçer, D.: Planet. Space Sci. 51, 665 (2003). doi:10.1016/S0032-0633(03)00102-8

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Vainio, R.: Astrophys. J. Suppl. Ser. 131, 519 (2000). doi:10.1086/317372
Vainio, R., Schlickeiser, R.: Astron. Astrophys. 343, 303 (1999)
Vainio, R., Pönni, A., Battarbee, M., et al.: J. Space Weather Space Clim. 4, A08 (2014).
doi:10.1051/swsc/2014005

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Chapter 4

Charged Particle Transport
in the Interplanetary Medium
Angels Aran, Neus Agueda, Alexandr Afanasiev, and Blai Sanahuja

Abstract The scenario and fundamentals of the physics of charged particle interplanetary transport are briefly introduced. Relevant characteristics of solar energetic
particle (SEP) events and of the interplanetary magnetic field are described. Next,
the motion of a charged particle and the main assumptions leading to the description
of the focused and diffusive particle transport equations utilised in the next chapters
are discussed. Finally, two different models are applied to interpret SEP events.

4.1 Introduction
4.1.1 Energetic Particles in the Solar System
Major solar eruptive phenomena, solar flares and coronal mass ejections (CMEs),
are usually accompanied by outbursts of charged particles that have been accelerated
up to several hundred MeV/nucleon, in some instances up to a few GeV/nucleon.
These solar energetic particle (SEP) events are mostly composed of ionised H with
10% He and <1% heavier elements. The acceleration, injection, and propagation
of SEPs from their source to an observer in interplanetary space have been
investigated over the last decades by a combination of in situ (space) and remotesensing observations. SEP acceleration processes are described in Chap. 3. Here the
focus is on the transport processes of SEPs in interplanetary space.
SEP events are usually classified into two types: impulsive events and gradual
events. Impulsive events last for hours, are rich in electrons, 3 He and heavy ions,
have relatively high charge states, and are produced by solar flares. Gradual events
can last for days, are electron poor, have relatively low charge states, and are
A. Aran () • N. Agueda • B. Sanahuja
Dep. de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos (ICCUB), Universitat de
Barcelona, c. Martí i Franquès, 1, E-08028 Barcelona, Spain
e-mail: angels.aran@fqa.ub.edu; agueda@fqa.ub.edu; blai.sanahuja@ub.edu
A. Afanasiev
Department of Physics and Astronomy, University of Turku, Turku FI-20014, Finland
e-mail: alexandr.afanasiev@utu.fi
© The Author(s) 2018
O.E. Malandraki, N.B. Crosby (eds.), Solar Particle Radiation Storms Forecasting
and Analysis, The HESPERIA HORIZON 2020 Project and Beyond, Astrophysics
and Space Science Library 444, DOI 10.1007/978-3-319-60051-2_4

63

64

A. Aran et al.

associated with coronal and interplanetary shocks driven by CMEs that move
rapidly through the solar wind plasma. Gradual SEP events are more intense (i.e.,
much higher intensities and higher fluences) than impulsive events. Hybrid SEP
events have also been observed; they show mixed characteristics which partially
correspond to impulsive and gradual events, suggesting that solar particle events
can have distinct components (i.e., flare-accelerated particles and shock-accelerated
particles).
Impulsive events are generally limited to within a 30ı longitude band around
the footpoint of the nominal field line magnetically connected to their parent
active region. On the other hand, gradual events are able to produce much wider
longitudinal distributions due to the extended nature of the propagating interplanetary shock. In this way, observers located at different places in the heliosphere
can be magnetically connected to different parts of the front of such a shock by
interplanetary magnetic field (IMF) lines. In gradual events, in addition to the
various transport effects at play, the shape of the particle intensity temporal profiles
depends also on both the dynamic evolution of the shock strength and the relative
location of the observer with respect to the traveling shock. The point along the
shock front at which successive magnetic field lines connect with the observer is
termed the cobpoint (connecting with the observer point, see Heras et al. 1995); and
the gradual SEP event intensity-time profiles recorded in interplanetary space can
be interpreted in terms of the cobpoint evolution, after deconvolving the transport
effects. The SEP propagation in interplanetary space is controlled by the largescale structure of the magnetic field and the turbulent magnetic field fluctuations
superposed on the mean magnetic field.

4.1.2 The Interplanetary Magnetic Field
At a certain distance from the Sun, the solar wind flow speed is much higher than
the local sound and Alfvén speeds. Near the Earth’s orbit (1 AU), typical values
for the sound and aflvénic speeds are 60 km s1 and 40 km s1 , respectively,
whereas for the solar wind speed is 400 km s1 . This implies that the plasma
dynamic pressure is much higher than both the magnetic and thermal pressures (see
more details in e.g., Hundhausen 1995). The solar wind carries the magnetic field
from the Sun to interplanetary space, with the magnetic field frozen-in in the nearly
radially expanding solar wind flow, given the very high conductivity of the solar
wind plasma (for a deduction of the frozen-in condition see e.g., Bittencourt 2004).
Field lines can then be seen as stream lines of the fluid flow. However, the situation
becomes complicated because of the solar rotation which has an average period of
27.3 days. One can interpret the radially outflowing plasma streams as parcels of
plasma emitted from the same source region. These parcels carry the magnetic field
with them, and because they are tethered to the rotating Sun, the IMF lines that trail
behind them are spirals. By assuming a constant solar wind speed, u, an IMF line

4 Charged Particle Transport in the Interplanetary Medium

65

depicts an Archimedean spiral (known as the Parker spiral after the model proposed
by Parker 1958).
The equation of the Archimedean spiral can be derived from the displacement in
radial and angular directions. Assuming as initial conditions of a plasma parcel on
the Sun, a source longitude 0 , and a source radius r0 , at time t, the parcel is found
in the equatorial plane at position, r
r D r0 C u.  0 /=˝

(4.1)

where ˝ is the solar rotation speed. The angle between the radial direction and the
magnetic field B, , is given by tan D r=a where a D u=˝. Figure 4.1 shows
a sketch of an IMF line. Assuming a solar wind speed of 400 km s1 ,  45ı at
1.0 AU. The spiral configuration represents a smooth average of the large-scale IMF.
Variations in solar wind velocity and processes acting in the solar wind and corona,
including reconnection, create a spread in directions around the spiral angle. In fact,
individual vectors can point to any angle superposed on this average field because of
small-scale random fluctuations and, in addition, individual field lines can meander
relative to the average direction.
The path length, z.r/, along the spiral can be estimated from dz D sec dr:
13
0
2 s
s
2
a 4r
r2
r
r
z.r/ D
1 C 2 C ln @ C 1 C 2 A5
2 a
a
a
a

Fig. 4.1 Sketch of an
Archimedean spiral
interplanetary magnetic field
line crossing the Earth. is
the angle between the radial
direction and the magnetic
field B

(4.2)

66

A. Aran et al.

close to the Sun (i.e., for r=a  1), z  r, and well beyond 1 AU (i.e., in the limit
for r=a  1), z  r2 =2a.
By assuming that the frozen-in condition holds in interplanetary space and that
IMF lines are Archimedean spirals, the strength of the IMF is given by:
p
B.r/ D B0 .r0 =r/2 .1 C .r=a/2 /

(4.3)

where r0 is the heliocentric radial distance at which the field is completely frozen
into the solar wind, being r0 > 2 Rˇ and B0 D B.r0 /. Thus, close to the Sun, B.r/
decreases as r2 while well beyond 1 AU it decreases as r1 . Figure 4.2 shows the
dependence of the magnetic field line length and the magnetic field strength with
the radial distance from the Sun.
Depending on the magnetic polarity of the photospheric footpoint of the field
lines, the magnetic field spirals outward (positive) or inward (negative) from the
Sun. The global interplanetary positive-negative magnetic domains are separated by
a huge electric current system, the heliospheric current sheet (HCS). The HCS is
tilted out of the solar equatorial plane a few tens of degrees. Changes in the coronal
magnetic field due to solar activity are carried outward to space, and manifest as
spatial and temporal variations (e.g., magnetic sectors). This overall picture of the
IMF is known as the ballerina skirt model. As the HCS rotates along with the
Sun, the peaks and troughs of the skirt pass through the Earth’s magnetosphere,
interacting with it. A detailed description of the global heliospheric magnetic field
can be found in Smith (2008).

Fig. 4.2 Dependence of the magnetic field line length and the magnetic field strength with the
radial distance from the Sun. The dotted line indicates the length of a radial line for comparison

4 Charged Particle Transport in the Interplanetary Medium

67

4.1.3 Motion of Charged Particles. First Adiabatic Invariant
Space and time variable magnetic fields, with a large variety of characteristic lengths
and times, play a key role in the description of the transport of SEPs in interplanetary
space. The solar wind is a collisionless plasma highly conductive in which SEPs
propagate basically tracking the IMF. It is also assumed here that SEPs are not
able to modify the external, non-uniform and time-varying, magnetic fields. This
section shortly reviews the most relevant aspects of electrodynamics that will later
be used in Sect. 4.2 when introducing the transport of SEPs in interplanetary space.
An extended description can be found elsewhere (e.g., Bittencourt 2004; Kallenrode
2004).
Let’s consider a charged particle of rest mass m, charge q, moving with velocity v,
in a given electric field, E, and in a magnetic field, B. Neglecting collisions and any
other external force (e.g., a gravitation force), the motion of the particle is governed
by the Lorentz force
dp
D q.E C v  B/
dt

(4.4)

where v D p=. m/ and  D .1 C p2 =.mc2 //1=2 is the Lorentz factor of the particle.
Then, the Larmor (or gyration) radius of the particle is given by
rL D

v?
p?
D
!c
jqjB

(4.5)

Where v? and p? are, respectively, the components of the velocity and momentum
perpendicular to the magnetic field. The gyro frequency of the motion is !c D
jqjB=. m/.
To give some numbers, at 1 AU, for a typical IMF strength value (B D 5 nT),
the Larmor radius of a proton with a kinetic energy of 700 MeV is rL  9  105 km
(2:3 times the mean distance between the Earth and the Moon).
Each particle describes an helicoidal motion that can be decoupled into motions
parallel (vk ) and perpendicular (v? ) to the magnetic field. The parallel component
describes the motion of the centre of gyration of the particle along B while v?
consists of a gyration motion (characterised by !c ) around B plus a drift velocity
component, vF , also perpendicular to B. Then the particle motion is described by the
gyration and the motion of the guiding centre, which is the addition of the motion
parallel to B and a drift.
A charged particle moving under the presence of time-varying or non-uniform
fields is affected by a number of velocity drifts: plasma drift (e.g., associated with
an electric field), the gravitational drift, field line curvature and gradient drifts
(associated with the magnetic field), or the polarisation drift (when there is a timevarying electric field). The drift velocity term, vF , represents the drift velocities
caused by the aforementioned fields (see detailed descriptions of the various particle
drifts in e.g., Bittencourt 2004; Kallenrode 2004).

68

A. Aran et al.

The pitch angle, ˛, gives the relative size of the perpendicular and parallel
components of the particle velocity, it is given by
˛ D tan1 .v? =vk /

(4.6)

In the description of SEP transport, the cosine of the pitch angle,  D cos ˛, is
frequently used.
The magnetic moment, m, of a charged particle moving in a magnetic field is a
measure of the magnetic flux traversing the circular section defined by the particle’s
Larmor radius. The kinetic energy can be written as the sum of its parallel and
perpendicular components to the magnetic field, W D Wk C W? . It can be shown
(e.g., Bittencourt 2004) that
jmj D

W?
W sin2 ˛
v? p?
D
D
2B
B
B

(4.7)

Note that in a static uniform magnetic field, vk is constant, so the particle moves
at constant velocity along B, and W and Wk are constant. Hence, it follows that, W?
and v? are also constants of the motion.
The first adiabatic invariant can be derived from the equation of motion. It states
that the magnetic moment of a particle, jmj, is constant when moving in a slowly
varying magnetic field (there are also other conditions for specific scenarios; e.g.,
no wave-particle interactions or that !c does not go through zero).
A particle moving into a converging magnetic field increases its W? while its Wk
decreases, to keep jmj and W constant; hence, its Larmor radius decreases and its
pitch angle increases. The opposite is true if the magnetic field strength decreases
(e.g., diverging IMF).
In the absence of parallel electric fields (W constant) the pitch angle of a particle
at two locations, with respective magnetic field strength B1 and B2 , must satisfy:
B2
sin2 ˛2
D
2
B1
sin ˛1

(4.8)

If the magnetic field becomes strong enough, then vk D 0, the direction of the
particle is reversed. The particle’s speed increases in the direction of decreasing B by
the parallel component of the gradient force of the field, thus, the particle is reflected
from the region of converging field lines. The parallel component of the average
Lorentz force is called the mirror force because it leads to mirroring trajectories
for a particle in a converging field. This effect is relevant for SEP propagation in
interplanetary space. For example, it can explain that, for certain SEP events, solaror near Sun- accelerated particles are later observed travelling back to the Sun (e.g.,
Tan et al. 2009).
If a particle is in a region of space between two high magnetic field regions, then
the particle may be reflected at one side, travel towards the second, and also reflect
there. Thus the particle motion is confined to a certain region of space, bouncing

4 Charged Particle Transport in the Interplanetary Medium

69

back and forth between two regions of large field strength. Examples of such a
magnetic trapping scenario are the bidirectional SEP events sometimes observed in
the downstream region of interplanetary shocks.
The same force that causes mirroring in a converging magnetic field, causes
particle focusing in a diverging (decreasing) magnetic field. In this latter case, the
particle will describe orbits with increasingly larger rL (i.e., the pitch angle tends to
approach zero). This focusing process is particularly important in the context of SEP
transport given that energetic particles travel from Sun to Earth along the divergent
interplanetary magnetic field. If no particle-diffusion process is considered, an
isotropic energetic particle population released at the Sun will appear to come in
a very narrow cone pitch angle (1ı wide) when observed at 1 AU.

4.2 Particle Transport
The solar wind is a collisionless plasma, hence SEPs mainly experience the effect
of the electromagnetic fields. In the interplanetary space, one can assume that the
average electric field vanishes due to the large conductivity of the solar wind plasma.
The interplanetary magnetic field is turbulent (waves and fluctuations may be treated
as perturbations added to the large-scale magnetic field configuration) and as such,
it scatters particles in pitch-angle. Given the different scales involved, the transport
of particles is often described by the evolution of the particle distribution, i.e., in an
ensemble-averaged manner. The main objective of this section is to provide the key
elements to contextualise the interplanetary models used later in this book.

4.2.1 Particle Transport Equations
The particle distribution function, f , is defined so that the number of particles dN in
a phase space volume .r C d3 r; p C d3 p/ at a time t is given by
dN D f .r; p; t/d3 rd3 p

(4.9)

The phase-space volume element as well as the number of particles are Lorentz
invariants, and therefore, the phase space density, f .r; p; t/, is an invariant. The
Boltzmann equation is the fundamental equation of motion in the phase space. For
a particle of charge q and mass m under an external electromagnetic force, it reads
@f
@f
C v  r f C q.E C v  B/ 
D
@t
@p



@f
@t


(4.10)
s

where the first term of the right hand side does not represent collisions but may
describe the scattering of particles by electromagnetic waves and random magnetic

70

A. Aran et al.

field fluctuations. Given the random nature of the scattering processes, Eq. (4.10)
is a Fokker-Planck equation. A thorough derivation of the transport equations in
different scenarios can be found in e.g., Zank (2014). Another approach to study
SEP transport is to start from the Vlasov equation that describes self-consistently the
non-linear coupling between particles and fluctuating wave fields (e.g., Kallenrode
2004). It is widely used in plasma physics and has the same form as Eq. (4.10) but
without the right hand side term. A discussion on the relation of the Vlasov and the
Boltzmann equations can be found in e.g., Bittencourt (2004).

4.2.2 Focused Transport
For describing the transport of SEPs in the interplanetary space, the frame of the
focused transport is the most adequate. In the focused transport model, energetic
particles are considered to undergo pitch-angle scattering due to small scale irregularities in the IMF, and focusing and mirroring due to the large-scale weakening
of the IMF at increasing distance from the Sun. Focused transport for SEP particles
is mainly a competition between the focusing effect and the pitch-angle scattering
processes. The standard equation derived by Roelof (1969) from Eq. (4.10) is:


@f
1  2 @f
@
@f
@f
C v C
v
D
D
@t
@z
2L
@
@
@

(4.11)

where f is a function of the spatial coordinate, z, measured along the IMF line, the
particle momentum, p, the pitch-angle cosine, , and time t. v is the velocity of
the particles, D is the pitch-angle diffusion coefficient describing the stochastic
forces, and L is the focusing length which involves spatial variations of the guiding
field (assumed to be static), given by L.z/ D B.z/=.@B=@z/. The second term of
the left hand side of Eq. (4.11) describes the streaming of the particles along the
IMF; the third term, the focusing of particles and the term in the right hand side,
accounts for the scattering in pitch-angle.
In order to describe SEP events, a particle source term, Q, is added in the right
hand side of Eq. (4.11) to account for the injection of particles by either a fixed
source (like flares) or a mobile source (i.e., coronal/interplanetary shock waves).
By following the quasi-linear theory (QLT), the interaction between particles
and waves is treated here to the first order only. The irregularities of the IMF
are considered to be sufficiently small so that several gyrations of a particle are
needed to modify significantly its pitch-angle. Also, it is assumed that the magnetic
field irregularities can be described as waves of axially-symmetric transverse
components, with wave vectors parallel to the average field (known as the ‘slab
model’). The combination of QLT with the slab model is known as the ‘standard
model’ of particle scattering. The magnetic field fluctuations can be described by
a power-density spectrum, P.k/ / kNq where qN is the spectral slope. Under these

4 Charged Particle Transport in the Interplanetary Medium

71

assumptions D can be expressed analytically as Jokipii (1971):
D D

0 qN 1
jj .1  2 /;
2

(4.12)

where 0 D 6v=Œ2k .4  qN /.2  qN / and provides the relation between the diffusion
coefficient and the particle’s mean free path parallel to the IMF, k . Values of qN
have been determined from observations in the range 1:3  qN  1:9 with an average
value of qN D 1:63 (Kunow et al. 1991). More details of the standard model and other
equivalent descriptions for D can be found in e.g., Agueda and Vainio (2013).
Once the form of D is fixed, the other main parameter of the transport models
is k . For protons, there is a dependence of the mean free path on the magnetic
rigidity of the particles, R D pc=q, where c is the speed of light. For the standard
model, k / R2Nq , as long as qN < 2 (Hasselmann and Wibberenz 1970).
As is generally done, in the models by Pomoell et al. (2015) used in Chap. 9 and
by Agueda et al. (2008) used in Chap. 10, the lMF is modelled as an Archimedean
spiral. In this case, the radial mean free path of the particles, r is related to k by
r D k cos2 .
In the description above, transport of particles perpendicular to the average
magnetic field is neglected, because in the inner heliosphere (1) particles move much
smaller distances per time unit in the perpendicular direction than in the parallel
direction e.g., Bieber et al. (1995) and (2) in the case of a mobile particle source,
the continuous injection (during days) of shock-accelerated particles has a stronger
contribution in shaping the SEP intensity profiles than cross-field diffusion does.

4.2.3 Diffusive Transport
When the spatial scales are larger than the particle’s mean free path and the
scattering time is small compared to the time scales of the phenomena under study,
the standard diffusion equation can describe the variation of the particle distribution
function. In this assumption, the spatial diffusion tensor, , reflects the effects of the
fluctuations of the magnetic field (Jokipii 1971). In 1965, Parker (1965) was the first
to describe the evolution in space of the cosmic-ray distribution using the following
Fokker-Planck equation:
1
@f
@f
C u  rf  p.r  u/
D r  .  rf / ;
@t
3
@p

(4.13)

This equation describes the effects of spatial diffusion, advection due to the
movement of the scattering centres with the solar wind, and energy changes of
the particles. Equation (4.13) is only valid when the pitch-angle distribution of the
particles is nearly isotropic. This is the assumption made in Chap. 9 to describe
the transport of (quasi)relativistic protons from shocks low in the corona towards

72

A. Aran et al.

the Sun. However, Parker’s equation is not applicable when the anisotropy of the
distribution of particles is large (Jokipii 1987), as generally happens in the case of
SEP events associated with interplanetary shocks e.g., Heras et al. (1995).

4.3 Application: Description of Solar Energetic Particle
Events
The main application of interplanetary transport models is for the description of
SEP events. First, different methods to solve the transport equations and approaches
to perform data fitting are presented. Next, two interplanetary transport models, the
Shock-and-Particle (SaP) model by Pomoell et al. (2015), used in Chap. 9, and the
inversion model by Agueda et al. (2008), used in Chap. 10, are applied to briefly
describe the observations needed for the modelling of SEP events and the derivation
of the main transport parameters.

4.3.1 Numerical Techniques
Different numerical techniques can be applied to solve transport equations. Particularly, the interplanetary transport models used in Chap. 9 (i.e., Lario et al. 1998)
and in Chap. 10 (i.e., Agueda et al. 2008) employ finite-difference and Monte Carlo
methods, respectively. Both have advantages and drawbacks, and therefore there
are models in the literature that utilise either methods or even a combination of the
two. The main advantage of finite-difference methods (e.g., Ruffolo 1995; Lario
et al. 1998; Dröge 2000) is that they are computationally fast, whereas the main
advantage of Monte Carlo methods (e.g., Agueda et al. 2008; Afanasiev and Vainio
2013) is that tracking of individual particles is allowed by them.
Also, numerical models may follow two methods for data fitting: forward and
inversion modelling. Forward models, like SaP (Pomoell et al. 2015), are inductive
and based on the prediction of measurements with a given set of model parameters.
On the other hand, inversion models, like SEPinversion (Agueda et al. 2008, 2012),
are deductive and make use of the measurements to infer the actual values of the
model parameters, and hence, no a priori assumption about the particle injection
profile, Q, is needed.

4.3.2 Observations
SEP events are intensity enhancements above a background level detected typically
for an extended particle energy range. The particle intensities obtained for a
particular energy window are called differential intensities, J, or dJ=dE. Differential

4 Charged Particle Transport in the Interplanetary Medium

73

intensities, with units of [(MeV sr s cm2 )1 ], are related to the particle distribution
function by J D p2 f , where p is the particle’s momentum.
The top panel of Fig. 4.3 shows a gradual SEP event starting on 2000 April 4,
with 0.115–101 MeV proton differential intensity enhancements measured by the
ACE and SOHO spacecraft. The source of this particle event was a travelling CMEdriven shock that originated near to the solar west limb (e.g., Pomoell et al. 2015).
This panel exemplifies the energy dependence of the intensity-time profiles observed
during a single SEP event. Whereas at high energies (>30 MeV) proton intensities
show a rapid onset, a maximum peak intensity, followed by a slow decay with

106

ACE/EPAM/
LEMS120–LEMS30
0.115–0.195 MeV
0.195–0.321 MeV
0.310–0.580 MeV
0.587–1.060 MeV
1.060–1.900 MeV

105

Intensity [p/cm2 s sr Mev)]

104
103

SOHO/ERNE/LED
1.8–2.2 MeV
2.2–2.7 MeV
2.7–3.3 MeV
3.3–4.1 MeV
4.1–5.1 MeV
5.1–6.4 MeV
6.4–8.1 MeV
8.1–10.0 MeV
10.0–13.0 MeV

102
101
100

SOHO/ERNE/HED
14–17 MeV
17–22 MeV
21–28 MeV
26–32 MeV
32–40 MeV
40–51 MeV
51–67 MeV
64–80 MeV
80–101 MeV

10–1
10–2

Vsw

f[°]

q[°] B [nT][km/s]

10–3
10–4
800
600 ACE/SWEPAM
400
50
30 ACE/MAG (RTN)
10
50
0
–50
300
200
100
95.5
96.0

96.5

97.0

97.5

98.0

2000

Fig. 4.3 April 4, 2000 SEP event. Top panel: 0.115–101 MeV proton differential intensities
measured by 23 energy channels (colour coded) of different detectors (ACE/EPAM (Gold et al.
1998) and SOHO/ERNE (Torsti et al. 1995)). The second panel shows the solar wind speed
measured by ACE/SWEPAM (McComas 1998) and the three bottom panels show the magnetic
field strength, latitude and longitude (in RTN coordinates) recorded by ACE/MAG (Smith et al.
1998). The solid vertical line marks the time of the shock passage by the ACE spacecraft and the
arrow marks the onset time of the associated CME

74

A. Aran et al.

intensities being already at background level prior to the shock passage (the vertical
solid line in Fig. 4.3), low energy (<2 MeV) intensities keep increasing with a
marked peak at the shock. The smooth transition of the shape of flux profiles from
high to low proton energies suggests that the efficiency of the shock at accelerating
particles gradually diminishes with energy as it propagates away from the Sun.
Information of the solar wind and IMF is needed in order to perform the
modelling and to know how the assumptions made in the models comply with the
actual conditions. The bottom panels of Fig. 4.3 show smooth profiles for the solar
wind speed and magnetic field strength in the pre-shock region, and variations in
the IMF direction that do not modify significantly the shape of the intensity-time
profiles; hence, the SaP model can be applied to describe this SEP event. First, the
shock propagation is modelled to obtain the position of the particle source, and next
the simulation of the transport of particles up to the observer’s position (in this case,
located at L1) is performed. For this, particles are assumed to be injected by the
shock at the points in the shock front connected with the spacecraft through a Parker
IMF line (i.e., at the cobpoints; Heras et al. 1995). In the SaP model, Eq. (4.11)
is solved with the inclusion of the solar wind effects on the low-energy protons
(Ruffolo 1995; Lario et al. 1998).
From the particle transport models, the evolution of the injection rate, Q and
the proton mean free path, k can be obtained by fitting the observed time profiles
of particle (omnidirectional) intensities1 and of the first order anisotropies (when
available, e.g., Lario et al. 1998) or by fitting directly directional intensities (e.g.,
Agueda et al. 2008). For the April 2000 event, the omnidirectional intensity-time
profiles are simultaneously fitted for eighteen energy channels and the first order
anisotropies for E < 2 MeV, to better constrain the values of the parameters used
(see details in e.g., Pomoell et al. 2015).
The resulting values of k at 9.1 MeV are: 1:30 AU for t < 11:0 h, 0:65 AU for
11:0  t < 15:8 h and 0:33 AU for t 15:8 h, assuming qN D 1:6 for its rigidity
dependence. Figure 4.4 shows the derived evolution of the source function, Q, that
continuously changes from low to high energies. For E > 36:4 MeV, Q decreases
rapidly (two orders of magnitude in 10 h). After this time, the shock, located already
at 80 Rˇ is no longer efficiently injecting >40 MeV protons. For lower energies,
Q continuously decreases, this decrease being slow for lower energies. The use
of a particle transport model (in this case the SaP model) yields the quantitative
description of how the shock is gradually losing efficiency at injecting particles as it
moves away from the Sun and as the magnetic connection with the observer varies.

1

Hereafter ‘intensity’ is used for ‘differential intensity’.

4 Charged Particle Transport in the Interplanetary Medium

75

Fig. 4.4 Evolution of the injection rate of shock-accelerated particles, Q, derived from the
modelling of the SEP event with the SaP model. Each curve, colour coded as indicated in the
inset, corresponds to the injection rate profile derived for each of the eighteen energy channels
modelled and computed from the first cobpoint up to the shock arrival at the ACE spacecraft

4.3.3 Inferring Transport Conditions
An important aspect to consider when inferring the transport conditions is the level
of freedom in performing the fitting of observed intensities. If Q and r values are
derived employing only the omnidirectional intensity profile, for a given energy
channel, the problem is ill-posed. Additional information is needed and can be
extracted from first order anisotropies or from directional intensities. To illustrate
this point the inversion model by Agueda et al. (2008, 2012) is utilised. This model
assumes a fixed source of near-relativistic electrons placed at 2 Rˇ from the Sun.
The middle column of Fig. 4.5 shows an omnidirectional intensity-time profile (red
curve) that is fitted with the model (black curves). In the left column are shown
four different electron injection histories, Q.t/, and values of r resulting from the
fitting. The injection profile and r shown in the first row do not fit the data, as it is
clearly seen in the middle panel; however, the remainder three combinations shown
in the next rows do fit the omnidirectional intensities perfectly; thus, indicating that

76

A. Aran et al.

Fig. 4.5 Example using the inversion model (Agueda et al. 2008) to illustrate the importance
of having directional information of particle intensities. Near-relativistic electron injection history
profiles and r (left column), omnidirectional intensities (middle column) and directional intensities
(right column) are shown for different scenarios. The model fits (black curves) reproduce the
observations (colour curves) only in the second case. See text for details

more information is needed to find the correct solution. In the right panel of Fig. 4.5
the corresponding directional intensities (colour curves) are shown. The model fits
(black curves) only reproduce the directional intensities correctly in the second
case; thus showing that directional intensities are crucial for inferring the correct
parameters. Directional intensities or angular information of the particle distribution
function is not always provided by instrumentation onboard spacecraft. It is usually
available for near-relativistic electrons and low-energy protons, but not for highenergy protons for which measurement statistics are relatively low.

4.4 Concluding Remarks
In this chapter the key basic facts of the interplanetary scenario and of the main
effects to consider when simulating the SEP transport in interplanetary space have
been presented. The interested reader may follow the various references provided to
deepen in the study of SEP transport. In summary, the main messages to take away
are: the average interplanetary magnetic field can be described by an Archimedean
spiral. Superposed on this average spiral field are small-scale random fluctuations.
In the co-rotating frame, the motion of the guiding centre of SEPs travels along

4 Charged Particle Transport in the Interplanetary Medium

77

the mean spiral direction and particles are scattered by small-scale fluctuations
embedded in the solar wind. Interplanetary transport models help to infer the particle
source function of SEP events.

References
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Bittencourt, J.A.: Fundamentals of Plasma Physics, 3rd edn. Springer, New York (2004)
Dröge, W.: Astrophys. J. 537, 1073 (2000). doi: 10.1086/309080
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included in the chapter’s Creative Commons license and your intended use is not permitted by
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Chapter 5

Cosmic Ray Particle Transport in the Earth’s
Magnetosphere
R. Bütikofer

Abstract The transport of the cosmic ray particles in the Earth’s magnetic field
must be considered for cosmic ray investigations based on cosmic ray measurements
in the geomagnetosphere. The motion of charged particles in a magnetic field is
defined by the Lorentz force. The trajectories of cosmic ray particles are curved
by the Earth’s magnetic field. In a first approximation the geomagnetic field can
be described by a dipole magnetic field. For a more accurate description the
geomagnetic magnetic field is divided into two parts: the inner part generated by
an internal dynamo and the outer part induced by different current systems in
the ionosphere and the magnetosphere. Models have been developed that describe
the inner and the outer magnetic field. The computations of the propagation of the
cosmic ray particles in the Earth’s magnetosphere are made with computer programs
based on numerical integration of the equation of motion. For the specification of
geomagnetic effects on cosmic ray particles the concept of cutoff rigidities and of
asymptotic directions have been introduced.

5.1 Introduction
Charged particles moving in a magnetic field are deflected. Investigations of cosmic
ray observations based on ground-based and on space-based detectors inside the
geomagnetosphere require therefore a detailed knowledge of the propagation of the
cosmic ray particles in the Earth’s magnetic field. The conditions under which a
cosmic ray particle has access to a specific point of observation are defined by the
Earth’s magnetic field, the energy of the particle as well as the direction of incidence.
The implementation of the quantity “magnetic rigidity” is useful as particles with
the same rigidity R, charge sign and initial conditions have identical trajectories in a

R. Bütikofer ()
University of Bern, Physikalisches Institut, Sidlerstrasse 5, CH-3012 Bern, Switzerland
High Altitude Research Stations Jungfraujoch and Gornergrat, Sidlerstrasse 5, CH-3012 Bern,
Switzerland
e-mail: rolf.buetikofer@space.unibe.ch
© The Author(s) 2018
O.E. Malandraki, N.B. Crosby (eds.), Solar Particle Radiation Storms Forecasting
and Analysis, The HESPERIA HORIZON 2020 Project and Beyond, Astrophysics
and Space Science Library 444, DOI 10.1007/978-3-319-60051-2_5

79

80

R. Bütikofer

static magnetic field. The rigidity R is defined as R D Zp ce , where p is the momentum,
c is the speed of light and Ze is the charge of the cosmic ray particle. The unit of the
rigidity R is volts. A convenient unit is GV (109 V).
History:
1st cent. AD
13th cent. AD
In early 1890s

1912
1930
1957/58

First known magnetic compass was invented in China
First theories about geomagnetism
Hendrik Lorentz derived the equation that describes the forces
on a charged particle in an electromagnetic field, the so-called
Lorentz force
Discovery of the cosmic ray by the Austrian Victor Hess
First works were started by Störmer to understand the geomagnetic effects on cosmic rays (Störmer 1930)
International Geophysical Year
Systematic investigations of the effects of the Earth’s magnetic
field on the cosmic rays as observed on the ground

For a more detailed historical overview, see e.g. Smart et al. (2000).
The forces that act on moving charged particles in a electromagnetic field and their
effects on the particles’ trajectories are described in Sect. 5.2. The Earth’s magnetic
field, i.e. the inner and the outer part of the Earth’s magnetic field as well as the
models describing these fields, is addressed in Sect. 5.3. In Sect. 5.4 the differential
equations that describe the motion of the charged cosmic ray particles in the Earth’s
magnetic field and their numerical computation are summarised. The concepts
of “cutoff rigidities” and of “asymptotic directions” that have been introduced to
quantify the geomagnetic field effect are described in Sect. 5.5.

5.2 Motion of Charged Particles in a Magnetic Field:
Lorentz Force
The combination of electric and magnetic forces on a charged particle due to
electromagnetic fields is described by the Lorentz force F:
F D Ze E C Ze Œv  B

(5.1)

where
Ze
E
v
B

charge of the moving particle, e is the elementary charge
electric field
velocity of the particle
magnetic field

The effect of electric fields can be neglected in the geomagnetosphere due to its high
electric conductivity.

5 Cosmic Ray Particle Transport in the Earth’s Magnetosphere

81

The force equation becomes:
FDm

dv
D Ze Œv  B
dt

(5.2)

A charged particle is accelerated perpendicularly to the speed v, it follows that the
absolute value of the momentum jm  vj and its kinetic energy are conserved.
For relativistic particles with mass m D  m0 , where  is the Lorentz factor ( D
1
.1  v 2 =c2 / 2 ) and m0 is the rest mass of the particle, it follows:
dv
Ze
D
Œv  B
dt
 m0

(5.3)

For a moving charged particle in a uniform magnetic field, the speed vector v can be
split into a component parallel vk and perpendicular v? to the magnetic field B. The
motion of the particle is then described by a movement with constant speed along
the magnetic field vk and a circular motion around the magnetic field lines.
The centripetal acceleration is
Ze
v? 2
D
 v?  jBj
rc
 m0

(5.4)

where rc is the cyclotron radius or gyroradius.
For the cyclotron radius rc follows:
rc D

 m0  v?
Ze  jBj

(5.5)

The above formula for the cyclotron radius can be rearranged to give a more
practical expression for an estimation of the cosmic ray trajectory characteristic:
rc Œmeter D 3:3 

. m0 c2 ŒGeV/  .v? = c/
.Z  jBj ŒTesla/

(5.6)

where GeV is the unit of Giga-electronVolts.
A proton with kinetic energy Ekin D 10 GeV in the Earth’s magnetic field close
to the Earth where jBj
30;000 nT (Sect. 5.3.1) and v ? B, i.e. v? D 0:99 c, has a
gyroradius in the order of 106 m or 0.15 Earth radii.

5.3 Earth’s Magnetic Field
The geomagnetosphere is the region close to the Earth where the motion of
charged particles is mainly determined by the Earth’s magnetic field. The size,
the shape and the inner structure of the geomagnetosphere is configured by the

82

R. Bütikofer

interaction of the solar wind with the Earth’s magnetic field. The extension of the
geomagnetosphere in space is therefore determined by the equilibrium between
the pressure of the streaming solar wind plasma and the magnetic pressure of the
magnetosphere. The front end of the magnetopause is at a standoff distance of 10–
12 Earth’s radii (Re) from the Earth’s centre during quiescent solar wind conditions.
The magnetotail has a length of at least 100 Re. During times of disturbed solar wind
conditions the characteristics of the geomagnetosphere are changed and are defined
by the solar wind speed, the particle density in the solar wind, the strength and the
direction of the interplanetary magnetic field. In addition, the relative position of the
magnetic dipole inside the Earth defines the characteristics of the geomagnetic field.
In the models of the inner Earth’s magnetic field these effects must be considered.
The magnetosheath, the space between the magnetopause and the bow shock, is
the consequence of the fact that the solar wind can not penetrate the Earth’s magnetic
field because of its high electric conductivity and that therefore the magnetic field of
the solar wind must be swept around the magnetopause. The magnetic field strength
in the magnetosheath may be in the order of a few 10 nT (Kobel and Fluckiger
1994). The geomagnetic field line topology in the geomagnetosphere is illustrated
in Fig. 5.1.

Fig. 5.1 Illustration of the Earth’s magnetic field line topology. From Bütikofer et al. (1995)

5 Cosmic Ray Particle Transport in the Earth’s Magnetosphere

83

Close to the Earth the magnetic field can be described in a first approximation
by a geocentric dipole (Sect. 5.3.1). In a more accurate description the Earth’s
magnetic field is divided into an inner and an outer part. The inner magnetic field is
produced by sources in the interior of the Earth. It is described by the IGRF model
which is based on magnetic field measurements at the Earth’s surface (Sect. 5.3.2).
The external magnetic field is produced by the different electric current systems
in the ionosphere and the inner magnetosphere. There exist different field models
that describe the external Earth’s magnetic field. The models by Tsyganenko—
the models that are mainly used for cosmic ray trajectory computations within the
geomagnetosphere—are presented in Sect. 5.3.4.

5.3.1 The Magnetic Field of the Earth as a Dipole Field
In a first approximation the Earth’s magnetic field can be described by a geocentric
magnetic dipole.
The magnetic moment m of a circular current is:
jmj D I  S

(5.7)

where
I
S

electric current
area that is spanned by the circular current

For the Earth dipole: jmj D 8:1  1022 A m2
The geomagnetic moment is defined as:
MD

0
m
4

(5.8)

where the vacuum permeability 0 D 4  107 Vs = Am
jMj D 8:1  1025 Gauss cm3
D 8:1  1015 V s m
In polar coordinates the components of the magnetic field B.r; ; '/ are:
2 jMj sin 
r3
jMj cos 
B D 
r3
B' D 0
Br D 

(5.9)

84

R. Bütikofer

where
r

'

distance from Earth’s center
geomagnetic latitude
geomagnetic longitude

Magnetic field strength at the geomagnetic equator: B D M
, Br D 0, i.e. at Earth’s
r3
surface (r D 6:4  106 m) B
30;000 nT.
Magnetic field strength at the poles: B D 0, Br D 2rM
3 , i.e. at Earth’s surface
Br
60;000 nT.
The magnetic strength as function of  and r is:
jBj D

jMj p
1
1 C 3 sin 2  3
r3
r

(5.10)

Units:
1 Gauss .G/ D 104 V s=m2 D 104 Tesla .T/
1 Gamma . / D 1 nT

5.3.2 Magnetic Field Model Due to Internal Sources: IGRF
The main geomagnetic field is generated primarily by a hydrodynamic geodynamo
in the Earth’s fluid outer core which varies slowly with time. The geodynamo has
an underlying offset dipolar configuration which is currently tilted at an angle of
about 10ı with respect to the Earth’s rotational axis. The time dependence in the
magnetic field models is usually approached by a sequence of static configurations.
For a static magnetic field the equations of the magnetostatics must be fulfilled as a
special case of the Maxwell’s equations:
r BD0
r  B D 0 j

jW current density

There are no currents to the center of the Earth:
j D 0; i:e: r  B D 0
From this it follows that there exists a potential V, so that
B D r V

5 Cosmic Ray Particle Transport in the Earth’s Magnetosphere

85

Since the magnetic field B is divergence-free (Gauss’s law for magnetism) it follows
for r Re:
r 2 V D 0 or V D 0

.Laplace’s equation/

Assumption for the solution of the Laplace equation: only sources from the Earth’s
interior are considered.
The geomagnetic main field is usually described by spherical harmonics (Chapman and Bartels 1940). Here, the representation of the geomagnetic main field with
spherical harmonics according to the method by Gauss with the Schmidt normalization (Chapman and Bartels 1940) is used. In geographic spherical coordinates
(r; ; ) the corresponding geomagnetic potential V can be expressed:
V.r; ; / D a

n
1 X
X
a
m
m
. /nC1  Pm
n .cos /  fgn cos .m/ C hn sin .m/g (5.11)
r
nD1 mD0

where
a
Pm
n
m
gm
n , hn

mean Earth’s radius, a D 6371:2 km
Schmidt normalized (Chapman and Bartels 1940) associated Legendre
functions of degree n and of order m
Gauss coefficients

As a consequence of the secular variations in the geomagnetic field, the Gauss
coefficients must be determined periodically. The variation of the declination
is 0.13ı/year, the westward drift of the non-dipolar terms has a time period
of 2000 years, and the change in the dipole moment a period of some
1000 years (Merrill and McElhinny 1983). The International Union of Geodesy
and Geophysics (IUGG) and the International Association of Geomagnetism and
Aeronomy (IAGA) determine from measurements of the magnetic field B on the
m
ground and publish every 5 years the Gauss coefficients gm
n and hn (Thébault et al.
2015). Before the year 2000, the parameters until degree n D m D 10 were
determined and since the year 2000 until degree n D m D 13, see https://www.
ngdc.noaa.gov/IAGA/vmod/igrf.html.
The components of B.r; ; / in spherical coordinates are:
@V.r; ; /
@r
1 @V.r; ; /
B„ .r; ; / D 
r
@
1 @V.r; ; /
Bffi .r; ; / D 
r sin
@ˆ
Br .r; ; / D 

(5.12)

86

R. Bütikofer

where
r

ƒ


distance from Earth’s center
geographic co-latitude,  D 90ı  ƒ
geographic latitude
geographic length

The strength of the magnetic field at the Earth’s surface ranges from less than
30,000 nT or 0.3 Gauss in South America (South Atlantic Anomaly) to over
60,000 nT around the magnetic poles (northern Canada, Siberia and coast of
Antarctica, south of Australia). For comparison, the strength of the interplanetary
magnetic field near Earth is typically 5 nT, i.e. the Earth’s magnetic field at the
Earth surface is about four orders of magnitude larger.

5.3.3 Contributions to the Earth’s Magnetic Field by
Magnetospheric Electric Currents
In addition to the internal sources of the Earth’s magnetic field, there is also a
contribution of external origin: the electrical current systems in the ionosphere
and the magnetosphere. Figure 5.2 shows a schematic view of the different current

Fig. 5.2 Schematic view of the different current systems which contribute to the Earth’s magnetic
field.
(From Stern 1994, reproduced with permission from publisher John Wiley and Sons for electronic
and press publishing, license number: 4118701268653, license date: May 30, 2017)

5 Cosmic Ray Particle Transport in the Earth’s Magnetosphere

87

systems in the magnetosphere of the Earth. These current systems may vary rapidly,
depending on the solar activity. During quiet periods the amplitudes of these external
contributions are 20 nT at mid-latitudes and may increase to more than the tenfold during geomagnetic storms. The most important current systems are: the ring
current in the radiation belts, the Chapman-Ferraro current on the magnetopause
(magnetopause current), the field aligned (Birkeland) currents along geomagnetic
field lines connecting the Earth’s magnetosphere to the Earth’s high latitude
ionosphere, and the tail currents in the tail of the magnetosphere. The intensities of
these currents reach millions of amperes and are related to the solar activity. During
times of low solar activity, the standoff distance of the magnetopause currents is at
10.5 Earth radii and the generated magnetic field close to the Earth is 25 nT. The
ring current, i.e. the longitudinal drift of energetic (10–200 keV) particles that are
bouncing along the magnetic field lines between North and South polar regions, has
a radius of 6 RE during quiet times and its contribution to the magnetic field at the
Earth is about 40 nT.

5.3.4 Magnetic Field Models of the External Sources
Since the 1970s efforts were made to improve the quantitative quality of the
magnetospheric magnetic field models, see e.g. the review paper by Walker (1979).
Most of the models include currents in the inner magnetosphere in addition to the
boundary currents and the magnetotail current system. All the models include the
tilt angle of the internal magnetic dipole as an input parameter. With the advent of
the space era it became possible to extend the models from low to high altitudes,
eventually including even the entire magnetosphere. However, the modeling of the
magnetic field in that region is much more difficult, mostly because the magnetic
field from external sources (currents in the geomagnetosphere) predominates the
magnetic field with growing distance from the Earth. Vector measurements of
the magnetic field should be made throughout the entire space where the field should
be modeled, i.e. it is necessary to accumulate large amounts of space magnetometer
data taken in a wide range of the geomagnetosphere. In contrast to the main
geomagnetic field (variations on a timescale of thousands of years), the magnetic
field in the outer regions of the geomagnetosphere is a very dynamical system on
short time scales and depends on different factors. The first factor is the orientation
of the Earth’s magnetic axis with respect to the direction of the incoming solar
wind flow, which varies with time because of the Earth’s diurnal rotation and its
yearly orbital motion around the Sun, and the frequent variations of the solar wind
characteristics. Another important factor is the state of the solar wind, in particular,
the orientation and strength of the interplanetary magnetic field. The interaction
between the terrestrial and the interplanetary magnetic fields becomes strongly
effective when the interplanetary magnetic field is antiparallel to the Earth’s field
on the dayside boundary of the magnetosphere. In this case, the geomagnetic and
the interplanetary field lines connect across the magnetospheric boundary, which

88

R. Bütikofer

strongly enhances the transfer of the solar wind mass, energy, and electric field
inside the magnetosphere.
Different models have been developed to describe the magnetic field in the whole
geomagnetosphere (Mead and Fairfield 1975; Olson and Pfitzer 1988; Tsyganenko
1987, 1989, 1996; Ostapenko and Maltsev 1997; Tsyganenko 2002a,b; Tsyganenko
and Sitnov 2005). For the determination of cosmic ray particle trajectories mainly
the magnetic field models by Tsyganenko (1989, 1996, 2002a,b), Ostapenko and
Maltsev (1997) and Tsyganenko and Sitnov (2005) are used.
The Tsyganenko models are semi-empirical best-fit representations for the
magnetic field, based on a large number of satellite observations (IMP, HEOS,
ISEE, POLAR, Geotail, etc.). The models include the contributions from external
magnetospheric sources: ring current, magnetotail current system, magnetopause
currents and large-scale system of field-aligned currents.
Tsyganenko model T89 (Tsyganenko 1989) was primarily developed as a tail
model. It is based on satellite measurements at distances from the Earth less
than 70 RE , therefore its domain of validity is limited to this region in space.
It provides seven different states of the geomagnetosphere corresponding to
different levels of the geomagnetic activity represented by the Kp-index1 0, 1, . . . ,
6. The model does not consider the continuous variation of the structure of the
magnetosphere as a function of geomagnetic indices like Dst and of solar wind
parameters. The consideration of these parameters to describe the evolution of the
magnetosphere is in particular important during a magnetic storm. Therefore the
use of T89 is not reasonable during times when the geomagnetic field is strongly
disturbed.
Tsyganenko model T96 (Tsyganenko 1996) considers in contrast to the T89
model the continuous variation of the structure of the magnetosphere as a
function of the geomagnetic indices like Dst and of the solar wind parameters. In
this model the external magnetospheric magnetic field is generated by different
current systems where the shape and the strength depend on the dipole tilt angle,
on the solar wind dynamic pressure, on the Dst index and on the interplanetary
magnetic field components BGSM
and BGSM
in geocentric solar magnetospheric
y
z
coordinates (GSM). This model has an explicitly defined realistic magnetopause
which is represented by a semi ellipsoid of rotation towards the Sun and by a
cylindrical surface in the far tail for xGSM  60RE .
Tsyganenko model T01 (Tsyganenko 2002a,b) is based on the same principles
as the model T96 but has essential improvements. The T01 model considers
the variable configuration of the inner and near magnetosphere for different
interplanetary conditions and ground disturbance levels.

1

The Kp-index is a quasi-logarithmic quantity for the variation of the magnetic field intensity at
the Earth’s surface as function of time. The range of the Kp-index is 0ı (for quite conditions) over
0C; 1; 1C to 9ı (for extreme disturbed magnetic field (geomagnetic storm)). It is derived from
the maximum fluctuations of the horizontal components of the Earth’s magnetic field observed by
observation stations around the world and is published every 3 h.

5 Cosmic Ray Particle Transport in the Earth’s Magnetosphere

89

Tsyganenko model T04 (Tsyganenko and Sitnov 2005) is a dynamical model of
the storm-time geomagnetic field in the inner magnetosphere, using space
magnetometer data taken during 37 major events in 1996–2000 and concurrent
observations of the solar wind and the interplanetary magnetic field. Therefore,
this model is only applicable for times with strong disturbances of the geomagnetic field.
The Tsyganenko model T89 is usually used to compute cosmic ray trajectories in
the geomagnetosphere due to the much simpler utilisation with only a few input
parameters (date, time, Kp-index) and the much less time-consuming computation
effort compared to the other Tsyganenko models.
The magnetic field of the magnetosheath is usually not considered in the
computation of cosmic ray particle trajectories, although the change in the direction
of approach at the border of the geomagnetosphere due to the effect of the
magnetosheath may be a few 10ı at low rigidities (R  1GV) (Bütikofer et al. 1997).

5.4 Computation of the Propagation of Cosmic Ray Particles
in the Earth’s Magnetosphere
There exists no solution of the equation of motion of a charged particle in the
geomagnetosphere magnetic field in a closed form. Therefore the determination
of cosmic ray trajectories in the geomagnetosphere is almost exclusively made by
numerical integration on computer by using a model of the magnetic field in the
geomagnetosphere. The cosmic ray particle trajectories are computed backward,
i.e. starting at the location of observation and compute the trajectory away from the
Earth. Thereby the effect is used that the path of a negatively charged particle with
mass, m, charge, Ze, and speed, v, in a static magnetic field, B, is identical to that of
an identical but positively charged particle with reverse sign of the velocity vector.
For observation locations at ground the computations start at an altitude of typically
20 km above sea level as the interactions of primary cosmic ray particles with atoms
and atomic nuclei in the atmosphere become important below this altitude (Smart
et al. 2000).
The equations of motion of charged particles in a known magnetic field B.r; ; /
in a spherical coordinate system (r; ; ) are:
v2
v2
dvr
Ze
D
.v B  v B / C  C
dt
m
r
r
v2
dv
Ze
vr v
D
.v Br  vr B / 
C
dt
m
r
r tan 
v v
vr v
dv
Ze
D
.vr B  v Br / 

dt
m
r
r tan 

(5.13)

90

R. Bütikofer

dr
D vr
dt
v
d
D
dt
r
v
d
D
dt
r sin 
where Br ; B ; B are the known magnetic field components, vr ; v ; v are the
particle velocity components, c is the speed of light, Ze and m are respectively
the charge and the mass of the particle, and r is the radial distance of the location of
the particle from the center of the Earth.
The statement of the problem of the particle trajectory computation belongs to
the category of initial value problems. They start at a selected time t0 and with a
set of known variables r0 , 0 , 0 , vr0 , v0 , v0 . From this set of initial values the
corresponding values after a short time interval t, i.e. at time t0 C t, can be
computed.
There exist different types of numerical methods to solve the initial value problems e.g. Runge–Kutta or Bulirsch-Stoer method (Press et al. 1986). These methods
optimize in different ways the step size of the numerical integration, i.e. the interval
size t, on the one hand to prevent that the error per step exceeds a preset maximum
value and on the other hand to reduce the computation time. Different computer
codes for the cosmic ray trajectory computations in the Earth’s magnetic field
have been developed (see e.g. Shea and Smart 1975; Flueckiger and Kobel 1990;
Desorgher et al. 2006).
Figure 5.3 shows an illustration of charged particle trajectories with different
rigidities entering the Earth at the same location from zenith direction. The cosmic

Fig. 5.3 Charged particle trajectories with different rigidities in the Earth’s magnetic field.
(From Smart et al. 2000, reproduced with permission from publisher Springer for electronic and
press publishing, license number: 4118710609018, license date: May 30, 2017)

5 Cosmic Ray Particle Transport in the Earth’s Magnetosphere

91

ray particle trajectories labeled 1–3 have high rigidities and are therefore less bent
compared to the trajectories labeled with values >3. The trajectories 4 and 5 show
loops, but both can escape the geomagnetosphere, i.e. cosmic ray particles with
these rigidities can reach the specified location on Earth from zenith direction
(“allowed trajectories”). Particles with even lower rigidities are more bent and
the trajectories of these particles penetrate the Earth (re-entrant trajectories), i.e.
particles with these rigidities can not reach the location of observation from zenith
direction from outside of the geomagnetosphere (“forbidden trajectories”).

5.5 The Concept of Cutoff Rigidities and Asymptotic
Directions
The “cutoff rigidities” and the “asymptotic directions” have been introduced to
specify the geomagnetic effects on cosmic ray particles and to determine the cosmic
ray particle spectral characteristics and the anisotropy near Earth but outside the
geomagnetosphere from cosmic ray measurements at ground (neutron monitors,
muon detectors) or by space based detectors within the geomagnetosphere.
The cutoff rigidity at a selected location and with a specific direction of incidence
is defined as the rigidity below which the cosmic ray particles have no access to this
location from the given direction of incidence, i.e. trajectories with rigidities larger
than the cutoff are “allowed trajectories” whereas trajectories with rigidities below
the cutoff rigidity are “forbidden trajectories”. The asymptotic direction of cosmic
ray particles is used as the particle’s trajectory direction of approach at the boundary
of the geomagnetosphere.
The cutoff rigidities are determined by trajectory calculations at discrete rigidity
intervals starting from a value above the highest possible cutoff rigidity down below
the lowest possible allowed trajectory. The trajectories over this rigidity range
show different features: first discontinuity in asymptotic direction, first forbidden
trajectory, then usually a range of allowed and forbidden trajectories (co-called
cosmic ray penumbra), lowest allowed trajectory.
The following parameters are used to describe the cutoff rigidity (Cooke et al.
1991):
• main cutoff rigidity RM or upper cutoff Ru : rigidity of the last allowed trajectory
before the first forbidden. This cutoff rigidity is close to the first discontinuity
rigidity R1 , RM
R1
• Störmer cutoff RS or lower cutoff Rl : rigidity of the last allowed trajectory, i.e.
trajectories of particles with rigidities < RS are forbidden
• Rc : effective cutoff rigidity which is between Ru and Rl taking into account the
penumbra, see Eq. (5.15).

92

R. Bütikofer

Fig. 5.4 Function ˛.R/ for the station Jungfraujoch for vertical direction of incidence and
corresponding cutoff rigidity values: RS (Störmer cutoff), RM (main cutoff), and R1 (firstdiscontinuity rigidity)

For a location of observation and for a selected direction of incidence the effect of
the Earth’s magnetic field on the accessibility of cosmic ray particles is described
by the filter function ˛.R/:

˛.R/ D

0
1

W if trajectory is forbidden for rigidity R
W if trajectory is allowed for R

(5.14)

Figure 5.4 shows the function ˛.R/ for the station Jungfraujoch for vertical direction
of incidence.
The effective cutoff rigidity Rc is given by
Z
Rc D RS C

RM

˛.R/dR

(5.15)

RS

The effective geomagnetic cutoff rigidity Rc depends on the location of the
observer, the direction of incidence into the atmosphere, the date and time, and
the degree of disturbance of the geomagnetic field. The cutoff rigidities for groundbased cosmic ray stations and for vertical incidence range from Rc
0 GV at the
magnetic poles to Rc
15 GV at the geomagnetic equator.
If one follows the cosmic ray particle’s trajectory away from the Earth, the
amount of bending per path length caused by the magnetic field is decreasing, i.e. the
direction of the particle’s trajectory approaches asymptotically its direction with no
magnetic field. In the field of cosmic rays the expression asymptotic direction is used
for the direction of the cosmic ray particle trajectory when it penetrates the border
of the geomagnetosphere (magnetopause). The asymptotic direction of a cosmic ray
particle that reaches the location of observation from a selected direction depends on
the geographic coordinates of the observer and of the cosmic ray particle’s rigidity.
Figure 5.5 shows the trajectory of a cosmic ray particle reaching a location on the
Earth from a selected direction and its puncture through the magnetopause. The
arrow gives the direction of the trajectory at the puncture: the asymptotic direction.

5 Cosmic Ray Particle Transport in the Earth’s Magnetosphere

93

Fig. 5.5 Illustration of a cosmic ray particle’s trajectory through the geomagnetosphere reaching
a selected location on the Earth from a selected direction and of its related direction of approach at
the magnetopause (asymptotic direction)

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ray particle propagation in near-Earth space. Int. Cosmic Ray Conf. 4, 1070 (1995)
Bütikofer, R., Flückiger, E.O., Smart, D.F., Shea, M.A.: Effects of the magnetosheath magnetic
field on cosmic ray propagation near Earth. Int. Cosmic Ray Conf. 2, 377 (1997)
Chapman, S., Bartels, J.: Geomagnetism. Oxford University Press, Oxford (1940)
Cooke, D.J., Humble, J.E., Shea, M.A., Smart, D.F., Lund, N.: On cosmic-ray cut-off terminology.
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Desorgher, L., Flückiger, E.O., Gurtner, M.: The PLANETOCOSMICS Geant4 application. In:
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Flueckiger, E.O., Kobel, E.: Aspects of combining models of the earth’s internal and external
magnetic field. J. Geomag. Geoelectr. 42, 1123–1136 (1990)
Kobel, E., Fluckiger, E.O.: A model of the steady state magnetic field in the magnetosheath. J.
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Mead, G.D., Fairfield, D.H.: A quantitative magnetospheric model derived from spacecraft
magnetometer data. J. Geophys. Res. 80, 523–534 (1975)
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Perspective. International Geophysical Services, vol. 32. Academic Press, New York (1983)
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Ostapenko, A.A., Maltsev, Y.P.: Relation of the magnetic field in the magnetosphere to the
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Saturnino, D., Schachtschneider, R., Sirol, O., Tangborn, A., Thomson, A., Tøffner-Clausen,
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Chapter 6

Ground-Based Measurements of Energetic
Particles by Neutron Monitors
R. Bütikofer

Abstract Since the International Geophysical Year (IGY) in 1957/58, the worldwide network of neutron monitors is the standard instrument to investigate the
variations of the cosmic ray flux near Earth (11-year modulation of the galactic
cosmic rays, Forbush decreases, solar cosmic ray events) in the GeV range.
The ensemble of neutron monitors together with the geomagnetic field acts as a
giant spectrometer and enables to deduce information about the primary cosmic
ray spectrum near Earth in the energy range 500 MeV to 15 GeV. For the
interpretation of the ground-based neutron monitor measurements, the transport of
the cosmic rays in the Earth’s magnetic field as well as the transport in the Earth’s
atmosphere and the detection efficiency of the secondary nucleons by the neutron
monitors must be known. The Neutron Monitor Data Base (NMDB) developed in
2008/09 enables a rapid accessibility to the data of the worldwide neutron monitor
network. A considerable number of neutron monitor stations send their data to
NMDB in real-time which enables the operation of space weather applications based
on neutron monitor data.

6.1 Introduction
The ground-based neutron monitors are relatively simple instruments in respect to
technology and electronics. They are ideally suited to measure the intensity of the
nucleonic component of the secondary cosmic radiation in the Earth’s atmosphere
and respond to primary cosmic ray particles in the GeV-range. Even after 60
years of operation the neutron monitors remain the state-of-the-art instrument for
measuring the intensity variations of the primary cosmic rays in the energy range
from 500 MeV to 30 GeV. This energy region complements the range above the
energies covered by space-based cosmic ray detectors. The worldwide network of
R. Bütikofer ()
University of Bern, Physikalisches Institut, Sidlerstrasse 5, CH-3012 Bern, Switzerland
High Altitude Research Stations Jungfraujoch and Gornergrat, Sidlerstrasse 5, CH-3012 Bern,
Switzerland
e-mail: rolf.buetikofer@space.unibe.ch
© The Author(s) 2018
O.E. Malandraki, N.B. Crosby (eds.), Solar Particle Radiation Storms Forecasting
and Analysis, The HESPERIA HORIZON 2020 Project and Beyond, Astrophysics
and Space Science Library 444, DOI 10.1007/978-3-319-60051-2_6

95

96

R. Bütikofer

neutron monitors is an excellent tool to investigate variations of the primary cosmic
ray flux near Earth such as 11-year modulation and the sudden transient effects as
Forbush decreases1 and solar cosmic ray events. Since recently, neutron monitor
measurements are also an important input for space weather applications.
In the International Geophysical Year 1957/58 the worldwide network of standardised neutron monitors was developed to investigate the variations of the cosmic
ray intensity near Earth. There are two types of standardised neutron monitors
in operation. The IGY (for International Geophysical Year) type was designed
by Simpson (1955) in the early 1950s. About 10 years later Carmichael (1968)
designed the larger NM64 monitor with an increased counting rate. Figure 6.1 shows
the 18-IGY neutron monitor at Jungfraujoch, Switzerland (left) and the 6-NM64
monitor of Athens, Greece (right). The digits 18 respectively 6 give the number of
the counter tubes deployed in the respective neutron monitor.
The ensemble of neutron monitors together with the geomagnetic field acts as
a giant spectrometer and enables the determination of the spectral variations of the
galactic cosmic rays near Earth and the spectral characteristics of the sporadic solar
cosmic rays. In addition, the simultaneous detection of relativistic particles with the
entire global network of neutron monitors provides information about the anisotropy
of the cosmic ray flux near Earth as the viewing directions of each neutron monitor
station at the border of the geomagnetosphere depends on the neutron monitor’s
location, on the cosmic ray particle’s rigidity, and on the direction of incidence
above the neutron monitor station.
To deduce the variation of the primary cosmic rays near Earth but outside the
geomagnetosphere from neutron monitor measurements, the relationship between
the neutron monitor count rate and the primary cosmic ray flux must be known.

Fig. 6.1 18-IGY neutron monitor Jungfraujoch, Switzerland, (left) and 6-NM64 neutron monitor
Athens, Greece (right). The digits 18 respectively 6 give the number of the counter tubes of the
corresponding neutron monitor station

1

Decrease within hours in the galactic cosmic ray intensity near Earth caused by the passage of
a coronal mass ejection (CME) and slow recovery within days, named after the American cosmic
ray physicist Scott E. Forbush.

6 Ground-Based Measurements of Energetic Particles by Neutron Monitors

97

When primary cosmic ray particles approach the Earth, they enter first the geomagnetosphere, where the cosmic ray particles are deviated by the Earth’s magnetic field
(Lorentz force) and then penetrate into the Earth’s atmosphere, where the cosmic ray
particles make electromagnetic interactions with the atoms and molecules as well
as hadronic processes with the nuclei of the atmospheric constituents. A cascade of
various secondary particles is produced.
In Sect. 6.2 a short overview of the history of the neutron monitors is given. The
transport of cosmic rays in the Earth’s magnetic field is described in more detail
in Chap. 5. The transport of cosmic ray particles through the Earth’s atmosphere is
addressed in Sect. 6.3. The neutron monitor, i.e. its structure, layout, the functions
of the different parts of the detector, the response of the neutron monitor to primary
cosmic rays, and environmental effects on the measurements are described in
Sect. 6.4. As a single neutron monitor does not give information about the energy
spectrum and the direction of the flux of the primary cosmic rays, a network of
neutron monitors at different latitudes and longitudes is needed to retrieve this
information. Today this network contains about 50 operating stations. Section 6.5
gives an overview about the worldwide network of neutron monitor stations. The
neutron monitor database NMDB initiated in 2008/09 as an European FP7 project
is presented in Sect. 6.6.

6.2 History
After the discovery of the cosmic rays in 1912 by Victor Hess, mainly ionisation
chambers on ground were used to investigate the variations of the cosmic ray
intensities. The basic ideas for the development of neutron monitors as a continuous
recorder of the cosmic ray intensity originated from the measurements by Simpson
(1948). He found that the latitude dependences of the intensities of the energetic
nucleonic component and of the evaporation neutrons from the secondary cosmic
rays in the atmosphere are several times larger than those of the ionising component
(ionisation chambers) and the hard component (muon counters). In addition, the
measurement of the nucleonic component allows to study the time variations of the
primary cosmic rays at lower energies than this is possible with ionisation chambers
or muon counters. These facts stimulated the development of new detectors that
measure the secondary neutrons in the atmosphere.
The neutron monitor designed by Simpson (1955) was adopted as the standard
detector during the International Geophysical Year (IGY) 1957/58 and was called
IGY neutron monitor. It became evident soon that better statistical accuracy was
required, in particular for the study of short-term events as e.g. solar cosmic ray
events, so-called GLEs (Ground Level Enhancements or Ground Level Events). In
1959 large sized proportional counter tubes were constructed and produced at the
Chalk River Nuclear Laboratories, Ontario, Canada. This led to the design and the
construction of the supermonitor or NM64 monitor for the International Quiet Sun
Year (IQSY) (Carmichael 1968). The counting rate of the NM64 monitor per unit

98

R. Bütikofer

area of lead producer is about three times that of the IGY neutron monitor. Today
mainly NM64 monitors are in operation.
The different neutron monitor stations are mostly operated by research institutions that are located near the stations. For the data exchange in the days of the
advent of neutron monitors the operators of the stations sent their hourly data in the
form of tables on paper by mail to the World Data Centers (WDCs) (Pyle 2000),
later on magnetic tapes and afterward on floppy disks. With the internet the data
exchange became much easier.

6.3 Transport of Cosmic Ray Particles in the Earth’s
Atmosphere
Primary cosmic ray particles that penetrate the atmosphere undergo multiple
interactions resulting in showers of secondary particles. If the secondary nucleons
(neutrons or protons) reach the ground, they can be detected by neutron monitors.
To deduce the cosmic ray characteristics at the top of the atmosphere from
neutron monitor measurements, the transport in the atmosphere, i.e. the interactions
of energetic particles with matter, and the detection efficiency of the neutron monitor
must be known. The physics of the interactions in the atmosphere when cosmic
ray particles enter the atmosphere are today usually simulated with Monte Carlo
methods.
The Earth’s atmosphere, i.e. the medium in which the interactions take place, is
described by a model (Sect. 6.3.1). The essential nuclear interactions of the cosmic
ray particles when entering into the atmosphere, which are relevant for ground-based
neutron monitor measurements, are addressed in Sect. 6.3.2.

6.3.1 Model of the Earth’s Atmosphere
There exist several models that describe the properties (pressure, temperature,
density, chemical composition) of the Earth’s atmosphere primarily as a function of altitude (US Standard Atmosphere, International Standard Atmosphere,
NRLMSISE-00).
Within the Geant4 (Agostinelli et al. 2003) software PLANETOCOSMICS (Desorgher et al. 2006), which is often used to simulate the transport of cosmic ray
particles in the atmosphere, it is possible to select between the MSISE-90 model
and its upgraded version NRLMSISE-00 (Labitzke et al. 1985; Hedin 1991; Picone
et al. 2002). MSIS stands for Mass Spectrometer and Incoherent Scatter Radar,
E indicates that the model extends from the ground through the exosphere and
the number at the end of the short name is the year of release. NRL stands for
the US Naval Research Laboratory. Both models provide temperature, density and

6 Ground-Based Measurements of Energetic Particles by Neutron Monitors

99

concentration profiles vs. altitude from the ground to the exobase (450–500 km) as
function of geographic latitude, longitude, date and time in UT, F10:7 index (10.7 cm
solar radio flux used as solar UV proxy ), F10:7A index (3 month average of F10:7 )
and the geomagnetic index Ap. The dependence of the model on F10:7 , F10:7A , and
Ap is neglectable below 80 km. The Earth’s atmosphere is divided into superposed
homogeneous layers above a solid Earth. The density and composition of the layers
are computed according to the altitude or atmospheric depth from the atmospheric
model and are constant throughout each layer. The thickness of the layers may be
selected by the user. The models may take different geometries: flat or concentric
spherical geometry. In the case of the spherical geometry the Earth is modeled by a
sphere of 6371.2 km radius and overlying curved layers.

6.3.2 Particle Cascade in the Atmosphere
When primary cosmic ray particles enter the Earth’s atmosphere, they make
electromagnetic interactions with the atoms and molecules of the atmospheric gases
and hadronic interactions with the nuclei of the atmospheric matter. Thereby the
cosmic ray particles rapidly loose energy and produce various secondary particles.
The mean free path for nuclear interactions of a cosmic ray particle (proton) with
nitrogen or oxygen nucleus is 75 g/cm2 .
For the interpretation of neutron monitor measurements the nucleonic or hadron
component in the atmosphere is relevant. The products of the nucleonic interactions
are secondary nucleons and pions ( C ,   , and  0 ). The secondary protons lose
their energy mainly by ionisation. When the secondary nucleons have sufficient
energy, they continue to multiply in successive generations of nuclear collisions
until the energy of the particles drops below the energy that is required for multiple
pion production, i.e. about 1 GeV. Secondary protons and ions with energies
100 MeV no longer undergo hadronic interactions, they are rapidly decelerated
to rest by ionisation. On the other hand the neutrons still make nuclear interactions
at these energies as well as elastic collisions with nuclei in the atmosphere. Below
10 MeV the neutrons lose their energy continuously by elastic collisions with
atmospheric nuclei before they are captured by nucleons at thermal energies.
The neutral pions  0 have a very short mean lifetime
D 1:78  1016 s. The  0
decays immediately into two  -rays which initiate an electromagnetic cascade. The
charged pions  C and   decay into muons  C ! C C  and   !  C  
with a mean lifetime of 2:55  108 s. The muons are slowed down mainly by
ionisation. The low energy muons have time to decay (
D 2:2 106 s) before they
reach the ground. The reactions are C ! eC C e C   and  ! e C  e C  .
However, many of the muons are produced with very high energies in the uppermost
layers of the atmosphere and as these muons loose only little energy they have a
large path length and survive (time dilatation according to the theory of relativity)
and reach the surface of the Earth. The muons deep in the atmosphere and at sea level

100

R. Bütikofer

are the most dominant component of the secondary cosmic rays and are therefore
the dominant source of ionisation in this altitude range.
The primary particles at the top of the atmosphere must have an energy of roughly
500 MeV per nucleon to produce a cascade of secondary nucleons that can reach
the ground at sea level. In high latitude regions, where the shielding effect of the
Earth’s magnetic field for incident cosmic rays is low, the lower threshold of the
neutron monitor response is controlled therefore by the atmospheric mass which
is 1030 g cm2 at sea level. For high latitude neutron monitors at sea level this
atmospheric cutoff for primary cosmic rays is 450 MeV/nucleon. In regions like
Central Antarctica, at an elevation of 3 km above sea level (asl), the reduced
atmospheric mass lowers the threshold to 300 MeV/nucleon (Mishev et al. 2014).

6.4 Neutron Monitor Detector
Neutron monitors cover the energy range of primary cosmic ray particles from
0.5 to &100 GeV per nucleon. This energy range includes the solar modulation
of the galactic cosmic rays, Forbush decreases, sporadic GLEs or relativistic SEP
(Solar Energetic Particle) events, and geomagnetic effects. The longterm stability of
neutron monitors is generally excellent so that the cosmic ray effects of the 11-year
solar activity cycle can be investigated over several solar cycles. The longest time
series of single neutron monitor stations are available over a period of 60 years,
i.e. during a time range over more than five solar activity cycles. The comparison
of the measurements of different neutron monitor stations have however shown that
some neutron monitors may show a degrading of the detector efficiency (Bieber
et al. 2007).
As the name suggests, neutron monitors record predominantly the secondary
neutrons from the atmospheric cascades. The contribution to the total neutron
monitor counting rate of an NM64 are neutrons 85%, protons 7%, s 6%,
s 1% (Hatton 1971).
The functionality, construction and other properties of a neutron monitor are
described in Sect. 6.4.1. The response of the neutron monitor to primary cosmic
ray particles at the top of the Earth’s atmosphere is explained in Sect. 6.4.2. The
influence of the atmospheric effects on the neutron monitor measurements are
addressed in Sect. 6.4.3.

6.4.1 Components of a Neutron Monitor
Both neutron monitor types IGY (Simpson 1955) and NM64 (Carmichael 1964)
employ the same measurement strategy, i.e. the difference in the way high and
low energy neutrons interact with different nuclei. As a particle with no electric
charge, the neutron makes only interactions with nuclei and can therefore penetrate

6 Ground-Based Measurements of Energetic Particles by Neutron Monitors

101

large layers of material without interactions because of the small range of the strong
nuclear force. Energetic neutrons can make three different kinds of interactions with
nuclei: elastic and inelastic collisions as well as nuclear reactions. After a hadronic
interaction of an energetic neutron with a nucleus, the excited target nucleus emits
so-called evaporation neutrons. The production of these evaporation neutrons is
proportional to A2=3 according to the nuclear physics theory, where A is the atomic
weight of the target nucleus. In a material containing nuclei with low atomic mass,
the neutrons are effectively slowed down (moderated) in elastic collisions.
These facts led Simpson to the neutron monitor detector concept: production of
fast neutrons in a target with high atomic weight, braking of the fast neutrons in
a hydrogenous material, and finally detection of the thermic neutrons indirectly by
ionising particles that are produced in a neutron induced nuclear reaction.
Figure 6.2 shows a schematic diagram of the NM64 neutron monitor. A standard
NM64 neutron monitor with six counter tubes (6-NM64) has the following dimensions: width: 315 cm, depth: 220 cm, and height: 50 cm. The lead producer
with 9650 kg is by weight the major component of an 6-NM64 monitor.
The different components of a neutron monitor detector are described in
the following. The given specifications are valid for the NM64 neutron monitor (Carmichael 1964):
Reflector The whole assembly of the detector is enclosed by polyethylene (protonrich material) of an average thickness of 7.5 cm. The task of the reflector is to reflect
and to moderate the evaporation neutrons that are produced in the lead producer.
The polyethylene (moderator material) contains a significant fraction of hydrogen,
i.e. the energy loss per elastic collision of a neutron with the moderator material
is maximal as the mass of the projectile and of the hydrogen nuclei in the target
material are almost equal (conservation of momentum and energy). The neutron
elastic interaction pathlength with hydrogen in polyethylene is roughly 1 cm for

Fig. 6.2 Schematic view of a 6-NM64 neutron monitor

102

R. Bütikofer

neutrons with energies 1 MeV and in each collision the incident neutron reduces
its kinetic energy on average by a factor of 2, i.e. the evaporation neutrons are very
effectively slowed down in the reflector.
In addition, this neutron monitor component has the function to reflect and
to absorb the low energy neutrons that are produced by high energy nucleons in
interactions with the ambient material of the neutron monitor, e.g. detector housing.
In contrast, this reflector is largely transparent to the energetic neutrons that are
produced in the cosmic ray induced cascade in the atmosphere, i.e. these energetic
neutrons can easily reach and enter the lead producer.
Producer The core of the neutron monitor consists of a lead producer, a target
with high atomic mass (A), to produce secondary neutrons. The average depth of
13.8 cm (156 g/cm2 ) corresponds to about 75% of the inelastic mean-free path of
nucleons in lead. Thus 50% of the nucleons, that cross the reflector and enter the
lead, make at least one interaction in the producer. The production rate of neutrons
per inelastic nucleon-nucleus interaction is roughly proportional to A0:7 in the energy
range 100–700 MeV of the interacting nucleon and slowly decreases with increasing
energy (Shen 1968). The average number of produced neutrons (multiplicity)
depends weakly on the incident nucleon energy, i.e. a neutron monitor can be
used as an energy spectrometer by measuring the multiplicity only limited. On
average about 15 evaporation neutrons with mean energy 2.5 MeV are produced
per nuclear reaction (Hatton 1971). These neutrons amplify the cosmic ray signal
and can not easily escape the reflector. The lead producer is interspersed with a
moderator and the BF3 proportional counter tubes.
Moderator Each counter tube is surrounded by a polyethylene tube with a
thickness of 2 cm acting as a moderator for the evaporation neutrons that are
generated in the lead producer.
Proportional Counter The proportional counter tubes are filled with BF3 (boron
trifluoride) as counter gas. The BF3 has been 90% enriched with the 10 B isotope.
When the very slow neutrons (thermal neutrons, E D 32 k T D 0.04 eV) encounter
a 10 B5 nucleus in the proportional counter, the following favoured reaction may take
place:
10

B5

C

n

!

7

Li3

C

˛

(6.1)

The cross-section for this reaction is inversely proportional to the neutron speed and
has a value of about 3:0  1025m2 or 3000 barns at neutron energy 0.04 eV and only
roughly 0.2 barns at 1 MeV (Clem and Dorman 2000). The produced ˛-particle
and the Li-nucleus are accelerated by the applied high voltage within the counter
tube, ionize the counter gas and the produced electrons cause an electric signal. The
electric signal is amplified, discriminated and counted by a counter electronic. The
detection probability of the evaporation neutrons is 5.7% (Hatton 1971).
Later proportional counter tubes were filled with 3 He as an alternative to the
standard BF3 counters, as BF3 is highly toxic. The He counters require a higher

6 Ground-Based Measurements of Energetic Particles by Neutron Monitors

103

pressure to have an efficiency close to the BF3 counters and they have a much higher
temperature sensitivity and therefore require better environmental temperature
stability. Currently, new neutron monitor counter tubes use again BF3 because of
the very high price for 3 He.
As an incident neutron or proton into the neutron monitor may produce more
than one evaporation neutron in the lead producer, it can be expected that a group of
count signals is observed (multiplicity). However, the efficiency for detecting these
evaporation neutrons is low. Therefore, the average detected multiplicity is typically
not much larger than one. Due to the multiplicity effect in the neutron monitor the
count impulses are not equally distributed. Therefore thepvariance of the counting
rate .N/ is not Poisson distributed. One has .N/ > N. The variance of the
counting rate .N/ is given by:
.N/ D k 

p
N

(6.2)

where k is around 1.5 for an NM64 monitor (Hatton 1971).
The average count rate of an 6-NM64 monitor at high latitude and at sea level
is 4200 counts per minute. Due to the multiplicity effect in the neutron monitor
the relative random error for 1-min values is therefore 2.5%. The count rate of an
equatorial sea-level 6-NM64 monitor is 0.7 times the count rate of an identical
neutron monitor at high latitudes. Neutron monitors at high altitudes have higher
counting rates because of the smaller atmospheric attenuation. The count rate of a
neutron monitor at high latitudes and at an altitude of 3000 m asl is about a factor
of ten higher than at sea level.

6.4.2 Neutron Monitor Yield Function
The transport of cosmic ray particles through the Earth’s atmosphere and the
detection of the nucleonic component of the secondary cosmic rays by the neutron
monitors are combined in the so-called neutron monitor yield function. The neutron
monitor yield function can therefore directly be used to determine the cosmic ray
flux at the top of the Earth’s atmosphere from the measurements of the worldwide
neutron monitors. Essentially, two methods are used to determine the neutron
monitor response function:
• parameterisation of latitude survey observations (neutron monitor measurements
e.g. on a ship cruise along a large range of geomagnetic latitudes)
• Monte Carlo simulations of the cosmic ray transport through the Earth’s atmosphere and of the detection efficiency for the different secondary particles in the
neutron monitor
The most commonly used response function based on latitude surveys is the Dorman
function (Dorman and Yanke 1981). The Dorman function represents most latitude
surveys fairly well, however the trend of the response function at low rigidities

104

R. Bütikofer

can not be retrieved from latitude surveys. Belov and Struminsky (1987) made
modifications to the Dorman function for rigidities <2.78 GV.
Different authors have determined the neutron monitor yield function with
Monte Carlo simulations. In 1982 Debrunner et al. calculated the specific yield
function for sea level neutron monitors. Clem and Dorman (2000) applied the
FLUKA Monte-Carlo package (Fassò et al. 1993) for the simulations. In recent
years different groups (Flückiger et al. 2008; Matthiä 2009; Mishev et al. 2013)
used the Geant4 software package (Agostinelli et al. 2003) to compute the neutron
monitor yield function. For the transport in the atmosphere the Geant4 software
suite PLANETOCOSMICS (Desorgher et al. 2006) has been mostly used. Some of
the determined yield functions are valid only for neutron monitors at sea level. This
requires pressure corrections of the neutron monitor count rates to sea level. Mainly
for high altitude neutron monitor stations these corrections may be inaccurate as
the parameter for the barometric corrections depends on the cosmic ray spectrum,
see Sect. 6.4.3. The yield function by Flückiger et al. (2008) is valid for different
altitudes, i.e. the atmospheric depth of the neutron monitor station is a parameter of
this yield function.
The relation between the counting rate Nx of the neutron monitor station x and
the differential fluxes of the different components k of the primary cosmic rays at
the border of the geomagnetic field, k , can be described by the following formula:
Nx .h; ; ; t/ D

XZ
k

2
0

Z

=2
0

Z

1
0

˛.R; ; ; ; ; t/ 

k .R; ; ; ; ; t/

sin   Sxk .h; R; /  Ax  cos   dR d d
(6.3)
where
˛
R
; 
; 
t
Sxk

h
Ax

filter function which is 1 for allowed cosmic ray particle trajectories and 0
for forbidden trajectories (Chap. 5).
pc
where p is the
rigidity of the primary cosmic ray particle. R D Ze
momentum of the particle, Ze is its charge and c is the speed of light.
zenith and azimuth angle of the primary cosmic rays at the top of the
atmosphere.
geographic latitude and longitude of the neutron monitor station location.
date and time in UT.
yield function. It gives the number of count events produced by a primary
particle of type k in the neutron monitor station x. The yield function
depends on the rigidity, on the zenith angle, , of the incident particle, and
on the atmospheric depth, h, of the neutron monitor station.
atmospheric depth of the neutron monitor station.
area of the neutron monitor station, x.

6 Ground-Based Measurements of Energetic Particles by Neutron Monitors

105

6.4.3 Atmospheric Effects
Because of the interactions of the primary and secondary cosmic ray particles with
the matter of the Earth’s atmosphere, the neutron monitor count rate depends also
on meteorological conditions (Carmichael et al. 1968). With constant cosmic ray
intensity at the top of the Earth’s atmosphere the counting rate of a neutron monitor
depends mainly on the atmospheric mass above the detector and in much lower
degree on the temperature profile and on the water content in the atmosphere.
Because of the relative small effects and because of the large complexity to
determine the temperature profile and the water content in the atmosphere, only the
change in the atmospheric mass is considered for neutron monitor measurements.
In practice, the barometric pressure is used as a proxy for the air mass to correct the
neutron monitor data to a constant atmospheric depth.
The dependence of the neutron monitor count rate upon atmospheric pressure is
usually described by an exponential function:
N.p.t// D N.p/  exp .

p  p.t/
/


(6.4)

where
N.p.t//
N.p/


measured count rate at atmospheric pressure p and at time t.
neutron monitor count rate at some standard pressure p.
attenuation length of the nucleonic component of the cosmic radiation in
the Earth’s atmosphere.

The attenuation length  depends on the altitude, the geomagnetic latitude and on
the primary cosmic ray spectrum. The attenuation length is larger for harder primary
rigidity spectra and vice versa.
During a solar cosmic ray event measured by neutron monitors, the cosmic ray
near Earth includes a galactic and a solar component. The solar particles show a
softer rigidity spectrum compared to the spectrum of the galactic cosmic rays. The
attenuation length for galactic cosmic rays g is about 140 g/cm2 , whereas the value
for the solar cosmic rays s is typically around 100 g/cm2 . The two-attenuation
length method by McCracken (1962) considers this fact.
The pressure corrected neutron monitor counting rate to the selected standard
pressure p during a solar cosmic ray event can be written as follows by assuming
that the galactic cosmic ray intensity during the solar cosmic ray event does not
change:

N.t; p/ D N0 .p0 /  exp


p0  p
g


C


p0  p.t/
N .t; p.t//  N0 .p0 /  exp
g





p.t/  p
 exp
s



(6.5)

106

R. Bütikofer

where
N.t; p/
N0 .p0 /
g
N.t; p.t//
s

pressure corrected count rate to the standard pressure p of the neutron
monitor station during a solar cosmic ray event.
average measured count rate with an average atmospheric pressure p0
during the reference time interval (typically the full hour before the
onset of the solar cosmic ray event).
attenuation length for the nucleonic component of the galactic cosmic
rays in the Earth’s atmosphere.
measured count rate at time t and atmospheric pressure p.t/.
attenuation length for the nucleonic component of the solar cosmic rays
in the Earth’s atmosphere.

The first summand of equation (6.5) is the contribution to the count rate by the
galactic cosmic ray corrected to the standard pressure p. The second summand is
the pressure corrected count rate caused by the solar cosmic rays. The expression
between square brackets is the measured part to the counting rate caused by the solar
cosmic ray at time t. For the determination of this portion the measured counting
rate during the reference time interval N0 .p0 / has to be corrected to the current
atmospheric pressure p.t/ and has to be subtracted from the measured count rate
N.t; p.t// during the GLE.
The barometric pressure coefficient for galactic cosmic rays ˛ D 1 for a
neutron monitor has a value in the order of 1%/mmHg (or 0.0072 mbar1 ), i.e. the
change in the air mass above a neutron monitor station has a large effect upon the
count rate. Therefore, the barometric pressure at a neutron monitor station must
be determined very accurately, as an error in the pressure measurement of 1 mmHg
causes a change in the count rate of 1%. As the spectrum of the galactic cosmic ray
changes during the 11-year solar activity cycle, the barometric coefficient ˛ shows
a variation as well and should therefore be determined periodically.
Neutron monitor stations at exposed locations (e.g. high altitudes) may considerably be affected by environmental effects. These neutron monitor stations are
heavily exposed to high wind speeds and gusty winds which may strongly affect the
atmospheric pressure measurements. Consequently, the correction of the neutron
monitor count rates for the effects of changes in the air mass above the detector
using raw barometer data may lead to erroneous results (Bütikofer and Flückiger
1999). In addition, there are other environmental effects on the neutron monitor
counting rate, e.g. the accumulation of snow on the roof and around the detector
housing. This effect must usually not be taken into account during a solar cosmic ray
event. However, when investigating long time data series, the use of neutron monitor
stations, where possible changes of snow accumulations may occur on the roof and
around of the detector housing, must be considered with care. These effects must
be considered especially for the NM64 type as the thickness of the reflector is only
7.5 cm compared to 28 cm in the IGY neutron monitor. In the NM64 monitor the
evaporation neutrons, that are produced in the surrounding material of the neutron

6 Ground-Based Measurements of Energetic Particles by Neutron Monitors

107

monitor, contribute to the counting rate with 5% (Hatton 1971) and changes of
this matter in the immediate environment therefore affect the counting rate.

6.5 Worldwide Network of Neutron Monitor Stations
as a Giant Spectrometer
The ‘Simpson’ neutron monitor (Simpson 1955) was the standard cosmic ray
detector for the International Geophysical Year (IGY) 1957/58, and it was called
the ‘IGY’ neutron monitor. During the years 1957–1959 a worldwide network of 51
monitors was established. After the International Geophysical Year 1957/58 some of
the IGY neutron monitors stopped, however most stations continued operating. With
the launch of the NM64 or ‘supermonitor’ in the 1960s by Carmichael (1968) many
of the IGY neutron monitors were replaced by the new detector type. During this
transition time most principal investigators operated both neutron monitor types in
parallel for some months to determine a normalization factor for long term studies.
Today the majority of the worldwide network comprises NM64 monitors, however
there are still a few IGY neutron monitors in operation. Figure 6.3 shows a world
map with the locations of the neutron monitor stations that have been in operation in
2017 or only recently been closed. In 2017 about 50 neutron monitor stations have
been in operation.
The Earth’s magnetic field establishes the worldwide network of neutron monitors to a huge spectrometer. The rigidity range of this spectrometer is determined by
the atmospheric cutoff at the lower rigidity border and by the highest magnetic cutoff
rigidity at the other end. Although the magnetic cutoff rigidity near the geomagnetic

Fig. 6.3 World map with the locations of neutron monitors which have been in operation in 2017
or only recently been closed

108

R. Bütikofer

poles is 0 GV as the magnetic field lines enter vertically into the Earth, the primary
cosmic ray particles penetrating the top of the atmosphere must have a minimal
energy that the secondary nucleons can reach the ground. This atmospheric cutoff
energy for a sea level detector is 450 MeV, i.e. a rigidity of 1 GV for protons.
The maximum vertical magnetic cutoff rigidity is 15 GV. The measurements of
the worldwide network of neutron monitors enable therefore to determine spectral
variations of the galactic cosmic rays near Earth and the spectral characteristics of
GLEs in the energy range from 500 MeV to 15 GeV.
When working with neutron monitor data it is important to realise that the
neutron monitor stations of the worldwide network are operated by different
institutes, i.e. the measurements (e.g. obvious outliers in the count rate, data gaps
etc.) are handled differently. The neutron monitor stations are located at very
different locations (sea level, high altitude, polar regions), therefore e.g. the stability
of the temperature inside the detector housing, of the humidity as well as the
behaviour of the electronic devices may differ and cause different qualities of the
measurements. In earlier days there were also problems with the accuracy of the
used clocks.

6.6 Neutron Monitor Database: NMDB
In the early days of neutron monitors, the cosmic ray scientists exchanged their data
with data tables and books (mostly on a monthly/half-year basis and only with a
resolution of one hour). Later the operators of neutron monitor stations wrote the
measured data on storage media like magnetic tapes or floppy disks and sent these
media to the World Data Centers (WDC) in the USA, USSR, and Japan (Pyle 2000).
For neutron monitor data analysis the scientists ordered the data either directly from
the PIs or from the WDCs and received the data on magnetic tape and later on
compact discs. The advent of the internet made the data exchange much easier.
The different groups published their measurements on their own webpage. More
and more the cosmic ray scientists have the demand to have the measurements of
the worldwide network available in real-time. There were also some initiatives to
develop a data base for neutron monitor data, however only the project “NMDB
– Real-Time database for high resolution Neutron Monitor measurements” (http:
\www.nmdb.eu) funded by the Commission of the European Communities as an
FP7 project in the years 2008/09 was successful. A number of 12 institutions were
involved in the project. First only the data of the institutions involved in the project
were brought into NMDB. However, since then the number of neutron monitor
stations that send their data to the NMDB has increased and in 2017 a total of about
40 neutron monitor stations transmit their data regularly to NMDB, about 30 neutron
monitor stations in real-time or near real-time. The neutron monitor measurements
are stored in NMDB as 1-min and hourly data.

6 Ground-Based Measurements of Energetic Particles by Neutron Monitors

109

revised corr_for_efficiency values averaged to 2 min from 2006-12-13T01:00:00 to 2006-12-13T 11:59:00

150.0

ROME(R=6.27/Alt.Om)
KIEL(R=2.36/Alt.54m)
OULU(R=0.81/Alt.15m)
APTY(R=0.65/Alt.181m)

increase (%)

100.0

50.0

GLE70
:00
11

:00
10

:00
09

:00
08

:00
07

:00
06

:00
05

:00
04

:00
03

:00
02

01

:00

–50.0

NEST 29 Mar 2017

0.0

Fig. 6.4 Relative increase of pressure corrected 2-min data of the neutron monitor stations Oulu,
Apatity, Kiel and Rome during GLE#70 (13 December 2006) plotted with NEST

In addition to the database there are different applications available from the
NMDB webpage www.nmdb.eu (Mavromichalaki et al. 2011). NMDB provides
e.g. the application NEST (http://www.nmdb.eu/nest/) to generate plots of the count
rate of selected neutron monitor stations with different time resolutions. It is also
possible to plot neutron monitor data together with the sunspot number (smoothed
or monthly), geomagnetic Kp-index (3-hourly), or GOES data (channels >10 MeV,
>50 MeV, >100 MeV). The plots can be modified by different style adjustments.
The generation of plots during GLEs and Forbush decreases from the past can
be selected with one click. Figure 6.4 shows as an example the measured relative
increase in the count rate of a selection of neutron monitors during GLE#70 on 13
December 2006 as plotted with the NMDB NEST application. In addition to the
graphic output it is also possible to extract ASCII data from NMDB with NEST.
Other NMDB applications are e.g. GLE alarm systems or GLE characteristics
determination.
In addition to NMDB the Cosmic Ray Station of the University of Oulu
reactivated and operates the GLE database http://gle.oulu.fi/ where the neutron
monitor data of the worldwide network during GLEs are stored and are made
available for plotting and for downloading.

110

R. Bütikofer

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Chapter 7

HESPERIA Forecasting Tools: Real-Time
and Post-Event
Marlon Núñez, Karl-Ludwig Klein, Bernd Heber, Olga E. Malandraki,
Pietro Zucca, Johannes Labrens, Pedro Reyes-Santiago, Patrick Kuehl,
and Evgenios Pavlos

Abstract Within the HESPERIA Horizon 2020 project, two novel real-time tools
to predict Solar Energetic Particle (SEP) events were developed. The HESPERIA
UMASEP-500 tool makes real-time predictions using a lag-correlation between the
soft X-ray (SXR) flux and high-energy differential proton fluxes of the GOES satellite network. We found that the use of proton data alone allowed this tool to make
predictions before any Neutron Monitor (NM) station’s alert. The performance of
this tool for predicting Ground Level Enhancement (GLE) events for the period
2000–2016 may be summarized as follows: the probability of detection (POD) was
53.8%, the false alarm ratio (FAR) was 30%, and the average warning time (AWT)
to the first NM station’s alert was 8 min. The developed HESPERIA REleASE tool
makes real-time predictions of the proton flux-time profiles of 30–50 MeV protons
at L1 and is based on electron intensity measurements of energies from 0.25 to
1 MeV and their intensity changes. The performance was tested by using all historic
ACE/EPAM and SOHO/EPHIN data from 2009 until 2016 and has shown that
the forecast tools have a low FAR (30%) and a high POD (63%). Furthermore,
two methods using historical data were explored for predicting SEP events and

M. Núñez () • P. Reyes-Santiago
Universidad de Málaga, Málaga, Spain
e-mail: mnunez@uma.es
K.-L. Klein • P. Zucca
Observatoire de Paris, Meudon, France
e-mail: ludwig.klein@obspm.fr
B. Heber • J. Labrens • P. Kuehl
Christian-Albrechts – University of Kiel, Kiel, Germany
e-mail: heber@physik.uni-kiel.de
O.E. Malandraki • E. Pavlos
National Observatory of Athens, IAASARS, Athens, Greece
e-mail: omaland@astro.noa.gr
© The Author(s) 2018
O.E. Malandraki, N.B. Crosby (eds.), Solar Particle Radiation Storms Forecasting
and Analysis, The HESPERIA HORIZON 2020 Project and Beyond, Astrophysics
and Space Science Library 444, DOI 10.1007/978-3-319-60051-2_7

113

114

M. Núñez et al.

compared. The UMASEP-10mw tool was developed for predicting >10 MeV SEP
events using microwave data. The time derivative of the soft X-rays (SXR) was
replaced by the microwave flux density. It was found that the use of SXRs and
microwave data produced the same POD (78%) with the most notable difference
being that the use of microwave data does not yield any false alarm. Furthermore, a
study was carried out on the possibility for the microwave emissions to be used to
predict the spectral hardness of the SEP event and important results were deduced.

7.1 Introduction
Forecasting solar energetic particle (SEP) events is of potential interest for spacecraft and launching operations, and for the assessment of radio wave propagation
conditions in the polar ionosphere of the Earth. It will be mandatory for human
spaceflight beyond low-Earth orbit, especially outside the Earth’s magnetosphere.
Besides predicting SEP events in general, the prediction of particularly energetic
SEPs is a second aim of forecasting, because they penetrate deeper into the
terrestrial atmosphere and contribute to the radiation dose aboard aircraft.
Operational real-time SEP forecasts are currently supported by empirical models
which rely on observations of associated solar phenomena, including electromagnetic signatures of SEP acceleration/escape near the Sun and observations at the
near-Earth environment (L1 or 1 AU) of energetic particles. In this chapter the
two novel real-time SEP forecasting tools developed and operating within the
HESPERIA project are presented, based on the University of MAlaga Solar particle
Event Predictor (UMASEP) (Núñez 2011, 2015) and Relativistic Electron Alert
System for Exploration (REleASE) schemes (Posner 2007).
The developed and operational HESPERIA UMASEP-500 tool makes realtime predictions of the occurrence of Ground Level Enhancement (GLE) events,
from the analysis of soft X-ray (SXR) and differential proton flux measured by
the Geostationary Operational Environmental Satellites (GOES) satellite network.
Using near-relativistic as well as relativistic electrons as precursors for the arrival
of energetic protons, the developed HESPERIA REleASE tools make real-time
predictions of the proton flux-time profiles of 30–50 MeV protons at L1. Furthermore, two methods using historical data explored under the HESPERIA project for
predicting SEP events are presented and compared. We have tested if the UMASEP
scheme can be improved using microwave observations and also studied if the
microwave emissions can be used to predict the spectral hardness of the SEP event
and important results are deduced.
The first two sections of the chapter are dedicated to the investigations of whether
historical microwave emissions can be used in the forecasting of SEP events (Sect.
7.2 and 7.3), whereas the two following sections describe the real-time HESPERIA
SEP forecasting tools, using the REleASE and UMASEP proven concepts (Sect. 7.4
and 7.5). Concluding remarks as well as future possibilities are given in Sect. 7.6.

7 HESPERIA Forecasting Tools: Real-Time and Post-Event

115

7.2 Predicting SEP Event Onsets from Historical Microwave
Data by Using the UMASEP Scheme
Within the HESPERIA project we tested whether microwave emission could be
used in the forecasting of SEP events. This is not possible in real time, because no
real-time microwave data are presently provided. However, we attempted a proofof-concept by using historical SEP events.
The UMASEP forecasting scheme (Núñez 2011, 2015) uses the positive time
derivative of the observed SXR flux as an indicator of energy release at the Sun.
The SXR burst shows the heating of the corona during a flare. The UMASEP
scheme considers that a common positive derivative with the particle flux near
Earth, with a suitable time delay, indicates a magnetic connection between the
Earth and a site of particle acceleration near the Sun. It is well known (Neupert
1968; Dennis and Zarro 1993; Holman et al. 2011) that hard X-ray (HXR) or
microwave bursts, produced by non-thermal electrons in the solar atmosphere
through bremsstrahlung and gyrosynchrotron emission (see Chap. 2), have time
profiles that mimic the time derivative of the SXR. The reason is a common time
evolution of the energy release that goes to the electron acceleration on the one
hand and to the heating of the plasma during the related flare on the other. While
non-thermal electrons lose their energy rapidly through interactions with the solar
atmosphere, the heated coronal plasma cools on much slower time scales, and its
time evolution is therefore the integral over the distinct episodes of energy release
traced by the non-thermal signatures. So as long as the microwave emission is
due to gyrosynchrotron radiation of non-thermal electrons, its time profile can be
considered as being close to the time derivative of the SXR profile in the impulsive
flare phase.
Patrol observations of the whole Sun at microwaves can be conducted with
ground-based antennas. The US Air Force operates the Radio Solar Telescope
Network (RSTN) consisting of four stations around the world. These stations
observe independently from each other, but with identical equipment at selected
frequencies.
The most interesting frequencies for our purpose are 4.995 (henceforth referred
to as 5 GHz), 8.8 and 15.4 GHz. The data are publicly available after about 1 year via
the National Geophysical Data Center (NGDC).1 Data from the Nobeyama Radio
Polarimeters2 (NoRP), (Torii et al. 1979; Nakajima et al. 1985), operated by the
National Astronomical Observatory of Japan, were used for checking purposes and
to replace RSTN when necessary.
In order to test to which extent microwave data can support the UMASEP
scheme, we constructed a continuous time series of RSTN observations during a
13-month long period from December 2011 to December 2012. The observations

1
2

http://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-radio/rstn-1-second/
http://solar.nro.nao.ac.jp/norp/html/event/

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Fig. 7.1 The combined time history of the microwave flux density at two frequencies during the
13 months from 2011 Dec 01 to 2012 Dec 31, constructed from observations of the four RSTN
stations

of the individual RSTN stations have a number of problems that needed a careful
consideration. We applied a series of standard treatments to remove spikes, data
gaps, baseline drifts due to wrong antenna pointing. Then the corrected daily records
of the individual stations were combined into the 13-month long time series. A
uniform average background was added at each frequency, and smaller flux densities
were set to the background value. 5-min integration further smoothes out short-term
irregularities that remain after the data cleaning procedure.
Figure 7.1 shows the resulting flux density calculated for the 13 months interval
from December 2011 to December 2012. At both frequencies numerous bursts are
seen. During this period, nine SEP events were considered as well-connected events
and four were considered as poorly connected. An SEP event in the sense used here
is an event where the proton intensity at energies above 10 MeV exceeds 10 pfu.
Based on the UMASEP scheme the UMASEP-10mw tool was developed for
predicting >10 MeV SEP events using microwave data, the time derivative of the
SXR was replaced by the microwave flux density. The UMASEP thresholds were recalibrated. The tool UMASEP-10mw has been developed to be used for calculating
the correlation between the solar microwave flux densities at 5 GHz and 8.8 GHz,
which are monitored by patrol instruments, and the time derivatives of the nearearth differential proton fluxes measured in different energy channels (i.e. using the
GOES satellites).

7 HESPERIA Forecasting Tools: Real-Time and Post-Event

HESPERIA UMASEP–10mw SEP event forecaster

1000

100

100

SEP threshold: 10

MW flux
density
(log 10)

Forecast of integral
proton flux (E > 10 MeV)
(pfu)
10000

Integral
10000
proton flux
(> 10 MeV) 1000

Time (UTC) 00 Jul 12

now

117

10

0:00 Jul 13

Current
proton
flux:
32.0 pfu

12:00 Jul 13

4
3
2

Magnetic
connectivity
estimation high
medium
low

Model inferences in real-time:
The earth is well-connected
with the solar region 11520
(S15W01) in which a ×1.4
flare has erupted at 16:49.
Signatures of well-connected
protons were recognized in
the energy ranges:
. P3 (9—15 MeV)
. P4 (15—40 MeV)

Solar
Region
11520

Earth

Fig. 7.2 UMASEP-10mw output after processing microwave data at 5 GHz from 2012 July 12
and GOES proton fluxes of >10 MeV energies. The yellow/orange band in the proton intensity
plots gives the predicted range, with the colour scale shown by the vertical bar

We illustrate the forecast of the UMASEP-10mw tool using microwave data at
5 GHz for predicting the >10 MeV SEP event.
Figure 7.2 shows the forecast graphical output that an operator would have seen
if the UMASEP-10mw tool had processed real-time microwave data on 2012 July
12. The upper time series in both images shows the observed integral proton flux
with energies greater than 10 MeV. The current flux is indicated below the label
“now” at each image. To the right of this label, the forecast integral proton flux
is presented as a yellow/orange-coloured band. The central curve in each panel
displays the microwave flux density time profile, and the lower time series shows
the magnetic connectivity estimation with the best-connected coronal mass ejection
(CME)/flare process zone.
Figure 7.2 also shows the prediction at 18:05 (2012 July 12). This forecast is that
an event will start during the following 2 h and reach a peak intensity of 36 pfu 9
(see white section “Automatic forecast”). Below the forecast section, the system also
presents the model inference section, which shows that the Earth is well-connected
with the solar region 11520. The system also shows that the associated X1.4 flare

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M. Núñez et al.

took place at S15W01. As time passes, the integral proton flux also rises. At 18:35
UT, the flux exceeds the 10-pfu threshold, which indicates that a proton event is
occurring. Note that the well-connected SEP event was successfully forecast 30 min
earlier, when the enhancement of the integral proton flux was still weak (1.24 pfu).
To measure the overall performance of this tool, we run the UMASEP forecasting
schemes using on the one hand the SXR observations, on the other hand the
microwave observations at the two frequencies considered for the aforementioned
period. We evaluated two quantities: the probability of detection (POD) is the
number of the predicted SEP events divided by that of the SEP events that actually
occurred, i.e. nine events in the considered time interval. The false-alarm ratio
(FAR) is the number of false predictions over the number of predictions. Seven
predictions were triggered when microwaves were used, and eight with SXR. We
found that the use of SXR and microwave data produced the same POD D 77.8%
(7/9). The most notable difference is that the use of microwave data does not
yield any false alarm. The average warning time (AWT) is slightly higher when
microwave observations are used 30.7 min as compared to 26.4 min.
The probabilities of detection used above are adequate to compare the performance of SXR and microwaves within the UMASEP scheme, but overestimate the
expected ones: SEP events originating behind the solar limb are undetectable to
the UMASEP Well-Connected Prediction model (WCP), because it uses electromagnetic observations from a terrestrial vantage point. This bias affects SXR from
GOES and radio observations from ground alike.
A more detailed account of this work is given in Zucca et al. (2017).

7.3 Predicting SEP Energy Spectra from Historical
Microwave Data
Depending on their peak intensity and spectral hardness, SEP events constitute
different kinds of space weather hazard. Protons and heavy ions at energies
between several MeV and several tens of MeV may interact with spacecraft and
human beings above low-Earth orbit, and ionize the high polar atmosphere of the
Earth. GeV protons create atmospheric cascades down to the Earth and enhanced
radiation doses at aircraft altitudes. High intensities in the two energy ranges are
not necessarily observed in the same events (Mewaldt et al. 2007). Besides the
occurrence, spectral hardness is therefore a space-weather relevant information, and
a second goal in SEP forecasting.
It was shown in Grechnev et al. (2015 and references therein) that SEP events
above 100 MeV are often accompanied by strong microwave emission well above
the average peak frequency of 10 GHz. On the other hand the peak flux density
or peak fluence of microwave bursts also show some correlation with the peak
intensity of SEPs at tens of MeV (Kahler 1982; Trottet et al. 2015). Chertok et
al. (2009) went one step further and suggested that SEP events with hard proton

7 HESPERIA Forecasting Tools: Real-Time and Post-Event

119

Fig. 7.3 Scatter plots of the spectral hardness of the proton spectrum •, versus the peak microwave
flux density ratio at 8.8 and 15.4 GHz, labelled S9/S15. (a) Study by Chertok et al. (2009). (b)
Present work based on data from GOES integral intensities above 10 MeV and above 100 MeV
taken during solar cycles 23 and 24

spectra in space in the 10–100 MeV range tend to be accompanied by microwave
bursts where the flux density at the highest frequency continually monitored from
ground, which is 15.4 GHz, exceeds the flux density at 9 GHz. The ratio of flux
densities at the two frequencies, which is an easily observable parameter, seems
to correlate significantly (r D 0.55) with the proton spectral hardness during solar
cycles 22–23.
We re-examined the relationship during cycles 23 and 24, using the integral
proton intensities measured by the GOES. We consider integral intensities above
10 MeV (designated by J10 in the following) and 100 MeV (J100 ) for events
associated with activity in the western solar hemisphere, and calculated the ratio

ı D log10

J10
J100


(7.1)

In Fig. 7.3 the scatter plot between the proton spectral hardness • and the ratio
of peak flux densities at 8.8 and 15.4 GHz derived by Chertok et al. (2009) (a)
is compared with our work (b). Both plots suggest a slight trend that SEP events
with hard proton spectra are associated with microwave bursts that are stronger
at 15.4 than at 8.8 GHz. But the correlation is questionable in cycles 23–24: the
linear correlation coefficient of the sample in Fig. 7.3b is 0.26 ˙ 0.20 in solar cycle
23, and still weaker in solar cycle 24. So we find no convincing correlation that
could support a forecasting procedure of spectral hardness of SEPs. We also tested
a correlation between spectral hardness and the speed of the associated CME. This
was also inconclusive, with a correlation coefficient of 0.15 ˙ 0.16 in solar cycle
23.
There is a number of reasons why a relationship between the microwave peak
frequency and the SEP spectral hardness in the range (10–100) MeV could be
masked. One is the likely contribution of different acceleration processes to the SEP

120

M. Núñez et al.

populations (Trottet et al. 2015) and the variation of their contribution with particle
energy (Dierckxsens et al. 2015). If the SEPs above 10 MeV were predominantly
accelerated by CME shocks, and those above 100 MeV by flares or similar processes
lower in the corona, no direct correlation would be expected. The other reason is
that the microwave flux density spectrum depends strongly on the magnetic field
strength and orientation in the radio source, which is also not expected to have an
effect on the SEPs. Finally there is an interesting hint that radio bursts with relatively
high flux density at 15.4 GHz (and flat SEP spectra) were lacking in solar cycle 24.
Forecasting schemes can of course use empirical correlations independently of our
understanding of the physical relationships. But this does not seem convincing in
the present case.

7.4 Predicting 30–50 MeV SEP Events by Using
the RELeASE Scheme
The fact that near relativistic electrons (1 MeV electrons have 95% of the speed of
light) travel faster than ions (30 MeV protons have 25% of the speed of light) and are
always present in SEP events, a forecast of the arrival of protons from SEP events
can be based on real-time measurements of near relativistic electrons. The faster
electrons arrive 30–90 min before the slower protons at Lagrangian point 1. The
Relativistic Electron Alert System for Exploration (REleASE) forecasting scheme
uses this effect to predict the proton flux by utilizing the actual electron flux and
the increase of the electron flux in the last 60 min. A detailed description of the
REleASE scheme can be found in (Posner 2007). The original REleASE code uses
real-time electron flux measurements from the Electron Proton Helium Instrument
(EPHIN) (Müller-Mellin 1995) on board the Solar and Heliospheric Observatory
(SOHO) to forecast the expected proton flux.
REleASE is based on electron intensity measurements of energies from 0.25
to 1 MeV and their intensity changes. It utilizes an empirical matrix in order to
predict the proton intensity 30, 60 or 90 min ahead. Figure 7.4b displays the forecast
matrix for one proton channel and the 60-min interval. EPHIN provides realtime
data which are used with the REleASE scheme. One disadvantage of EPHIN data is
the limited time coverage in the realtime data of less than 4 h per day. If no realtime
data are available as input for the REleASE scheme, no forecast can be produced.
The Electron Proton Alpha Monitor (EPAM) onboard the Advanced Composition
Explorer (ACE) was selected to be a good candidate to deliver continuously input
for REleASE because of the nearly full time coverage. EPAM provides realtime
electron intensities in a comparable energy range (0.175–0.315 MeV vs. 0.25–
1.0 MeV) but in a time resolution of 5 min instead of 1 min.
The forecast depends on the measured electron intensities and their increase.
Hence we decided to determine a correlation between the intensities and the
increase parameter. Figure 7.4a shows the time profile of EPAM (red) and EPHIN

7 HESPERIA Forecasting Tools: Real-Time and Post-Event

a

b
EPHIN EPAM comparison

10

EPAM (0.175 – 0.315 MeV) *1e–2)

10

2

10

0

10

10

3
2

e flux / cm**2*Sr*S*MeV

4

2
*S*Str*MeV)

60 minutes forecast matrix p2
104

EPHIN (0.25 – 1 MeV)

3

10

1

2

0

1

–1

10
10

–2

0

10

–3
10–1

–2

10
0

100

200

log proton flux

6

e flux / (cm

121

300

–4

–2

–5
–3

–2

10

–1

10
10
rise parameter

day of 2014

Fig. 7.4 The left panel (a) shows the time series of EPHIN (black) and EPAM (red) electron
intensities. The electron intensity measured by EPAM is divided by 10. The right panel (b) displays
an example of one forecast matrix used within the REleASE scheme. This Matrix shows the
predicted intensity of protons in 1 h as function of the measured absolute electron intensities and
the intensity rise parameter

a

b
N / a.u.
100
2012

1000

6

10

4

10

2

10

0

10

–2

10

–2

10

0

10

2

4

10

10
2

EPAM e flux / (cm *s*str*MeV)

10

N / a.u.
1

EPHIN e flux / (cm2*s*str*MeV)

10

2

EPHIN e flux / (cm *s*str*MeV)

1

6

10

100
2012

1000

6

10

4

10

2

10

0

10
10

–2

–2

10

0

10

2

4

10

10

6

10

2

EPAM e flux / (cm *s*str*MeV)

Fig. 7.5 The left panel (a) displays 5 min electron intensities of EPAM (x-axis) and EPHIN (yaxis) plotted against each other. The right panel (b) shows the same plot for background subtracted
data

(black) electron intensities of 2014. Despite the high background of the EPAM
measurements there seems to be a good correlation. If there is an increase in EPHIN
electron intensity there is also one in EPAM.
To quantify this correlation Fig. 7.5a shows the EPHIN electron intensity on the
y-axis plotted against the corresponding EPAM intensities on the x-axis. The higher
background level of EPAM reflects itself by the nearly vertical line at low EPAM
intensities. In order to correct for that we subtracted a background intensity of 18
(cm2 s sr MeV)1 from the EPAM data. The result of this procedure is shown in
Fig. 7.5b in the right panel. Despite these differences the EPAM electron intensity
is roughly ten times higher as the one determined by EPHIN. This is indicated by
the black line showing the function where EPAM intensity is ten times higher than
EPHIN intensities.

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1

N / a.u.
100

10

N / a.u.

2012

0

100
EPHIN rise parameter

10
EPHIN rise parameter

10
2012

1

–1

10

–2

10

–3

10

–4

10

–5

10–1
10–2
–3

10

–4

10

–5

10

10
–5

10

–4

10

–3

10

10

–2

EPAM rise parameter

–1

10

10

0

–5

10

–4

10

–3

10

–2

10

–1

10

0

10

EPAM rise parameter

Fig. 7.6 Rise parameter of 5 min electron intensities measured by EPAM (x-axis) and EPHIN (yaxis). The EPAM intensity was background subtracted. The right panel displays all data from 2012
while the left panel shows only rise-parameters for strong enhanced electron fluxes

From our investigation, we conclude that there is a good correlation for intensities
higher than 20 (cm2 s sr MeV)1 . Due to the large background the correlation
breaks down for EPAM intensities below 20 particles (cm2 s sr MeV)1 . Since the
goal of the REleASE system is to forecast SEP events with high particle fluxes
the background uncertainties play a negligible role here. The EPAM intensity in
addition was raised to the power of 1.02 to correct for different correlation at very
high intensities.
The second parameter used in the REleASE forecast matrices (x-axis) is the
intensity rise parameter. This parameter is calculated by linear fits through the
logarithmic electron intensities of the last 5–60 min. The maximum of these
parameters is transferred to the rise parameter position in the forecast matrices. A
comparison of the rise parameters from EPHIN and EPAM is shown in Fig. 7.6. One
can see that most of the data points are close to the bisecting line, but do not show
a correlation between the rise parameters. If we only take electron fluxes higher
than 102 into account, the correlation gets stronger. Due to this and the fact that
the forecast matrix in Fig. 7.4 shows a much stronger dependence on the electron
intensity we decided to use the uncorrected EPAM rise parameter as input to the
REleASE scheme. Figure 7.7 shows an example of an SEP event where the EPHIN
based and EPAM based forecasts predicted the real proton flux very accurately.
Since forecasts are made for different time offsets (30, 60, 90 min) and
different overlapping energy channels (16–40 and 28–50 MeV), we investigated a
suitable forecast condition in combining the different forecasts. We tested different
combination of forecasts for different time offsets and found that the following
condition delivered the best performance of the forecast systems:
• Alarm: if any forecast > 101 (cm2 s sr MeV)1 and one 30 min forecast > 102
(cm2 s sr MeV)1 .
• Event: if real proton flux > 101 (cm2 s sr MeV)1 .

7 HESPERIA Forecasting Tools: Real-Time and Post-Event

123

proton flux vs. forecast 2012 (15.8 – 39.8 Mev)
103
proton flux
102

EPHIN forecast

pr2 / (cm2*s*str*MeV)

EPAM forecast
101
100
10–1
10–2
10–3
10–4
66.0

66.5

67.0
doy

67.5

68.0

Fig. 7.7 An example of an SEP event where the EPHIN and EPAM based forecasts predicted the
real proton flux accurately
Table 7.1 Results of
REleASE implementation
utilizing either SOHO/EPHIN
or ACE/EPAM

EPHIN
EPAM

T
24
24

M
14
14

F
10
13

POD (%)
63
63

FAR (%)
29
35

AWT (min)
107
123

The performance was tested by using all historic EPAM and EPHIN data from
2009 until 2016. All SEP events of this time period were investigated. The following
results for events are possible:
• True forecast (Alarm and Event): T
• Missed event (No/late Alarm and Event): M
• False alarm (Alarm and no Event): F
By using the total number of true forecasts, missed events and false alarms of the
analysed time period, it is possible to calculate the Probability of Detection (POD)
and False Alarm Ratio (FAR):
F
• False Alarm Ratio: FAR D TCF
• Probability Of Detection: POD D

T
TCM

The results of the described analysis are summarized in Table 7.1.
The described forecast tools have low FARs and sufficient PODs. The tools are
publicly available via the HESPERIA project web site. On this web site we provide
an e-mail alert system. Interested users are welcome to sign in for this alert system.

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7.5 Predicting >500 MeV SEP Events by Using the UMASEP
Scheme
Solar energetic particles (SEPs) are sometimes energetic enough and the flux is high
enough to cause air showers in the stratosphere and in the troposphere, which are
an important ionization source in the atmosphere. >500 MeV solar protons are so
energetic that they usually have effects on the ground, producing what is called a
Ground Level Enhancement (GLE). One of the goals of the HESPERIA project
was the development of a predictor of >500 SEP events at the near-earth (e.g. at
geostationary orbit). The implemented predictor, called HESPERIA UMASEP-500,
makes a lag-correlation between the SXR flux and high-energy differential proton
fluxes of the GOES satellites. When the correlation estimation surpasses a threshold,
and the associated flare is greater than a specific SXR peak flux, a >500 MeV SEP
forecast is issued.
The lag-correlation is carried out using the High-Energy UMASEP approach
explained in Núñez (2015). In this project, this approach uses 1-min SXR and proton
data. Firstly, it generates a bit-based time series from the SXR time-derivatives and
three bit-based time series from the time-derivatives of each of the P9–P11 channels
of the GOES6-GOES15 satellites. The “1s” in each bit-based time series are set
when its positive time derivative surpasses a percentage p of the maximum value of
the time derivative in the present sequence of size L (beyond which no influence is
assumed in the SEP event to be predicted); otherwise, the flux level is transformed
into a “0”. To avoid false alarms due to relatively strong fluctuations during periods
of low solar activity, a threshold d is necessary, which is the minimum value to
consider it as positive fluctuation (i.e., a “1”). This forecasting approach creates a
list of cause-consequence pairs as follows: it takes the first “1” of the SXR-based
time series, and the first “1” of the proton-based time series, to create a pair; it then
takes the second pair of “1s” in each time series, and thus successively, until all the
“1s” of the SXR-based time series are inspected. After following this procedure, if
a “1” does belong to any pair, it is classified as an “odd”. For each pair, the pair
separation between the SXR-based “1” and the proton-based “1” is calculated.
An ideal magnetic connection is detected when a sequence of SXR-based “1s”
in a row is followed by a sequence of proton-based “1s” in a row. In an ideal
magnetically connected event, all pairs have the same temporal separation, and no
odd “1” has been found; in other words, an ideal magnetic connection is detected
when all recently-measured strongest rises in the SXR flux are followed, some
minutes later (i.e. the lag), by all recently-measured strongest rises in a proton
channel. We say that this ideal magnetic connection would have a Fluctuation
Correlation of 1. In general, we need a formula, described in Núñez (2015), that
calculates the Fluctuation Correlation between the bit-valued SXR-based time series
and a proton-based time series. A >500 MeV SEP event is triggered when the lagcorrelation is greater than a threshold r, and the SXR intensity of the associated flare
is greater than a threshold f.

7 HESPERIA Forecasting Tools: Real-Time and Post-Event

125

It is important to mention that a >500 MeV SEP event is detected when the
integral proton flux surpasses a certain threshold pfu500. To calculate this threshold,
firstly we had to use the geometrical factors of P9, P10 and P11 proton channels
provided by the National Oceanic and Atmospheric Administration (NOAA). Then,
we manually varied this threshold to match each >500 MeV SEP event with each
GLE event. The study ended with a threshold of 0.8 pfu, which yielded a one-to-one
correspondence in 26 of the events of all 32 GLE events within the analyzed period
(1986–2016). In 8 cases, a GLE was observed at Earth; however, the enhancement in
>500 MeV integral proton flux did not surpass 0.8 pfu. In only one case (see Event
44.5 in Table 7.2) a >500 MeV SEP event took place, which was not observed at the
ground.
The UMASEP-500 model’s parameter calibration from historical data was an
optimization process whose purpose was to obtain a high POD and Advance
Warning Time (AWT), and a low FAR. We found that the same thresholds and
parameters found for predicting >500 MeV SEP events were also very appropriate
to predict GLE events; for this reason, this section also presents a summary of the
GLE forecast results. For more information about the GLE forecast results, please
consult Núñez et al. 2017.
The original purpose of the HESPERIA UMASEP-500 tool was to correlate SXR
with neutron and proton data. We found that the use of proton data alone allowed
this tool to make predictions before any Neutron Monitor (NM) station’s alert. This
satisfactory result became our operational criterion for classifying a GLE forecast
as successful. We found that the correlation of SXR and neutron counter data did
not trigger any hit additional to those generated using proton data alone. We also
found that the use of neutron data provoked the generation of many false alarms
due to some quality data problems (mainly spikes) caused by technical issues,
such as problems in the neutron sensor tubes and power supplies, among others
(Souvatzoglou et al. 2014). Since the use of neutron data did not increment the
POD, but did increment the FAR, we decided not to use neutron data for making
predictions.
Figure 7.8 presents the forecast output for the >500 MeV and GLE event on
October 28, 2003. The upper time series shows the recent >500 MeV proton flux;
the predicted flux is presented with a colored curve. The middle time series shows
the recent SXR flux. The plot at the bottom of the forecast output presents the
empirically-estimated level of magnetic connectivity. The Automatic Prediction
section (on the right) presents in red the prediction of the occurrence of the GLE
event. Below, the tool presents the details of the associated flare, and the proton
channels for which the SXR correlation was found. The small image at the topright shows the real evolution of the integral proton flux after this prediction.
The 1-min real-time forecast outputs of this tool are shown on the website of the
HESPERIA project (i.e. https://www.hesperia.astro.noa.gr/index.php/results/realtime-prediction-tools/umasep).
The overall prediction performance of event occurrences for the analyzed period
(1986–2016) was calculated in terms of POD, FAR and AWT. Table 7.2 presents
the list of GLEs, >500 MeV SEP events, and the HESPERIA UMASEP-500’s

Solar event
Event ID
GLE-40
GLE-41
GLE-42
GLE-43
GLE-44
Ev-44.5
GLE-45
GLE-46
GLE47
GLE-48
GLE-49
GLE-50
GLE-51
GLE-52
GLE-53
GLE-54
GLE-55
GLE-56
GLE-57
GLE-58
GLE-59
GLE-60

GLE Onset
(UTC)
25/07/1989
16/08/1989
29/09/1989
19/10/1989
22/10/1989
23/10/1989
24/10/1989
15/11/1989
21/05/1990
24/05/1990
26/05/1990
28/05/1990
11/06/1991
15/06/1991
25/06/1992
02/11/1992
06/11/1997
02/05/1998
06/05/1998
24/08/1998
14/07/2000
15/04/2001

GLE Forecast
Resulta
Miss
Hit
Hit
Hit
Miss

Miss
Miss
Miss
Miss
Miss
Miss
Hit
Hit
Miss
Hit
Miss
Miss
Miss
Miss
Hit
Hit

Time
8:50
1:25
11:40
13:00
17:55

18:18
7:00
22:29
20:49
20:55
5:34
2:30
8:35
20:15
3:50
12:10
13:55
8:25
22:50
10:34
13:57
10:36
13:57

12
1

20

Hit
Hit

Hit
Hit
Miss
Hit
Miss

Miss
Miss
Miss

23:02
21:06
21:10
3:18
8:40
20:18
3:24
12:27

>500 SEP
Forecast Result
Miss
Hit
Hit
Hit
Miss
Miss
Miss

>500 SEP Event
Onset Time (UTC)
9:13
1:37
11:51
13:03
17:57
12:42
18:24

24
2

20
6
8

GLE Forecast
Warning Time
(min)a

14
1

28

72
7

32
17
11

>500 SEP Forecast
Warning Time (min)

Table 7.2 HESPERIA UMASEP-500’s forecast results of the GLE and >500 MeV SEP events that took place during the analyzed period (1986–2016)

126
M. Núñez et al.

a

18/04/2001
04/11/2001
26/12/2001
24/08/2002
28/10/2003
29/10/2003
02/11/2003
17/01/2005
20/01/2005
13/12/2006
17/05/2012

2:33
16:55
5:39
1:23
11:17
21:02
17:27
9:52
6:47
2:50
1:55

Miss
Miss
Miss
Hit
Hit
Hit
Hit
Miss
Miss
Hit
Miss
15

13
9
3
3

Hits are predictions that are triggered before the first NM station’s GLE alert

GLE-61
GLE-62
GLE-63
GLE-64
GLE-65
GLE-66
GLE-67
GLE-68
GLE-69
GLE-70
GLE-71
Miss
Miss
Hit
Hit
Hit
Hit
Miss
Hit
Miss

16:44
6:08
1:30
11:31
21:19
17:35
6:46
2:59
2:07

24

20
23
20
11

7 HESPERIA Forecasting Tools: Real-Time and Post-Event
127

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M. Núñez et al.

Forecast of integral
HESPERIA UMASEP–500 (>500 MeV SEP event and GLE forecaster) now proton flux (E > 500 MeV)

Integral
1000
proton flux
(> 500 MeV) 100
10
SEP threshold (0.8) 1

Time (UTC) 00 Oct 28

9:00 Oct 28
Automatic forecast:
A GLE event is expected.

X-Ray flux
X
M
C

Magnetic
connectivity
estimation high
medium
low

This event would be associated
to a >500MeV SEP event that might
reach 3 pfu in space near-Earth.
Model inferences in real-time:
The earth is well-connected
with a solar flaring region
in which a ×17.2 flare has
erupted at 11:08.
Signatures of well-connected
protons were recognized in
the energy ranges:
. P11 (> 700 MeV)

Fig. 7.8 This figure shows the forecast output of HESPERIA UMASEP-500 for the event occurred
on October 28, 2003. This prediction, issued at 11:08, was successful because it was issued before
the >500 MeV integral proton flux surpassed 0.8 pfu (at 11:31), and before the first NM station’s
alert, issued at 11:17

prediction results for the events of the analyzed period. Column 1 presents the
GLE event ID; column 2 lists the time of the first detection of the event of an NM
station; column 3 presents the HESPERIA UMASEP-500 GLE prediction results
(hits are those events successfully predicted, and misses are those not-successfully
predicted); column 4 lists the warning times (i.e. the temporal difference between
the time at which the forecast was triggered by this tool and the time of the first
NM station’s alert); column 5 lists the time the occurrence of the SEP event (i.e. the
time when the >500 MeV proton flux surpassed 0.8 pfu); column 6 presents the SEP
prediction results; and, column 7 lists the warning times.
Regarding the prediction of >500 MeV SEP event, the forecast performance
results of this tool for the period 1986–2016 may be summarized as follows: the
POD was 50% (13/26), the FAR was 31.6% (6/19), and the average warning time to
the first NM’s alert was 13 min.
Regarding the prediction of GLE events, the forecasting results for the most
recent half of the evaluation period (i.e. 2000–2016) may be used to compare
UMASEP-500 with those of the GLE Alert Plus. These results may be summarized
as follows: the POD was 53.8% (7 of 13 GLE events); the FAR was 30.0% (3/10);

7 HESPERIA Forecasting Tools: Real-Time and Post-Event

129

the AWT to the first NM’s alert was 8 min; and, the AWT to the GLE Alert Plus’s
warning was 15 min. The GLE forecasting results for the first half of the evaluation
period (i.e. 1986–1999) are summarized as follows: the POD was 31.6% (6 of 19
GLE events); the FAR was 33.3% (3/9); and, the AWT to the first NM’s alert was
13.3 min. There are no forecasting results of the GLE Alert Plus for this period.
For the whole evaluation period, the GLE forecasting performance may be
summarized as follows: the POD was 40.6% (13 of 32); the FAR was 31.6% (6
of 19); and, the AWT to the first NM’s alert was 10.5 min. Note that the FAR of
the most recent period is similar to that of the oldest period (30.0% vs. 33.3%);
however, the POD of the most recent period (i.e. 53.8%) is better than the POD
of the oldest period (i.e. 31.6%). We do not know the reason for the better POD
performance in the most recent period; nevertheless, we think that the use of a
more recent and refined instrument technology and/or more experienced calibration
procedures yields better forecasting performance.

7.6 Concluding Remarks
We experimented the use of microwave time histories in the UMASEP prediction
scheme of the occurrence of SEP events. The test run over 13 months shows that
microwaves provide a comparable probability of detection, but a reduced falsealarm ratio as compared to the time derivative of the SXR flux, which is used in
the traditional UMASEP scheme.
The reduction of false alarms is due to the fact that microwave bursts are signature of non-thermal particle acceleration and are less frequent than the ubiquitous
thermal soft X-ray brightenings. This reduces the probability to interpret the chance
coincidence between a rise of the radiative signature and the rise of the particle
intensity at the spacecraft as an indication of a magnetic connection. The forecasting
scheme using microwaves fails when the microwave emission is thermal and slowly
rising. This is especially the case when SEP events are related to the eruption of
quiescent filaments.
A second test of microwave patrol observations in SEP forecasting was conducted with the aim to predict the hardness of proton spectra using the ratio of
peak flux densities at 15.4 and 8.8 GHz: the expectation was to find a preferential
association of hard proton spectra with microwave bursts that are particularly strong
at 15.4 GHz, as had been shown in previous activity cycles (Chertok et al. 2009).
We were unable to confirm this expectation: we found no significant correlation
between the proton spectral hardness and the microwave flux density ratio. The
intrinsic variations from event to event are much stronger than any underlying trend
that might exist.
The radio patrol observations used by our study are carried out with rather
simple patrol instruments, which monitor the whole Sun flux density using parabolic
antennas with a typical size of 1 m. Such data are presently not provided in real
time, but there is no technical obstacle to do so. But the results of our test run for the

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M. Núñez et al.

prediction of well-connected SEP events show that microwave observations have
the potential to improve SEP forecasting. An interesting perspective could be the
combination of the REleASE and UMASEP forecasting schemes, because, on one
hand they could correlate rises between microwaves at the Sun and electrons, and
on the other hand, forecasts may be provided for those SEPs whose parent solar
event is behind the limb. This combination of schemes could bring a major gain in
advance warning time.
The HESPERIA REleASE tools make real-time predictions of the proton flux
(30–50 MeV) at Lagrangian point 1 and are available via the HESPERIA web site.3
An analysis of historic data from 2009 to 2016 has shown that the forecast tools
have a low FAR (30%) and a high POD (63%).
The HESPERIA UMASEP-500 model makes real-time predictions of the occurrence of >500 MeV SEP and GLE events from the analysis of SXR and differential
proton flux measured by the GOES satellite network. Real-time predictions are
available in the HESPERIA web site.4 We assume that a prediction is successful
when it is reported before the first GLE alert is issued by any NM station. Regarding
the prediction of GLE events for the period 2000–2016, this tool had a POD of
53.8%, and a FAR of 30.0%. For this period, the tool obtained an AWT of 8 min
taking as reference the alert time from the first NM station; taking as reference the
time of the warnings issued by the GLE Alert Plus for the aforementioned period,
the HESPERIA UMASEP-500 tool obtained an AWT of 15 min.
In summary, the goal of the presented tools has been to improve mitigation of
adverse effects both in space and in the air from a significant solar radiation storm,
providing valuable added minutes of forewarning to space weather users.

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Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0
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the copyright holder.

Chapter 8

X-Ray, Radio and SEP Observations
of Relativistic Gamma-Ray Events
Karl-Ludwig Klein, Kostas Tziotziou, Pietro Zucca, Eino Valtonen,
Nicole Vilmer, Olga E. Malandraki, Clarisse Hamadache, Bernd Heber,
and Jürgen Kiener
Abstract The rather frequent occurrence, and sometimes long duration, of  ray events at photon energies above 100 MeV challenges our understanding of
particle acceleration processes at the Sun. The emission is ascribed to pion-decay
photons due to protons with energies above 300 MeV. We study the X-ray and radio
emissions and the solar energetic particles (SEPs) in space for a set of 25 Fermi
 -ray events. They are accompanied by strong SEP events, including, in most cases
where the parent activity is well-connected, protons above 300 MeV. Signatures of
energetic electron acceleration in the corona accompany the impulsive and early
post-impulsive  -ray emission.  -ray emission lasting several hours accompanies
in general the decay phase of long-lasting soft X-ray bursts and decametric-tokilometric type II bursts. We discuss the impact of these results on the origin of
the  -ray events.

K.-L. Klein () • N. Vilmer • P. Zucca
LESIA-Observatoire de Paris, CNRS, 92190 Meudon, France
PSL Research University, Universités P & M. Curie, Paris-Diderot, Meudon, France
e-mail: ludwig.klein@obspm.fr; pietro.zucca@obspm.fr; nicole.vilmer@obspm.fr
K. Tziotziou • O.E. Malandraki
National Observatory of Athens, IAASARS, Athens, Greece
e-mail: kostas@noa.gr; omaland@astro.noa.gr
E. Valtonen
Department of Physics and Astronomy, Space Research Laboratory, University of Turku, Turku,
Finland
e-mail: eino.valtonen@utu.fi
C. Hamadache • J. Kiener
CSNSM, IN2P3-CNRS, Univ. Paris-Sud, 91405 Orsay Cedex, France
e-mail: clarisse.hamadache@csnsm.in2p3.fr; Jurgen.kiener@csnsm.in2p3.fr
B. Heber
Christian-Albrechts-Universität zu Kiel, Kiel, Germany
e-mail: heber@physik.uni-kiel.de
© The Author(s) 2018
O.E. Malandraki, N.B. Crosby (eds.), Solar Particle Radiation Storms Forecasting
and Analysis, The HESPERIA HORIZON 2020 Project and Beyond, Astrophysics
and Space Science Library 444, DOI 10.1007/978-3-319-60051-2_8

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8.1 Introduction
The advent of the Fermi mission showed that the Sun is an occasional, but unexpectedly frequent, emitter of  -ray photons above 100 MeV. These are understood to
be produced by pion decays in nuclear interactions involving protons or He-nuclei
at energies above 300 MeV/nucleon. One did not expect that the Sun was able to
accelerate relativistic protons and nuclei even in seemingly modest flares. These
particles are rarely detected in space (<1 event per year). Furthermore, the duration,
several hours, of some  -ray events is much longer than that of hard X-ray signatures
of electron acceleration in the impulsive flare phase.
The question of how the  -ray emission is related to other signatures of particle
acceleration and energy release in the corona is crucial to understanding the origin of
the high-energy protons. It might also be expected that such high-energy populations
interacting at the Sun are accompanied by particularly energetic solar energetic
particle (SEP) events. This chapter is based on 25 events. The Fermi/LAT temporal
data were made available to the HESPERIA project by G. Share prior to their
publication in a comprehensive paper (Share et al. 2017). The present chapter
introduces the relevant process of emission and pre-Fermi observations of piondecay  -rays (Sect. 8.2), and gives an overview of the Fermi/LAT observations
(Sect. 8.3). Section 8.3 was prepared by Gerald Share and Ron Murphy. Related
X-ray and radio observations and associated SEP events are presented in Sects. 8.4
and 8.5, respectively. Preliminary conclusions on the interpretation of the  -ray
events are in Sect. 8.6.

8.2 Theory and Early Observations of Gamma-Ray Emission
at Photon Energies >60 MeV
On 1982 Jun 3 the gamma-ray spectrometer on the Solar Maximum Mission satellite
observed emission from 0.3 to 100 MeV from a X8.0 GOES-class flare (Forrest
et al. 1986). The impulsive flare lasted about 1 min and was followed by a distinct
harder emission phase that peaked in about 1 min and lasted for over 15 min.
The energy spectrum of this sustained emission displayed a characteristic hump
at photon energies above 60 MeV (Fig. 8.1a), which appeared to be consistent with
that from pion-decays produced by the interaction of >300 MeV protons in the
solar atmosphere (Forrest et al. 1985, see below); the authors speculated whether the
emission might be associated with the acceleration of solar energetic particles. There
were several more of these events in the ensuing years, all associated with intense
X-class flares, that were summarized in a paper entitled “Long-Duration Solar
Gamma-Ray Flares” (LDGRFs) (Ryan 2000). Various origins were suggested, and a

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Fig. 8.1 (a) The -ray spectrum showing the pion-decay bump of the 1982 Jun 3 event, observed
by SMM (Forrest et al. 1985). Credit: Forrest et al., Internat. Cosmic Ray Conf. 4, 146, 1985,
courtesy W.T. Vestrand. (b) Time profile of the first sustained -ray event detected by the Compton
Gamma-Ray Telescope (adapted from Kanbach et al. (1993); credit: Kanbach et al., A&A Suppl.
97, 349, 1993, reproduced with permission ©ESO)

key question was whether such emission would be observed when the accompanying
flare was weaker and did not produce impulsive gamma radiation.
Detection of such events continued with observations from GAMMA-1 (Akimov
et al. 1992), the Compton Gamma-Ray Observatory (CGRO) (Mandzhavidze and
Ramaty 1992; Kanbach et al. 1993; Dunphy et al. 1999), GRANAT (Debrunner
et al. 1997; Vilmer et al. 2003), CORONAS-F (Kuznetsov et al. 2011; Kuznetsov et
al. 2014). Around 20 events had been observed then with significant emission above
60 MeV from pion decay radiation (see Lockwood et al. 1997; Chupp and Ryan
2009; Vilmer et al. 2011 for reviews). For some of the events, pion decay radiation
is observed during the impulsive phase of the event as defined by the production of
hard X-rays above 100 keV. In some events, high energy emissions had also been
observed for hours after the impulsive phase of the flare, revealing that high energy
ions are present on time scales of several hours (e.g. Kanbach et al. 1993; Ryan et al.
1994; Ryan 2000; Rank et al. 2001).

8.2.1 Pion-Decay -Ray Emission
High-energy (>60 MeV) emission in solar flares results from nuclear interactions of
mildly relativistic ions (above a few hundred MeV/nucleon) with the ambient solar
atmosphere (most probably the dense chromosphere). These nuclear reactions result
in the production of pions. Charged pions decay to electrons and positrons, which
produce  -ray emissions through bremsstrahlung radiation. Energetic positrons also

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contribute to the  -ray continuum by annihilating in flight. The neutral pions decay
in two photons, one being emitted at high energies. The result is a very flat spectrum
with a broad-bump feature with a maximum at 67 MeV (Murphy et al. 1987). In a
magnetized region, synchrotron losses of electrons and positrons may be important
and reduce their contributions with respect to the radiation from neutral-pion decay
(Murphy et al. 1987; Vilmer et al. 2003). When energetic electrons are present
at energies above 10 MeV, they produce bremsstrahlung emission above 10 MeV
(Chap. 2), which may mask pion-decay radiation.
Early work on the modelling of pion decay radiation and  -ray emission
(produced by >10 MeV ions) (Murphy et al. 1997) gave a first determination of the
high energy spectrum of ions in flares. Assuming a spectral shape for the energetic
ions (either a Bessel function or a power law), number and spectra of energetic
protons were estimated for both the impulsive and the extended phase of the first
detected event (1980 Jun 21) and showed that the proton spectrum was steeper in
the impulsive phase than in the later, so-called ‘extended’ phase. This evolution of
the ion spectrum in the extended phase was confirmed by further observations such
as the ones of the 1991 Jun 11 event by CGRO/EGRET (Dunphy et al. 1999).
Quantitative analysis of several events with significant pion production
has been performed providing information on the ion energy spectrum above
300 MeV/nucleon and allowing a comparison of this spectrum with the one
deduced at lower energies from  -ray line spectroscopy (see, e.g., Alexander
et al. 1994; Dunphy et al. 1999; Kocharov et al. 1994, 1998; Vilmer et al. 2003).
These comparisons have shown that the ion energy distribution does not have a
simple power-law form from the  -ray line producing energy domain (1–10 MeV)
to the pion-producing energy domain (>300 MeV/nucleon).

8.2.2 Long-Duration -Ray Events
Even before the Fermi era, a few events had been observed where enhanced piondecay radiation lasted several hours, and the question of the origin of these long
duration events had been examined. On 1991 Jun 11 (Fig. 8.1b) emission above
50 MeV was detected for almost 8 h after the flare by COMPTON/EGRET. Several
interpretations had been proposed to explain these long duration emissions, either
the continuous acceleration of protons above 300 MeV (e.g., Ryan and Lee 1991)
or the trapping of protons on very long time-scales. In particular, Mandzhavidze
and Ramaty (1992) showed that the long duration phase could be explained by
the injection of energetic protons in the impulsive phase and subsequent trapping.
An efficient trapping on such long timescales required a strong mirror ratio in the
trapping region (>10) as well as a coronal density less than 5  1011 cm3 . The
question of how trapped particle populations could remain stable over hours was,
however, not explained satisfactorily. An observational justification of continuous
time-extended acceleration came from the discovery of sustained  -ray events of
moderate duration (1–2 h), which were accompanied by non-thermal microwave
emission (Kocharov et al. 1994; Trottet et al. 1994; Akimov et al. 1996).

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8.3 New Insights of Sustained Emission Events from Fermi
Observations
With the launch of the sensitive Fermi Large Area Telescope (LAT) (Atwood et al.
2009), it became possible to observe weak  -ray emission from the Sun due to its
large effective area and aperture, and excellent background rejection. This permitted
detection of quiescent  -ray emission from cosmic-ray protons interacting in the
solar atmosphere and cosmic-ray electrons interacting with sunlight (Abdo et al.
2011) with fluxes of 5 and 7 107  cm2 s1 , respectively. LAT first detected
transient >100 MeV solar  -rays on 2010 Jun 12 from the impulsive M2 class
flare (Ackermann et al. 2012a,b) during an 50 s period. The emission was delayed
about 10 s from the associated hard X-ray and nuclear-line emission and there was
no evidence for any >100 MeV  -ray emission in the hours after the flare. The
Fermi/LAT team reported the detection of 18 >100 MeV events associated with
solar flares covering the time period from 2008 August to 2012 August (Ackermann
et al. 2014) which they classified as being impulsive, sustained, or delayed. In
some cases they categorized the events as having both impulsive and sustained
characteristics. Only three of the events were classified as only having an impulsive
component. We prefer to use the name “sustained” to categorize all emission that is
distinct from the impulsive flare independent of its duration.
Details of the 2011 Mar 7 and 2011 Jun 7  -ray observations and related solar
measurements were also presented in Ackermann et al. (2014). The March 7 event
was reported as having both impulsive and sustained emission components, while
the June 7 event was classified as only having sustained emission because  -rays
were detected in only one LAT exposure about 1 h after the flare and there was
no exposure to the flare. The  -ray spectra were fit by two empirical models, a
power law and a power law with exponential cutoff; and a physical pion-decay
spectrum based on Murphy et al. (1987). Only heuristic arguments were presented
to justify that the observed spectrum was from pion decay and not from electron
bremsstrahlung. There was clear evidence for spectral softening over the 13 h period
that the March 7 event was observed. As LAT’s instrumental point spread function
is about 1ı , even above 1 GeV, only the location of the centroid of the  -ray source
could be deduced. The centroids of both sources were consistent with the active
regions with uncertainties on the scale of a solar quadrant.
Ajello et al. (2014) reported detection on 2012 Mar 7 by LAT of what appeared
to be distinct impulsive and sustained-emission phases associated with X5.4 and
X1.3 (actually about M7 when the tail of the X5 flare is subtracted) flares, CMEs
with speeds of about 2700 and 1800 km s1 , and a strong solar energetic particle
event. The  -ray flux was one of the brightest observed by LAT; it lasted close to
20 h and the fitted spectrum again softened with time. The time integrated centroid
of the emission was consistent with the location of the flares with a 1  uncertainty
of 10ı. There is evidence that the source of the emission moved from the eastern
to the western hemisphere about 7 h following the flares. Once again there was no
information on the spatial extent of the emission.

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With detection of >100 MeV  -ray emission associated with two behind-thelimb solar flares, it has become clear that emission can extend as much as 40ı from
the flare site (Pesce-Rollins et al. 2015; Ackermann et al. 2017). The events occurred
on 2013 Oct 11 and 2014 Sep 1 and were associated with fast CMEs and strong solar
energetic particle events. The centroids of the  -ray emission for both events were
close to the solar limb. The centroid for the October 11 event was consistent with the
N21 latitude of the active region, located about 13ı behind the East limb, and its 1
 uncertainty extended to about 50ı East. In contrast, the centroid of the September
1 event was significantly north (15ı) of the flare site that was located about 35ı
behind the East limb.
More information on the characteristics and origin of these solar  -ray events
became available with the completion of a comprehensive study of 29 sustained
emission events observed by LAT between 2008 and 2016 (Share et al. 2017). This
study indicates that the emission is not spatially distributed globally on the Sun
but is probably distributed over a few tens of degrees around the centroid location.
From this study it is also clear that the sustained >100 MeV emission is temporally
distinct from the impulsive flare phase, which often emits hard X-rays extending
only to hundreds of keV. The time profile of the first event observed by LAT on
2011 Mar 7, discussed above and plotted in Fig. 8.2, provides an example of such a
distinct sustained-emission phase. While the analysis done by Share et al. (2017) is
different from that of Ackermann et al. (2014), it uses the same source-class data and
yields comparable fluxes and spectral results. It is simply a ‘light-bucket’ in which
photons arriving with directions <10ı of the Sun are accumulated, as long as the
Sun is far from the Earth’s horizon. The main plot in Fig. 8.2 shows the hours-long
time profile of this 13 h event with LAT solar exposures every 3 h. The background
level contains roughly equal contributions from the quiescent Sun, and Galactic and
extra-galactic  rays. The emission began during the time of the GOES flare and
rose to peak about 6 h later.
The inset in Fig. 8.2 shows >100 MeV fluxes plotted at 4 min resolution after the
hard X-ray peak of the March 7 flare. For comparison, the dotted line follows the
high-energy time profile observed in the 1991 June 11 event which exhibited both
impulsive emission and sustained emission lasting 8 h. The >100 MeV emission on
March 7 appears to increase during the observations after the impulsive phase. There
is also no evidence for nuclear line emission during the impulsive flare, suggesting
that >1 MeV protons were not present in significant numbers. A limit on the
2.223 MeV neutron capture line during the flare suggests that the flare had at most
only 20% of the number of >500 MeV protons observed in the sustained emission
phase (Share et al. 2017). This indicates that only sustained >100 MeV emission
was observed by LAT on March 7, in contrast to what was reported by Ackermann
et al. (2014). The same conclusion can be reached about other events reported by
Ackermann et al. (2012b) to have impulsive >100 MeV phases. Specifically, Share
et al. (2017) find that the first >100 MeV outburst on 2012 Mar 7 described in
detail by Ackermann et al. (2014) was distinct sustained emission and not directly
associated with the X5.4 flare.

8 X-Ray, Radio and SEP Observations of Relativistic Gamma-Ray Events
4×10 -5

Flux, γ cm-2 s-1

4×10 -5

3×10 -5

Flux, γ cm-2 s-1

139

2×10 -5

3×10 -5

X

2×10 -5

M

1×10 -5

C

0

19:45

20:00

20:15

20:30

20:45

B
21:00

Time (Start at 07-Mar-11 19:40:00)

1×10 -5

08:00

18:00

04:00

14:00

00:00

10:00

Time (Start at 07-Mar-11 04:00:00)
Fig. 8.2 Time history of the >100 MeV flux from 10ı of the Sun revealing the 2011 Mar 7
LAT event (data points and ˙1 statistical uncertainties). Vertical dashed lines show the GOES
start and end times. The inset shows 4-min accumulation LAT data points and the merged and
arbitrarily scaled >100 keV count rates observed by RHESSI and Fermi/GBM during the impulsive
flare. The dashed curve shows the GOES 1–8Å profile (scale on right ordinate) and the <  >
symbol shows the range in CME onset times in the CDAW catalog derived for linear and quadratic
extrapolations. The vertical solid arrow depicts our estimate of the CME onset from inspection
of SDO/AIA images and the vertical dashed arrow shows the estimated onset of Type II radio
emission

Share et al. (2017) also find that 19 of the 29 sustained-emission events had time
profiles distinct from the impulsive phase and most of these had onset times after the
hard X-ray peaks. For the remaining events, there were not enough data to determine
whether the sustained emission was distinct from or primarily associated with the
impulsive phase, but in no case is there clear evidence that the sustained emission is
the tail of the impulsive flare.
Pion-decay spectra from protons having different power-law spectral indices fit
the spectra from the 2011 Mar 7 event and the other 28 events (Share et al. 2017).
In general the results are consistent with those obtained by Ackermann et al. (2014,
2017) and Ajello et al. (2014). In addition, Share et al. (2017) demonstrated that
only pion-decay spectra are consistent with the brightest sustained emission events
and that any plausible electron bremsstrahlung spectra are not. Using nuclear line
observations during these same bright sustained emission events, it was also possible
to demonstrate that the proton spectra from 10 to 300 MeV were flatter than the
spectra at higher energies. In addition to the two events found to have spectra that
softened with time, Share et al. (2017) found two more that softened in time and
two that hardened in time.

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Detailed spectroscopic studies of many of the events observed by LAT revealed
that the number of >500 MeV protons producing the sustained emission was
typically at least a factor ten more than found in the accompanying impulsive flare.
This is consistent with the distinctly different nature of the time profiles of the
impulsive flares and the sustained emission discussed above. As Share et al. (2017)
discuss, it is now clear that another energy source is necessary to accelerate protons
to energies >300 MeV in order to produce the pion-decay emission observed in
the sustained events. These energetic considerations and the rise in sustained  ray emission following the impulsive phases in many events suggests the likely
source of the energy is the accompanying fast CME, possibly through its shock
that is thought to produce gradual SEPs. The authors (Share et al. 2017) find that
the number of >500 MeV SEP protons is on average about 100 times the number
returning to the Sun to produce the sustained  -ray emission. This is consistent with
what shock wave models estimate (Kocharov et al. 2015).
The 2013 Oct 13 and 2014 Sep 1 behind-the-limb events (Ackermann et al. 2017)
were also studied by Share et al. (2017). The time profile of the latter event, which
lasted at least 2 h, is plotted in Fig. 8.3. Both >100 MeV  -ray and >100 keV
electron bremsstrahlung rose about 7 min following the impulsive hard X-ray flare,
as inferred from SAX observations on MESSENGER (Schlemm et al. 2007). The
bremsstrahlung extended up to at least 10 MeV and is consistent with production by

0.006
0.005

Flux, γ cm-2 s-1

Flux, γ cm-2 s-1

10

-3

0.004
0.003
0.002

10 -4
0.001
0.000
11:00

11:10

11:20

11:30

11:40

Time (Start at 01-Sep-14 10:50:00)

10 -5

10 -6
06:00

09:00

12:00

15:00

18:00

21:00

0:00

Time (Start at 01-Sep-14 06:00:00)
Fig. 8.3 Time history of the >100 MeV flux of the Sun revealing the 2014 Sep 1 LAT event (data
points and ˙1 statistical uncertainties). Vertical dashed lines show the soft X-ray start and end
times from MESSENGER/SAX. The inset shows 1-min accumulation >100 MeV data points (˙1
statistical uncertainties) and the arbitrarily scaled 100–300 keV count rates observed by GBM. The
dashed curve shows the soft X-ray profile from SAX and the thin solid curve its derivative. The
vertical solid arrow depicts our estimate of the CME onset from inspection of SDO/AIA images

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electrons interacting in a thick target, indicating the electrons were produced by the
same CME shock that accelerated the protons producing the sustained  radiation
(Share et al. 2017). This conclusion is consistent with the finding that a direct
magnetic connection exists between the shock wave and the low solar atmosphere
at the onset of the hard X-rays and  -rays in both behind the limb events (Plotnikov
et al. 2017).
The conclusion reached by Share et al. (2017) is that the sustained emission
events are likely due to shock-accelerated particles, associated with those in SEPs,
that are imparted to field lines that return to the Sun and those that return to the Sun
on open field lines from an SEP reservoir. This interpretation will be discussed in
Sect. 8.4.

8.4 Multiwavelength Observations of Fermi/LAT ”-Ray
Events
In this section we examine the relationship between the  -ray events and other
manifestations of energy release in the corona, namely heating as revealed by soft
X-ray bursts, and electron acceleration traced by hard X-ray and radio emission.
We use especially hard X-ray observations from RHESSI (Lin et al. 2002) and
INTEGRAL/ACS (Rodríguez-Gasén et al. 2014), whole-Sun radio fluxes from the
RSTN and Nobeyama Observatories (Torii et al. 1979; Nakajima et al. 1985) on
ground, and from the radio spectrographs aboard Wind (Bougeret et al. 1995) and
STEREO (Bougeret et al. 2008).
At decametric and longer waves (referred to as DH in the following) all 25  -ray
events were accompanied by type III bursts, and 23/25 by type II bursts. The type III
bursts show that electrons (particles) had access to open field lines during all  -ray
events. The bursts occurred in general during the impulsive and early post-impulsive
phase of the parent flare, as commonly observed in SEP events. They were not found
later on during long-duration  -ray events. The presence of type II bursts shows that
shock waves in the high corona are a common counterpart of  -ray events. Metric
continuum emission (type IV bursts) is observed in some events.

8.4.1 Impulsive and Early Post-impulsive -Ray Emission
A rare Fermi/LAT observation showing a  -ray event during and after the impulsive
flare phase is illustrated in Fig. 8.4. Hard X-rays (INTEGRAL/ACS, photon energies
>80 keV; Rodríguez-Gasén et al. 2014) rise and decline during the rise of the
soft X-ray flux, as do the radio flux densities at 15,400 and 8800 MHz. The
 -ray emission, which is observed with much poorer time coverage, shows a
similar rise and initial decay, but then stays on an enhanced level until the end of

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Fig. 8.4 Time evolution of the high-energy -ray, X-ray and radio emission in the impulsive and
early post-impulsive phase of a flare

the observations. This long persistence is the key feature of the sustained events
introduced in Sect. 8.3. While the microwaves 8800 MHz show no counterpart,
emissions at 2695 and 245 MHz have a prolonged tail that accompanies the
observed part of the post-impulsive  -ray emission. Renewed energy release after
the impulsive phase is also suggested by the bump in the decaying soft Xray profile. The continued emission of both pion-decay  -rays and microwaves
in the early post-impulsive phase is consistent with the earlier observations by
GAMMA1 (Kocharov et al. 1994; Akimov et al. 1996) and SMM (Trottet et al.
1994).

8.4.2 Long-Duration -Ray Events
As shown in Fig. 8.2,  -ray emission may rise again well after the impulsive phase.
Among the 25  -ray events studied, a total of twelve had duration longer than 2 h.
Long-duration  -ray emission occurs most often during the decay of the associated
soft X-ray burst, as illustrated in Fig. 8.5. In EUV images taken by AIA/SDO or
SWAP/Proba2 the decay of the soft X-ray bursts is accompanied by the formation
of post-flare loop arcades.
Although there is still some microwave burst activity at low frequencies
(2.695 MHz) in Fig. 8.5, the long-duration  -rays are in general not accompanied
by time-extended or recurrent hard X-ray or microwave burst activity. On 2011 Mar
7 the long-duration  -rays are accompanied by several flares, rather than the decay
of a single soft X-ray burst. But the microwave or hard X-ray emissions are weak,
and in any case are only observed during a short fraction of the  -ray event. In

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Fig. 8.5 Time evolution of the high-energy -ray, soft and hard X-ray and radio emission from
the impulsive phase throughout the rise and decay of sustained -ray emission

summary, we find no evidence of repeated efficient electron acceleration in the low
corona during most parts of this or any other long-duration  -ray event.

8.4.3 Soft X-Ray Bursts and -Ray Events
The close relationship between the durations of  -ray and soft X-ray emissions is
confirmed by the quantitative analysis of the decay profiles of soft X-ray bursts
associated with  -ray events: short duration  -ray bursts (<2 h; the exact duration
is difficult to determine because of gaps in the solar observations of Fermi/LAT)
are found to have relatively short soft X-ray decay phases, while the long  -ray
events accompany comparatively long soft X-ray decay phases. There are some
intermediate events, showing the distribution of burst durations is not bimodal. But
it is clear from this observational analysis that long-duration  -ray events tend to be
associated with long-duration energy release in the solar corona.
Although the long-duration  -ray emission may start more than an hour after the
peak of the associated soft X-ray burst, the logarithms of the peak fluxes of the two
emissions correlate, with a linear correlation coefficient 0.72, and a probability that
the same or a higher value is obtained from two unrelated samples of 0.8%. The
corresponding values for the CME speed and the logarithm of the  -ray peak flux
are 0.61 and 3.7%, respectively. These are rough evaluations, because the  -ray time
profile is not densely covered by the Fermi/LAT observations, and the peak fluxes
are only lower limits.

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Fig. 8.6 Time history of high-energy -rays and the decametric-hectometric radio emission,
showing a type II burst accompanies the -rays. The grey vertical stripes in the bottom panel
show time intervals of unfavourable solar observing conditions for Fermi/LAT

8.4.4 Coronal Shock Waves and -Ray Events
The only signature of electron acceleration that we found to accompany long-lasting
 -ray emission are DH type II bursts, which are ascribed to CME-driven shocks
(Reiner et al. 2007). The type II burst in Fig. 8.6 mostly shows up as a sequence
of patches after 7 UT that gradually drift from higher to lower frequencies. The
noticeable fact is that this emission persists throughout the several hours duration of
the  -ray emission.
It is tempting to interpret the association between sustained  -ray events and DH
type II bursts as evidence that the CME shock accelerates protons to relativistic
energies, which then stream back from the downstream region of the shock to
the low solar atmosphere, where they create pions (see Sect. 8.3 and Chap. 9). We
consider in the following the implication of this interpretation on the number of
particles that must be present in the downstream region of the shock in order to
account for the observed  -ray emission. To this end we analyze the events with a
long duration sustained emission that occurred on 2011 Mar 7, 2012 Jan 23, Mar 5
and May 17.
All four events were accompanied by CMEs well-observed by the LASCO
coronagraphs. The quasi-parallel shock often invoked as the site of SEP acceleration
is expected to be located around the summit of the CME, following the trajectory

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shown by the height-time curves given in the LASCO CME catalogue.1 The type
II source is usually believed to be located in the quasi-perpendicular region of the
shock (Pulupa and Bale 2008), hence on the flank of the CME rather than near its
summit. We therefore considered separately the heights of the CME estimated by
the LASCO catalogue and of the type II source, inferred from the electron density
model of Leblanc et al. (1999), both at the peak of the long-duration  -ray emission.
The heliocentric distances of the CME apices range from 11 Rˇ to 26 Rˇ , those of
type II sources from 7 Rˇ to 18 Rˇ .
Particles accelerated at the shock must hence stream to the solar chromosphere
over a distance of many solar radii without being mirrored by the magnetic field
before. This implies that they are injected into coronal magnetic field lines near the
shock with a pitch angle smaller than some limiting value ˛0 such that sin2 ˛0 D
B.r/=B.Rˇ /. The magnetic field decreases outward from the low corona with some
power of the heliocentric distance r. If we just extrapolate the radial component
of the solar wind magnetic field back to the photosphere, hence assuming that
B.r/  r2 , the maximum pitch angles allowed for protons that reach the low solar
atmosphere are 2ı –5ı when the particles start from the CME apex, and 3ı –8ı when
they start from the type II source. Hence only protons injected nearly parallel to the
coronal magnetic field lines near the shock can reach a sufficiently dense part of the
solar atmosphere to undergo nuclear reactions. If we suppose that the protons are
isotropically distributed at the shock, only a fraction 1cos ˛0 is expected to achieve
this. This fraction is 1% of the initial population for ˛0 D 8ı (6  104 for ˛0 D 2ı ).
It will be further reduced by the expected stronger decrease of the magnetic field
within the solar wind source surface.

8.5 Solar Energetic Particle Events Associated
with Fermi/LAT Gamma-Ray Events
All Fermi/LAT  -ray events discussed in Sect. 8.3 are associated with SEP
events observed at 1 AU from the Sun, by instruments at L1 or by the twin
STEREO spacecraft, or both. Proton and/or electron enhancements are observed
with SoHO/ERNE (Torsti et al. 1995), STEREO/LET (Mewaldt et al. 2008),
STEREO/HET (von Rosenvinge et al. 2008), STEREO/SEPT (Müller-Mellin et al.
2008), and ACE/EPAM (Gold et al. 1998) over a wide range of energy (55 keV to
4 MeV for electrons and 1.6 to 130 MeV for protons). Higher energy protons are
available from SoHO/EPHIN (penetrating protons at 100–1000 MeV energies) as
well as from GOES/HEPAD (only for 9 of the 25 investigated Fermi/LAT events,
see Fig. 8.7 for an example) in three differential energy channels ranging from 330
to 700 MeV and an integral channel >700 MeV.

1

https://cdaw.gsfc.nasa.gov/CME_list/.

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Fig. 8.7 GOES 15/HEPAD proton fluxes on 2012 May 17. The vertical purple dashed and the red
dotted lines indicate respectively the flare onset and the derived SEP onset with the sigma-method
(see text)

8.5.1 SEP Characteristics and Association with Fermi/LAT
Most of the SEP events show a slow rise phase, but some show a fast rise phase
in all observed energy ranges (see Reames 1999 for a review on general SEP
characteristics). This distinction is somewhat subjective, but we mean by “fast” a
rise in 2–3 h, and by “slow” a rise within several hours, sometimes one day. Onset
times for all observed SEP events can be derived either by implementing a threshold
to be exceeded by the flux as described in Malandraki et al. (2012) or a PoissonCUSUM analysis (Huttunen-Heikinmaa et al. 2005). For SEP events with a fast rise
a velocity dispersion analysis (VDA) can be used (Krucker et al. 1999; Malandraki
et al. 2012) to estimate both the release time at the Sun and the apparent path length
of the particles: the solar release time of the first particles seen at the spacecraft
is obtained from a linear fit of the derived onset times of electrons and protons at
different energies as a function of their respective inverse velocity. Such an analysis
could only be performed for 11 of the 25 Fermi/LAT events. For a comparison of
derived release times with photon arrival times measured at the observer’s distance
(1 AU) we add 8 min.
Hereafter, we will discuss the events of 2011 Mar 7, 2012 Mar 7, 2013 Apr 11 and
2014 Feb 25, for which a VDA analysis could be performed at L1 and/or STEREO,
as well as the events of 2012 Jan 23 and May 17 that are of particular interest
for numerical transport simulations discussed in Chap. 9. Table 8.1 gives the date
and location, soft X-ray class, start and peak time, start and end of the decametricto-hectometric type III bursts and CME speed from the LASCO/CME catalogue.
SEP parameters are given for STEREO A and B (STA, STB), for SoHO/ERNE or
ACE/EPAM at L1, and for GOES/HEPAD (HEP) such as the characterization of the

8 X-Ray, Radio and SEP Observations of Relativistic Gamma-Ray Events

147

Table 8.1 Characteristics of the 6 SEP event cases discussed in this section (see text for further
information)

Date
2011 Mar 7

Soft X-rays
Class
Start
CME
Location Peak DH III
[km s1 ]
M3.7
19:43 19:50–20:10 2125
N30W47 20:58

23 Jan 2012

M8.7
03:38 03:40–04:20 2175
N33W21 04:34

2012 Mar 7

X5.4
N17E27
X1.2
N17E27
2012 May 17 M5.1
N07W88

00:02 00:15–01:00 2864
00:40
01:05 01:15–01:30 1825
01:23
01:25 01:30–01:40 1582
02:14

2013 Apr 11 M6.5
N07E13

06:55 07:00–07:30
07:29

25 Feb 2014

00:39 00:45–01:15 2147
01:03

X4.9
N00E78

861

SEP
(s/c, rise, energy)
STA (s) 60 MeV
L1 (f)  80 MeV
HEP no detection
STB (f) 60 MeV
STA (s) 100 MeV
L1 (f) 100 MeV
HEP (s)  600 MeV
weak
STB (s) 100 MeV
STA (s) > 130 MeV
L1 (s) >100 MeV
HEP (s) >700 MeV
STB (f) >100 MeV
STA (s) 100 MeV
L1 (f)  130 MeV
HEP (f) >700 MeV
STB (s) 100 MeV
STA (s) weak
L1 (f)  130 MeV
HEP very weak 600
MeV
STB (f) 100 MeV
STA (f) 100 MeV
L1 (s)  130 MeV
HEP very weak
STB (f) 100 MeV

SRT + 8 min
[min]
–
20:26˙00:04
–
–
–
–
–
–
–
23:21˙00:51
–
00:37˙00:01
–
–
–
–
–
07:24˙00:08
–
07:10˙00:01
01:06˙00:01
01:22˙00:20
–
00:56˙00:01

SEP flux rise as “fast” (f) or “slow” (s), the approximate energy up to which the
SEPs are observed and the derived solar release time (SRT) from VDA.
2011 Mar 7: The event had moderate SEP flux. The Fermi/LAT sustained emission
(Fig. 8.2) was observed 15 min after the CME onset (defined from inspection of
SDO/AIA images) and peaked several hours later (7 h). The derived SRT from the
L1 observations is 20 min later than the Fermi/LAT emission onset and the particle
path length of 1.9 AU does not indicate substantial scattering.
2012 Jan 23: An intense SEP event was observed by ACE/EPAM at L1. VDA
could not produce reliable SRT results, while GOES/HEPAD indicates a very weak
event with a poorly determined onset (7 h after the flare). The weak event was
preceded by a slow rise right after the flare. The interaction between the parent
CME and a preceding much slower one (1400 km s1 ), associated with an earlier

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K.-L. Klein et al.

M1.1 class flare, may be responsible for both the observed high SEP flux and
the significant changes in the SEP intensity profile (Joshi et al. 2013). Sustained
Fermi/LAT emission was observed 15 min after the hard X-ray flare peak, lasting
for many hours while the delayed observed GOES/HEPAD onset with respect to
the Fermi/LAT onset could be related to this several-hours lasting sustained  -ray
emission.
2012 Mar 7: For the double solar event with considerable SEP flux, GOES/HEPAD
saw a steep rise 6 h after the first flare. It was, however, preceded by a continuous
slow rise starting immediately after the flare, as often observed in eastern SEP
events. According to Kouloumvakos et al. (2016) (a) the first flare/CME was
responsible for the SEP event observed at different spacecraft, (b) the proton SRT
observed by STEREO B is consistent with the arrival of an observed EUV wave on
the Sun at the STEREO-B footpoint, and (c) the considerably delayed SRT at L1
compared to STEREO B suggests a release of particles further away from the Sun
consistent with the timing and location of the shock’s western flank. No plausible
explanations could be derived from the observed behaviour at STEREO A. Our
L1 VDA analysis is not reliable as the derived apparent particle path length is 8
AU. The observed large Fermi/LAT sustained fluxes, peaking after the first flare
and lasting for several hours, have a derived first onset near the first flare peak time,
while the second Fermi/LAT onset is estimated 45 min after the second flare onset.
The derived STEREO B release time is co-temporal, within errors, with the first
Fermi/LAT onset.
2012 May 17: The strong SEP event was associated with the first Ground Level
Enhancement (GLE) of solar cycle 24. VDA could not produce reliable SRTs.
GOES/HEPAD registered a fast rising intense event starting right after the flare
(see Fig. 8.7). The expansion of the shock forming in the corona was studied using
a new technique based on coronal magnetic field reconstructions, full magnetohydrodynamic simulations and multi-point imaging inversion techniques (Rouillard
et al. 2016). This analysis concluded that GeV particles were released when
this shock became super-critical (Mach numbers >3). The magnetic connectivity
between the shock and L1 was established via a magnetic cloud that erupted from
the same active region 5 days earlier. Fermi/LAT observations (Fig. 8.5) indicate
significant sustained emission starting after the flare and lasting several hours, while
the GOES/HEPAD flux onset coincides with the Fermi/LAT emission onset.
2013 Apr 11: A fast-rising strong SEP event was observed at L1 and STEREO B,
but only a small slowly rising one at STEREO A. GOES/HEPAD recorded a very
weak event with a poorly-determined onset 3 h after the flare. By determining the
angular extent of the observed EUV wave and CME, Lario et al. (2014) concluded
that while the particle SRT from STEREO B is within uncertainties consistent
with the arrival of the EUV wave and CME-driven shock at the footpoint of the
spacecraft, the EUV wave did not reach the footpoint of the field lines connecting to
L1; the observed intense SEPs at L1 were most likely originating from the western
flank of the CME-driven shock as it was propagating higher in the corona. Our
analysis indicates (a) a particle release time to L1 that coincides within errors with
the peak of the flare and is at least 15 min later than the SRT from STEREO B and

8 X-Ray, Radio and SEP Observations of Relativistic Gamma-Ray Events

Flux > 100 MeV
[gcm–2s–1]

0.0016

149

FERMI/LAT data
1–min FERMI/LAT data

0.0014

0.0012

0.0010

00:00

01:00
01:30
00:30
Start Time (24–Feb–14 23:37:26)

02:00

Fig. 8.8 Fermi/LAT observations for the 2014 Feb 25 event. Vertical light and dark green lines
indicate respectively the derived STEREO A and B onsets, while purple and orange vertical lines
indicate the respective L1 and Fermi/LAT onsets. Horizontal lines indicate the derived error ranges

(b) an apparent path length of 2.1 AU, consistent with the picture emerging from
Lario et al. (2014). The derived STEREO B SRT coincides precisely with the onset
of the Fermi/LAT sustained emission that lasts for 20 min and peaks a few minutes
after the soft X-ray flux.
25 Feb 2014 (Fig. 8.8): The SEPs rose fast to high fluxes at STEREO A and B,
while a weak slowly-rising event was recorded at L1. GOES/HEPAD showed a very
weak SEP event with a poorly-determined onset >5 h after the flare. According to
Lario et al. (2016), despite the considerable distance between the footpoints of the
field lines connecting the Sun with STEREO A, B and L1 and the small extent of
the observed EUV wave, the expansion of the extended shock, accompanying the
CME, to higher latitudes into the corona determined the release of particles and the
observed intense SEP event. Our analysis indicates a SRT at both STEREO satellites
and L1 well after the flare in accordance to these findings. However, the VDA at L1
and the respective SRT are not reliable as the particle path length is 5.2 AU. Due
to gaps in the observing time, sustained  -ray emission is only observed for a short
time, starting 15 min after the onset of the flare, then peaking and dropping quite
rapidly within 20 min. The STEREO B SRT coincides with the Fermi onset, while
the STEREO A SRT is 10 min later.

8.5.2 SEP Spectra
Event-integrated energy spectra of oxygen, neon, and iron+nickel as a group, and
the abundance ratios Ne/O, (Fe+Ni)/O, and (Fe+Ni)/Ne were investigated by using

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SOHO/ERNE measurements. Heavy ion signatures were searched for in all 25  ray events, and were observed above the quiet-time background in twelve of them.
For events occurring in a close sequence of time it was not possible to distinguish
possible multiple injections of heavy ions that could have been associated with each
individual  -ray event. This was the case, e.g., for the four events during the time
period of 2012 Mar 7–10. The heavy ions observed were associated with the first
 -ray event of this period. Continuous data coverage over an entire event was also
required, and this limited the investigation to eight of the 25  -ray events.
The event-integrated intensities of O, Ne and Fe+Ni were calculated for 10
energy channels between 3.2–160 MeV/nucleon of each ion species by integrating
from the event onset in each energy channel till the time when the backgrounddetrended cumulative intensity at that energy reached 95% of the maximum. Thus,
individual integration times were used for each ion at each energy channel. The
energy spectra were fitted by using double power-law functions by Band et al.
(1993). The fitting procedure gave the low and high-energy spectral indices (a and
b ), the break energy (EB ), and the normalization constant for the spectra. These
quantities for oxygen and iron+nickel are given in Table 8.2 for the events of 2012
Mar 7 and 2013 Apr 11. The measured abundance ratios Ne/O and (Fe+Ni)/O as
function of energy are shown in Fig. 8.9. The  -ray events were characterized by
the peak fluxes of 94105 cm2 s1 (2012 Mar 7) and 3.9105 cm2 s1
(2013 Apr 11) with event durations of 9.9 h and 1.2 h, respectively. Both were
eastern events (Table 8.1).
Figure 8.9 shows that the Ne/O ratios in these two events are similar and roughly
constant (0.2) up to 30 MeV/nucleon, but differ at higher energies with the ratio
decreasing with energy in the 2013 Apr 11 event. On the other hand, the (Fe+Ni)/O
ratios are quite strongly increasing with energy. The ratio is significantly higher in
the event of 2013 Apr 11 than on 2012 Mar 7 reaching the maximum of 0.7 in
the 8–20 MeV/nucleon energy range and then decreasing with energy. The changes
with energy in the abundance ratios and the differences between the two studied
events can be explained by the differences in the energy where the high-energy
spectral index is predominant. The high-energy spectral indices are believed to be
dependent on the contribution of suprathermal flare material in the seed population.
The high (Fe+Ni)/O ratio in the 2013 Apr 11 event indicates a more impulsive
nature and larger flare material contribution in this smaller  -ray event. It should be
noted, however, that both of these events were large proton events lasting for several
days. The abundance ratios can be compared with the average values of Ne/O =
0.157 and Fe/O = 0.131 in gradual solar energetic particle events at energies 2–15

Table 8.2 Heavy ion spectral parameters for the events of 2012 Mar 7 and 2013 Apr 11
Event
2012 Mar 7
2013 Apr 11

Oxygen
a
1:03
1:53

b
5:22
4:01

EB (MeV)
9.8
18

Iron+Nickel
a
b
0:3
4:9
0:2
3:1

EB (MeV)
6:4
3

8 X-Ray, Radio and SEP Observations of Relativistic Gamma-Ray Events
(Fe+Ni)/O ratios: γ–ray events 07–Mar–2012 and 11 Apr–2013
1.0E+01

1.0E+00

07–Mar–2012
11–Apr–2013

1.0E–02

Element abundance ratio

Element abundance ratio

Ne/o ratios:γ–ray events 07–Mar–2012 and 11 Apr–2013
1.0E+01

1.0E–01

151

1.0E+00

07–Mar–2012
11–Apr–2013

1.0E–01

1.0E–02
1

10

100

Energy (MeV/n)

1

10

100

Energy (MeV/n)

Fig. 8.9 Abundance ratios Ne/O and (Fe+Ni)/O for the events of 2012 Mar 7 and 2013 Apr 11

MeV/nucleon (Reames 2014) and Ne/O = 0.478 and Fe/O = 1.17 on the average in
impulsive SEP events (Reames et al. 2014).

8.6 Summary and Discussion
This overview on electromagnetic and SEP signatures that accompany sustained
 -ray emission of 25 events detected by Fermi/LAT is summarized as follows:
• High-energy  -ray emission during the impulsive and early post-impulsive
phase is accompanied by hard X-ray and radio signatures of energetic electron
acceleration in the solar atmosphere. This is similar to the earlier findings for
pion-decay  -ray events (Kocharov et al. 1994; Trottet et al. 1994; Akimov et al.
1996) and GLEs (e.g., Klein et al. 2014). The manifestations in the early postimpulsive phase are visible at lower microwave frequencies than those of the
impulsive phase, and at dm-to-m wavelengths (type IV bursts).
•  -ray emission lasting several hours is not accompanied by similarly extended
emissions in hard X-rays or radio waves. In all cases (but 2011 Mar 7) these longduration events accompany the gradual decay of the soft X-ray flux. Although
the parent soft X-ray burst starts sometimes more than an hour before the longlasting  -ray enhancement, there are statistical relationships between (1) the
importance of the parent soft X-ray burst and the peak flux of the long-duration
 -ray emission, and (2) the duration of the decay phase of the soft X-ray burst
and the duration of the long-duration  -ray emission.
• The 2011 Mar 7  -ray event was accompanied by several distinct flares. But only
the first of them showed conspicuous hard X-ray and radio emission. There is
no indication that the long-lasting  -ray emission could be understood as the
superposition of several successive acceleration episodes in independent flares.
• Besides decaying soft X-ray emission and the related post-flare loop arcades, the
only other electromagnetic counterpart of long-duration  -rays are decametricto-hectometric type II bursts. They accompany the  -ray emission of all longduration events.

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• SEP events are associated with all high-energy  -ray events. In most wellconnected  -ray events with long duration GOES/HEPAD detected protons
above 300 MeV, and in several cases above 700 MeV. The 2011 Mar 7  -ray
event is again an exception.
• At energies of several MeV to about 100 MeV the SEP events are strong, but we
found no characteristic feature that distinguishes them from strong SEP events in
general. All are associated with DH type III bursts, as are SEP events in general
(Cane et al. 2010; Vainio et al. 2013). When the solar release time of the first
SEPs could be inferred from velocity dispersion analysis, it was found close to
the interval of the type III bursts. A temporal relationship with the rise of the
late long-duration  -ray emission could not be excluded, but definite evidence
for such a relationship could not be established either.
• The event-integrated abundances of O, Ne, Fe+Ni, and 3 He in the analysed
SEP events show no unambiguous classification with respect to the conventional
impulsive or gradual SEP values. There are, however, significant event-to-event
variations in the 3 He and heavy ion abundance ratios and in their energy
dependence. The sources of these variations and their possible relationships to
the characteristics of the  -ray emission need further analysis.
We conclude from the observations that pion-decay  -rays during the impulsive
and early post-impulsive phase are a manifestation of common particle acceleration
with electrons, seen through hard X-ray and radio emissions. In the post-impulsive
phase the signatures are mostly seen at long-centimetric to metric waves.
The association of  -ray events with soft X-ray emission from the thermal
plasma is not a direct clue to the origin of the mildly relativistic protons. Particle
acceleration at the CME-driven shock in the high corona appears as an attractive
interpretation, because it can explain that  -rays are observed from flares behind
the solar limb (Sect. 8.3) and because type II bursts are the unique systematic
radio counterpart of long-duration  -ray emissions (Sect. 8.4). Stereoscopic CME
observations and sophisticated modelling allow one to estimate Mach numbers.
Modelling of the shock acceleration (Chap. 9) shows that the highest Mach numbers,
observed in restricted regions on the CME surface (Rouillard et al. 2016), may
explain shock-accelerated protons up to GeV energies. This modelling shows
furthermore that magnetic connections exist between the CME shock and the solar
surface (Plotnikov et al. 2017). The interpretation faces two challenges from our
present analysis: First, only a small fraction of the particles at the shock, less than
1% as estimated by a simple model, can reach the low solar atmosphere where
nuclear interactions can take place. This may still be consistent with the estimation
of proton numbers in space and the low solar atmosphere mentioned in Sect. 8.3. The
second challenge is to explain why SEPs were only observed up to about 80 MeV
during the long-duration  -ray event on 2011 Mar 7.
The HESPERIA sample of 25 events is too small to draw firm general conclusions on the origin of high-energy events and their relationship with SEPs. But it
is rich enough to provide constraints on the processes of acceleration and coronal
transport of mildly relativistic protons.

8 X-Ray, Radio and SEP Observations of Relativistic Gamma-Ray Events

153

Acknowledgements The authors are grateful to Gerald Share and Ron Murphy for preparing the
text of Sect. 8.3.

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statutory regulation or exceeds the permitted use, you will need to obtain permission directly from
the copyright holder.

Chapter 9

Modelling of Shock-Accelerated
Gamma-Ray Events
Alexandr Afanasiev, Angels Aran, Rami Vainio, Alexis Rouillard,
Pietro Zucca, David Lario, Suvi Barcewicz, Robert Siipola, Jens Pomoell,
Blai Sanahuja, and Olga E. Malandraki
Abstract Solar  -ray events recently detected by the Fermi/LAT instrument at
energies above 100 MeV have presented a puzzle for solar physicists as many of
such events were observed lasting for many hours after the associated flare/coronal
mass ejection (CME) eruption. Data analyses suggest the  -ray emission originate
from decay of pions produced mainly by interactions of high-energy protons deep
in the chromosphere. Whether those protons are accelerated in the associated flare
or in the CME-driven shock has been under active discussion. In this chapter, we
present some modelling efforts aimed at testing the shock acceleration hypothesis.

A. Afanasiev () • R. Vainio • S. Barcewicz • R. Siipola
Department of Physics and Astronomy, University of Turku, 20014 Turku, Finland
e-mail: alexandr.afanasiev@utu.fi; rami.vainio@utu.fi; t09susaa@utu.fi; roamsi@utu.fi
A. Aran • B. Sanahuja
Departament de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos (ICCUB),
Universitat de Barcelona, Barcelona, Spain
e-mail: angels.aran@fqa.ub.edu; blai.sanahuja@ub.edu
A. Rouillard
Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse, Toulouse, France
e-mail: arouillard@irap.omp.eu
P. Zucca
LESIA - Observatoire de Paris, CNRS, 92190 Meudon, France
e-mail: pietro.zucca@obspm.fr
D. Lario
Applied Physics Laboratory, Johns Hopkins University, Laurel, MD 20723, USA
e-mail: david.lario@jhuapl.edu
J. Pomoell
Department of Physics, University of Helsinki, 00014 Helsinki, Finland
e-mail: jens.pomoell@helsinki.fi
O.E. Malandraki
National Observatory of Athens, IAASARS, Athens, Greece
e-mail: omaland@astro.noa.gr
© The Author(s) 2018
O.E. Malandraki, N.B. Crosby (eds.), Solar Particle Radiation Storms Forecasting
and Analysis, The HESPERIA HORIZON 2020 Project and Beyond, Astrophysics
and Space Science Library 444, DOI 10.1007/978-3-319-60051-2_9

157

158

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We address two  -ray events: 2012 January 23 and 2012 May 17 and approach
the problem by, first, simulating the proton acceleration at the shock and, second,
simulating their transport back to the Sun.

9.1 Introduction
The novel  -ray observations by the Large Area Telescope (LAT) on the Fermi  ray Space Telescope spacecraft (Atwood et al. 2009), taken in a systematic way
at unprecedented high energies, have presented a puzzle to the solar energetic
particle (SEP) research community. More than two dozen >100 MeV  -ray events
were observed between 2008 and 2016 (see Chap. 8), many of which have properties
that challenge the traditional idea that high-energy (>300 MeV) protons needed for
the production of the  -rays, via the pion-decay process deep in the chromosphere,
are accelerated in solar flares (Ackermann et al. 2014). Specifically, the Fermi/LAT
observations indicate that particles are precipitating to the solar atmosphere for
up to a day after the impulsive phase of the flare, which is difficult to reconcile
with a model of impulsive acceleration followed by particle trapping in the coronal
magnetic field. On the other hand, coronal mass ejection (CME) driven shock waves
can emit protons with energies above 300 MeV for several hours after the onset of
the associated solar eruption as observed at 1 AU (e.g., the 2012 May 17 SEP event,
see Chap. 8). Therefore, as an alternative view on the genesis of the long-duration
 -ray events, shock acceleration needs to be considered.
One of the challenges of the shock-acceleration hypothesis is that the SEP events
observed in connection with the Fermi/LAT  -ray events are not always very large,
nor do they extend to very high energies when observed at 1 AU (see Chap. 8).
Therefore, one of the key aspects to understand about these events is the spatial
distribution of the accelerated particles at the CME-driven shock wave as well as the
relation between interplanetary and interacting protons. Several factors contribute
to this relation: (1) In-situ observations are local, i.e., performed in a particular
interplanetary flux tube, whereas the observed high-energy  -rays are produced
over an extended emission region involving contributions from different field lines.
(2) The energy spectrum of the particles accelerated at the shock is modified by
transport effects when the particles propagate both downstream and upstream to
reach the Sun and 1 AU. (3) Particles can modify their own transport conditions
upstream of the shock due to amplification of Alfvén waves, so the fluxes observed
at 1 AU can be partially decoupled from the fluxes at the shock. (4) Compressive
and stochastic acceleration in the downstream region close to the CME can modify
the spectrum of particles propagating toward the Sun.
We tackle the problem by conducting simulations of acceleration of protons in
the shock and of their transport to 1 AU and back to the Sun for two long-duration
 -ray events: 2012 January 23 and 2012 May 17, of which the latter is associated
with a ground level enhancement (GLE) of SEPs. In what follows, we outline in
Sect. 9.2 the modelling techniques applied, then we present simulation results in
Sect. 9.3 and their discussion as well as conclusions in Sect. 9.4.

9 Modelling of Shock-Accelerated Gamma-Ray Events

159

9.2 Model Description
In this section, we outline the Shock-and-Particle (SaP) and Coronal Shock
Acceleration (CSA) simulation models used to infer the proton spectrum at the
shock and describe in detail the DownStream Propagation (DSP) model developed
in the frame of High Energy Solar Particle Events foRecastIng and Analysis
(HESPERIA) project and used to simulate proton transport from downstream of
the shock to the Sun’s surface.

9.2.1 Shock and Particle Model
The Shock-and-Particle (SaP) simulation model allows one to determine the
injection rate of energetic particles from a propagating shock, using simulations
of the shock propagation and particle transport, combined with the fitting of the
simulation results to the observations. The particle injection rate Q at the shock
is defined as Q D df .zs ; E; t/=dt, where f is the particle phase-space distribution
function and zs .t/ is the shock position along the magnetic field line, which is,
of course, a function of time. In SaP, the Parker spiral magnetic field is assumed.
Instead of Q, one can consider the injection rate integrated over the cross-section
A of the magnetic tube, G D QA.zs /. See Chap. 4, Pomoell et al. (2015) and Aran
et al. (2007) for further details.

9.2.2 Coronal Shock Acceleration Model
The Coronal Shock Acceleration (CSA) model is a Monte Carlo simulation model
dealing with acceleration of ions in a coronal shock, taking into account ion-induced
generation of Alfvén waves in the solar wind upstream of the shock. CSA simulates
evolution of particles and Alfvén waves on a single radial magnetic field line. The
shock is treated as a magnetohydrodynamic (MHD) discontinuity, the gas and
magnetic compression ratios of which are computed through Rankine-Hugoniot
relations, using the shock speed along the field line Vs , the shock-normal angle
Bn (the angle between the magnetic field vector B and the shock normal n) and
the ambient solar wind parameters (the plasma density n, the magnetic field B and
the temperature T) at the shock position. All these parameters vary as the shock
propagates outward from the Sun, which is implemented in CSA by using analytic
functions of time or heliocentric distance to describe such variations. The analytic
functions are determined by a number of free parameters that have to be provided
as input in a simulation (see Afanasiev et al. 2017 for details). For instance, the

160

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variation of the magnetic field strength B with heliocentric distance r is implemented
in CSA as
"
#

 r 2
Rˇ 6
˚
1 C brf
;
(9.1)
B.r/ D B0
r
r
where Rˇ is the solar radius, r˚ D 1 AU, and B0 and brf are free parameters.
The parameter brf accounts for a super-radial expansion of the associated radial
magnetic flux tube close to the solar surface. In HESPERIA, the free parameters
were determined by fitting the analytic functions used to the data obtained by using
techniques of semi-empirical modelling of the shock (see Rouillard et al. 2016).
The treatment of wave-particle interactions in CSA is based on quasi-linear
theory, assuming only outward-propagating Alfvén waves, i.e., waves propagating
away from the Sun. Particles experience elastic pitch-angle scattering in the wave
frame, which is governed by the quasi-linear pitch-angle diffusion coefficient:
D D



 fres P. fres /

1  2 ;
2
4
B

(9.2)

where P. f / is the wave power spectrum, fres D V=.2v/ is the resonant wave
frequency, v and  are the particle speed and pitch-angle cosine as measured
in the wave-rest frame, V is the Alfvén wave propagation speed as measured in
the solar-fixed frame and  is the ion cyclotron frequency. The expression given
for the resonance frequency fres represents a simplified (pitch-angle-independent)
resonance condition of particle pitch-angle scattering (see, e.g. Afanasiev et al.
2015). If considered in other reference frames, in particular in the plasma frame,
pitch-angle scattering leads to the energy exchange between particles and waves.
Pitch-angle scattering of particles off outward-propagating waves, as viewed in the
plasma frame, can give rise to growth of waves. After a series of approximations
(Vainio 2003), the wave growth is given as
. fres / D

 pres S.r; pres ; t/

;
2
nVA

(9.3)

R C1
where S.r; p; t/ D 2 1 p2 vf .r; p; t/d is the particle streaming, pres is the
resonant particle momentum corresponding to the resonance frequency fres , n is the
proton density and VA is the Alfvén speed.
Particles are followed in the guiding-center approximation in the shock’s
upstream. The seed particle population is modelled by a kappa distribution in speed
with an exponential cutoff energy E0 . The spatial distribution of seed particles is
parameterised as nseed D
n, where nseed is the density of seed particles and
is
the injection parameter. Particle injection at the shock as well as particle-shock
interactions are modelled by testing particles hitting the shock from the upstream
for reflection/transmission from/through the shock front and for their transport back

9 Modelling of Shock-Accelerated Gamma-Ray Events

161

to the upstream, if transmitted. Alfvén waves are followed in the Wentzel-KramersBrillouin (WKB) approximation, with an additional diffusion term in frequency
accounting for wave energy cascading. For a comprehensive description of CSA
see Battarbee (2013).

9.2.3 DownStream Propagation Model
The DownStream Propagation (DSP) model is a Monte Carlo simulation model that
has been devised to simulate proton transport from the shock’s downstream back
to the Sun. It is based on Parker’s equation, which assumes quasi-isotropic particle
distributions and, hence, diffusive transport:
@f
1
@f
C u  rf  p.r  u/
D r  .  rf / ;
@t
3
@p

(9.4)

where f D hd6 N=.d3 x d3 p/i is the isotropic part of the particle distribution function,
u is the velocity of the background fluid (solar wind plasma) and  is the diffusion
tensor. The second term on the left-hand side describes advection of particles with
the solar wind, the third term describes adiabatic cooling due to the solar wind
expansion and the right-hand side term describes spatial diffusion of particles.
Hence, DSP describes the propagation of particles in the test-particle approximation.
Assuming that particles are confined within a magnetic flux tube, which gives
 D bb with b being a unit vector along the magnetic field, and that u jj b, Parker’s
equation can be reduced to


@f
1 1 @.Au/ @f
1 @
@f
@f
Cu  p
D
A
;
@t
@z 3 A @z @p
A @z
@z

(9.5)

where z is the (curvilinear) coordinate measured from the solar surface along the
field and A.z/ is the cross-sectional area of the flux tube. Changing to F D 4p2 Af ,
one can obtain

 


@
1 @.A/
@ 1 1 @.Au/
1 @2
@F
.2F/ : (9.6)
C
uC
F 
p
F D
@t
@z
A @z
@p 3 A @z
2 @z2
Equation (9.6) is equivalent to the following set of stochastic differential equations
(SDEs):


p
@

dt C 2 dWt ;
dz D u C C
L
@z


u
@u
1
C
dt ;
dp D  p
3
L
@z

(9.7)
(9.8)

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Fig. 9.1 Spatial simulation
domain in the DSP model

where L.z/ D A=.dA=dz/ is the focusing length of the magnetic flux tube, dWt is a
stochastic differential normally distributed with zero mean and variance dt. Note that
the term .=L/dt in Eq. (9.7) represents the net effect of focusing to a quasi-isotropic
particle population (Kocharov 1996). These SDEs are solved for each Monte Carlo
particle in the simulation, using the standard explicit Euler-Maruyama method.
The simulation is performed in an expanding 1-D spatial simulation box in the
shock’s downstream, i.e., the box is confined by the solar surface from one side and
by the moving shock front from the other side, and, thus, expands with time along
the magnetic field line (Fig. 9.1). For the plasma speed u and the spatial diffusion
coefficient  in the simulation box, the following linear models are adopted:
u.z; t/ D

.z; p; t/ D

u0 z
;
Vs t

1
p Vs t  z
0
;
3 mp V s t

(9.9)

(9.10)

where u0 is the plasma speed immediately behind the shock front and Vs is the
shock speed along the field, both measured in the solar-fixed frame, mp is the proton
mass and 0 is the particle mean free path at the solar surface. One can see from
Eqs. (9.9) and (9.10) that the plasma speed decreases linearly from u D u0 at the
shock (z D Vs t) to u D 0 at the Sun (z D 0), and the mean free path recovers from
 D 0 at the shock to  D 0 at the Sun. Hence the transport of particles from
the upstream through the shock is purely advective. On the other hand, the linear
dependence of the spatial diffusion coefficient  on Vs t  z secures that no particles
escape from the downstream beyond the shock.
The focusing length L is specified in a form similar to the one that can be derived
from Eq. (9.1):
1
L.z/ D .Rˇ C z/
2

"
# "
#1


z 6
z 6
1C
C bf
C 4bf
;
1C
Rˇ
Rˇ

where bf is a free parameter.

(9.11)

9 Modelling of Shock-Accelerated Gamma-Ray Events

163

The initial size of the simulation box is specified by the initial position of the
shock zs0 . This gives the initial value for time t as t0 D zs0 =Vs . The shock speed Vs
is assumed constant and u0 D Vs .rc  1/=rc with rc being the gas compression ratio
taken constant as well.
To be consistent with the chosen form of , the amount of particles being injected
into the simulation from the shock is determined by the net particle flux to the far
downstream. This flux is given by
Z
F D

d3 pvf . p; / D

Z

d3 p0 u2 f 0 . p0 / ;

(9.12)

where  is the pitch-angle cosine, v is the particle speed, u2 is the downstream
solar wind speed; the unprimed symbols designate quantities as measured in the
shock frame and the primed symbols in the downstream plasma frame. The second
expression in Eq. (9.12) is derived under the assumption that the particle pitch-angle
distribution as measured in the downstream plasma frame is isotropic. Then, it can
be derived to the first order in u2 =c (c is the speed of light in vacuum), taking into
account that  ! 0 at the shock, that
dF
D 4u2 p2 f0 . p/ ;
dp

(9.13)

where f0 . p/ is the isotropic part of the particle distribution function at the shock (on
the upstream side). This equation is used to relate the amount of particles injected
to the downstream with the particle intensity at the shock, js D p2 f0 . p/, which
is the output of CSA simulations. Specifically, the number of particles per unit
momentum injected downstream from a source (at the shock) of size As .z/ in time
dt is determined by
Vs
dN
D 4 As .z/js .t; E/dt :
dp
rc

(9.14)

In case the particle injection rate G.t; E/ is given (output of SaP), the particle
intensity at the shock is computed as
js .t; E/ D

p2 Crg G.t  t0 ; E/
;
v
r2 cos .r/

(9.15)

where v is the particle speed, C D 3:524 is a constant determined by the numerical
scheme implemented in SaP, rg is the spatial grid size in SaP simulations, r is the
heliocentric distance and it is taken into account that in SaP the injection rate G is
determined under the assumption of a Parker-spiral upstream magnetic field, i.e.,
cos .r/ D Œ1 C .ˇ r=usw /2 1=2 with constant solar wind speed usw (ˇ is the
angular speed of the solar rotation).

164

A. Afanasiev et al.

The proton injection into the downstream is implemented in the following way.
We introduce an injection time step t and deposit a certain number of Monte
Carlo particles into the simulation box at each t. A Monte Carlo particle is a
representative of a group of physical particles and is characterised by its weight w.
To obtain weights of injected Monte Carlo particles at a given time t0 , we compute
values of the spectrum dN=dp at the momentum grid using Eq. (9.14) and interpolate
those spectral values by power laws between the grid nodes. Then, the weight of
a Monte Carlo particle with momentum p between the grid points pj and pjC1 is
given by
1
wD
NMC

pjC1
Z

dN
dp;
dp

(9.16)

pj

where dN=dp / pqj and NMC is the number of Monte Carlo particles assigned
to the interval Œpj ; pjC1 . Note that the particle momentum p is randomly chosen
from a pqj distribution in this interval and qj D  ln.SjC1 =Sj /= ln. pjC1 =pj / with
Sj. jC1/ D dN=dpjj. jC1/ .
The Monte Carlo particles injected at a given time t0 are placed into a small
spatial 1-D volume z D u2 t behind the front, to mimic their advection by the
bulk plasma during t. Then, each of these particles is propagated by solving the
SDEs until it hits the Sun, i.e., precipitates, or up to t D tmax . The particle transport
time step ıt must fulfil the condition ıt  L2 =. Furthermore, the linear dependence
of  on distance from the shock dictates that Monte Carlo particles that might appear
in the upstream side during a simulation have to be returned to the downstream side.
This requires a reflective boundary condition for particles to be applied at the shock.
During the simulation, Monte Carlo particles that hit the Sun are collected
and, based on their momenta, precipitation times and weights, the flux and
time-integrated energy spectrum of absorbed protons are calculated. The latter is
compared with the proton spectra derived from  -ray observations.

9.3 Results
The simulations based on the models presented above were conducted for two longduration >100 MeV  -ray events occurred on 2012 January 23 and 2012 May 17.
These  -ray events are associated with substantial SEP events as observed at 1 AU
(the 2012 May 17 event is also a GLE). The event characteristics are described in
Chap. 8 (see also Rouillard et al. 2016). In what follows we first present modelling
results for the 2012 May 17 event due to its association with a GLE and then results
for the 2012 January 23 event.

9 Modelling of Shock-Accelerated Gamma-Ray Events

165

9.3.1 2012 May 17 Event
9.3.1.1 Modelling of the SEP Event
We begin with results of the SaP modelling of the accelerated proton population at
the shock, which utilises the observations of the shock and SEP event at 1 AU.
Figure 9.2 presents results of simulations of the ambient solar wind and shock
propagation to the Earth. The solar wind was simulated starting from the onset
time of the SEP event. Table 9.1 provides values of the input solar wind parameters
at 1:03 Rˇ . The input parameters of the shock-driving disturbance are its density
cme D 0:3  1013 kg m3 , speed vcme D 1000 km s1 , and the shock-front shape
parameter  D 0:5acme determined by the angular extent acme of the disturbance
(see Pomoell et al. 2015 for details). One can see that the simulations reproduce
quite well the average characteristics of the solar wind at 1 AU prior to the shock
arrival (note, however, that the temperature is somewhat underestimated) as well
as the shock arrival time. At the same time, the observed jumps in the plasma
characteristics are reproduced well with some underestimation of the magnetic field
increase.
In order to derive the proton injection rate from the shock into the magnetic
flux tube connecting the observer with the shock front, we fitted the proton

Fig. 9.2 Simulated characteristics of the solar wind (blue lines) superposed on the observed
characteristics (shown in orange and red) before and during the shock arrival at 1 AU for the 2012
May 17 SEP event. Shown are: the plasma density, the solar wind radial velocity, the magnetic
field magnitude and the solar wind proton temperature. The temperature was measured by the
Wind spacecraft and the other parameters by the ACE spacecraft. Time counts from the time of the
interplanetary shock passage by the ACE spacecraft (marked by a dotted vertical line)

166

A. Afanasiev et al.

Table 9.1 Input solar wind parameters used in the SaP simulations of the 2012 January 23 and
2012 May 17 SEP events
Event
Jan 2012
May 2012

0 .kg=m3 /a
1:169  1013
1:169  1013

T0 .K/
1:22  106
1:18  106

S0 .W=m3 /
0:335  107
0:35  107

L .Rˇ /

0.735
0.70


1.55
1.55

Br0 .T/
2:15  104
1:26  104

The parameters provided are the plasma density 0 , temperature T0 and the radial component of
the magnetic field Br0 at the heliocentric distance r0 D 1:03 Rˇ ; S0 and L are the coronal heating
function parameters (Pomoell et al. 2015); and  is the adiabatic index.

a

Fig. 9.3 Examples of the
intensity-time profiles from
the SEPEM reference data
and the GOES/HEPAD
detector (shown in red) with
superposed fits (light blue
lines). The short green
horizontal lines indicate the
pre-event background
intensities that have been
subtracted from the measured
intensities. The two solid blue
vertical lines indicate the
times of the shock arrival at
the ACE and GOES
spacecraft positions. The
dotted orange vertical line
indicates the onset of the
associated X-ray flare and the
dotted purple line indicates
the time of a change in the
interplanetary magnetic field
direction

intensity-time profiles provided by the ACE/EPAM instrument (in the energy range
0.59–4.8 MeV), SEPEM reference data (Jiggens et al. 2012) (6–166.3 MeV) and
GOES/HEPAD detector (330–700 MeV). The fitting was performed using SaP
particle transport simulations, following the method described in Pomoell et al.
(2015). Figure 9.3 shows examples of the fitted intensity-time profiles for several
high-energy channels. Note that when performing the fitting, we focused on the first
several hours of the event as the corresponding  -ray event lasted for about 2 h.
Figure 9.4 shows the proton injection rates G.t/ resulting from the fitting of the
intensity-time profiles at selected energies. The obtained injection rates were used

9 Modelling of Shock-Accelerated Gamma-Ray Events

167

Fig. 9.4 Temporal evolution
of the proton injection rate G
at high energies. Black lines
represent polynomial fits to
the simulated G functions

as input for the DSP simulations. The simulations reveal that the injection rate at
high energies drops by more than one order of magnitude several hours after the
X-ray flare onset, which agrees with rather short duration of the associated  -ray
event (2 h).

9.3.1.2 Simulations of Proton Acceleration at the Shock
To carry out the CSA simulations of proton acceleration at the shock in this
event, we utilised the ambient plasma and shock parameters derived from the semiempirical modelling of the shock (Rouillard et al. 2016). Those parameters are the
plasma density n, the magnetic field strength B, the shock speed Vs and the shocknormal angle Bn , which were determined along individual magnetic field lines. The
parameters were fitted by the analytic functions of time/distance implemented in
CSA (Afanasiev et al. 2017). Figure 9.5 shows an example of the data obtained for
a single field line, superposed by the corresponding fits. In total, the data for over
100 field lines were available and fitted. Among the field lines possessing goodquality fits, nine were chosen for simulations with CSA.
The detailed analysis of the simulation results presented in Afanasiev et al.
(2017) reveals that the parameter mainly controlling the acceleration efficiency is
the Alfvénic Mach number of the shock. Figure 9.6 shows examples of the evolution
of the Alfvénic Mach number of the propagating shock for three different magnetic
field lines and simulated proton energy spectra at the shock, corresponding to these
field lines, obtained at t D 1000 s. The simulated spectra (for one of the simulated
field lines) were then used as the other input for the DSP simulations.

A. Afanasiev et al.
Fieldline 1
1.0
0.8
0.6

+

Fieldline 1

+
+ + + + + +
+ +

10000
shock speed(km/s)

shock–normal cosine (+) & 1/MA ( )

168

+

0.4
0.2
0.0
0

500

1000

1500

2000

+

+ + ++
+++++++

1000

100
10

2500

100

time (s)
Fieldline 1

10000

Fieldline 1
108

10.000

0.010

–3

+
0.100

+

107

+

1.000

density (cm )

magnetic field (G)

1000
time + 20 s

++
+++
++++
+

+

106

+
+
+
++
+++
++

105
104

0.001
1

10
position (Rs)

1

10
position (Rs)

Fig. 9.5 Example data set obtained with the semi-empirical shock modelling approach in the 2012
May 17 event, plotted together with the corresponding fits. The upper left panel shows the shocknormal cosine cos Bn (“plus” symbols) and the inverse Alfvénic Mach number MA1 (asterisks) vs.
time; the upper right panel shows the shock speed Vs along the magnetic field line vs. time. Note
that time is counted from the moment when MA > 1:5. The bottom left panel shows the magnetic
field magnitude B vs. radial shock position and the bottom right panel shows plasma density n vs.
radial shock position

Fig. 9.6 Alfvénic Mach number of the shock versus simulation time for three different magnetic
field lines (left panel) and corresponding proton energy spectra at the shock at t D 1000 s, resulting
from CSA simulations (right panel). Note the correspondence between the Alfvénic Mach number
and the spectral cutoff energy

9 Modelling of Shock-Accelerated Gamma-Ray Events

169

9.3.1.3 Modelling of the Proton Transport Back to the Sun
The proton transport back to the Sun was simulated with the DSP model, assuming
a radial magnetic field in the shock’s downstream. The particle source size at the
shock was modelled as As .z/ D .Rˇ C z/2 0 . The parameter 0 , which can be
interpreted as the global angular size of the shock, was taken to be 1 steradian. In
fact, the realistic effective source size should be smaller because of the substantial
difference in the particle acceleration efficiency along different field lines, as
revealed by the CSA simulations for this event. We took this into account by
considering an additional parameter, so-called filling factor, afill that is the relative
fraction of field lines at which high-energy,  -ray-productive, protons can be
produced. Based on the ascertained dependence between the particle acceleration
efficiency and the Alfvénic Mach number magnitude, and available data on >100
individual field lines, we estimated that afill D 0:1. To compare the proton spectra
resulting from the DSP simulations with the proton spectrum obtained from the
Fermi/LAT observation, we multiply the simulated spectra by afill . The parameters
of the observationally-derived spectrum (the total number of >500 MeV protons and
the power-law spectral index of >300 MeV protons) were kindly provided to us by
G. Share (see Chap. 8 for references). The other DSP model parameters were taken
to be zs0 D 1:6 Rˇ (1:15 Rˇ), in the case of CSA(SaP) input, Vs D 1510 km s1 ,
rc D 3:6 and usw D 387 km s1 .
The DSP simulations were conducted for a set of values for the downstream
transport parameters 0 and bf . The resulting (integrated over the duration of the
 -ray emission; i.e., 2 h) energy spectra of protons hitting the Sun are presented
in Fig. 9.7 along with the shock-injected spectrum and the observationally-derived

Fig. 9.7 Time-integrated energy spectra of protons precipitated at the Sun, resulting from DSP
simulations using the results of SaP (left panel) and CSA simulations (right panel) for the 2012
May 17 event. The spectra are shown by blue and green lines with the corresponding DSP model
parameters indicated. The integration time is 2 h, which is approximately the duration of the
>100 MeV -ray event. Also shown are the time-integrated spectrum of protons injected by the
shock to the downstream (black dashed line) and the spectrum of interacting protons derived from
the Fermi/LAT observation (red line)

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spectrum of interacting >300 MeV protons. It can be calculated that the number of
>500 MeV protons injected from the shock in the CSA+DSP simulation exceeds by
more than 104 the corresponding number of protons derived from the observation.
On the other hand, the number of absorbed high-energy protons is sensitive to
the transport parameters. In particular, it can be easily reduced by increasing the
parameter bf controlling the focusing length, which enhances proton mirroring from
the flux tube base and adiabatic cooling, in accord with Eqs. (9.7) and (9.8). Note
also that the DSP model completely neglects the possibility for particles in the
downstream side of the shock to escape to the upstream side. This process, if taken
into account, should decrease the number of absorbed particles as well.
In contrast, the spectrum of shock-injected protons obtained from the SaP+DSP
simulation and the absorbed spectrum corresponding to bf D 0 (radial flux tube) are
in good correspondence with the observed spectrum. However, it should be noted
that this correspondence holds only for rather idealistic conditions of the DSP model
(no particle escape to the upstream) and one can expect a lack of high-energy protons
in the simulations, if a more realistic downstream transport model is considered. The
possible reasons of this result are discussed in Sect. 9.4.

9.3.2 2012 January 23 Event
9.3.2.1 Modelling of the SEP Event
The results of simulations of the ambient solar wind and shock propagation to
1 AU are shown in Fig. 9.8. The input parameters describing the initial shock-driven
disturbance in this case are cme D 0:3  1013 kg m3 , vcme D 1650 km s1 , and
 D 0:25acme (see also Table 9.1 for the initial solar wind parameters). Like for
the 2012 May 17 event, the modelling reproduces well the average characteristics
of the solar wind at 1 AU prior to the shock arrival and the shock arrival time.
The observed jump in the magnetic field magnitude is reproduced well too, but
the jumps in the density, the solar wind speed and the temperature are somewhat
overestimated. Note that due to the data gap in the ACE data, the value of the
average temperature (2:5  104 K) in the upstream region has been taken from the
plot provided by the IP shocks data base of the University of Helsinki,1 based on the
WIND data. A similar value is estimated by the CfA interplanetary shock list.2
Like for the previous event, we fitted the observed intensity-time profiles
provided by the ACE/EPAM instrument and the SEPEM reference data (Jiggens
et al. 2012). The proton enhancements observed in this event by GOES/HEPAD in
the high-energy channels ranging from 330 to 700 MeV are weak. From Fig. 9.9, it
can be seen that already at 166.3 MeV the background-subtracted enhancement is
lower than the background level itself. For this reason, instead of fitting the observed
1
2

http://ipshocks.fi/database.
https://www.cfa.harvard.edu/shocks.

9 Modelling of Shock-Accelerated Gamma-Ray Events

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Fig. 9.8 Same as in Fig. 9.2, but for the 2012 January 23 event

Fig. 9.9 Left panel: Examples of the observed proton intensity-time profiles (in red) with
superposed fits/synthetic profiles (light blue lines) for the 2012 January 23 SEP event. The short
green horizontal lines indicate the pre-event background intensities that have been subtracted from
the measured intensities. The meaning of the other lines is the same as in Fig. 9.3. Right panel:
Temporal evolution of the proton injection rate G at high energies. Black lines are polynomial fits
to the simulated G functions

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intensities, we computed synthetic intensity-time profiles for the GOES/HEPAD
energy channels by extrapolating the particle injection rate G.t; E/ from the highest
energies in the SEPEM reference dataset. Such a profile is shown in Fig. 9.9 at
605 MeV. Figure 9.9, right panel shows the proton injection rate resulting from the
SaP simulations of this SEP event.

9.3.2.2 Simulation of Proton Acceleration at the Shock
To conduct CSA simulations of proton acceleration at the shock in the same fashion
as it was done for the 2012 May 17 event, we used white-light (WL) images of
the corona from SOHO and STEREO A and B and the Potential Field Source
Surface (PFSS) modelling of the magnetic field. The WL images were fitted using a
spherical representation for the CME. This allowed us to obtain the magnetic field,
the shock speed and the shock-normal angle along different field lines (Fig. 9.10).
As concerns the plasma density, we used the following representation:
n.r/ D n2

 r 2
˚

r


C n8

Rˇ
r

8

;

(9.17)

with n2 D 10 cm3 and n8 D 8  108 cm3 . Since the plasma density was not
constrained using the real observations, we performed a CSA simulation only for
one magnetic field line. The simulation showed a typical buildup of the proton
energy with time and formation of a power-law energy spectrum with a roll-over,
similar to the spectra presented in Fig. 9.6. The maximum proton energy at the shock
attained the value 1 GeV at t D 1130 s after the start of the simulation, but then
was decreasing and reached 500 MeV at t D 2000 s.

Fig. 9.10 The shock-normal cosine s , the shock speed along the field line Vs and the magnetic
field B with the fits superimposed for a selected magnetic field line

9 Modelling of Shock-Accelerated Gamma-Ray Events

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Fig. 9.11 Time-integrated energy spectra of protons precipitated at the Sun, resulting from DSP
simulations using the results of SaP (left panel) and CSA simulations (right panel) for the 2012
January 23 event. The spectra are shown by blue and green lines with the corresponding DSP model
parameters indicated. The integration time is 6 h. Also shown are the time-integrated spectrum of
protons injected by the shock to the downstream (black dashed line) and the proton spectra obtained
from the Fermi/LAT observation (red line)

9.3.2.3 Modelling of the Proton Transport Back to the Sun
Similar to the DSP modelling for the 2012 May 17 event, we assumed a radial
magnetic field in the shock’s downstream and As .z/ D .Rˇ C z/2 0 was taken
for the particle source at the shock. The model parameters were taken to be zs0 D
0:6 Rˇ (3:1 Rˇ) in the case of CSA(SaP) input, Vs D 1450 km s1 , rc D 3:7, usw D
414 km s1 , 0 D 1 sr, and afill D 0:1.
Figure 9.11 shows the simulated spectra of protons absorbed at the Sun together
with the shock-injected spectrum and the proton spectrum derived from the
Fermi/LAT observation of >100 MeV  -photons. Similar to the simulation for the
2012 May 17 event, in the CSA+DSP simulation, there is a substantial excess of
shock-injected protons as compared to the number of interacted protons derived
from the observation. In contrast, there is a lack of shock-injected protons against
the observed number in the SaP+DSP simulation.

9.4 Discussion and Conclusions
We have modelled particle acceleration at coronal shocks driven by CMEs and
proton transport from the shock to both the Sun and the far upstream region
(towards the 1-AU observer). The purpose of our study is to find out, whether
shock-accelerated protons streaming back from the shock could be responsible for
the long-duration  -ray events observed by Fermi/LAT. We simulated the shock
propagation from the Sun to 1 AU using a two-dimensional MHD model. We
also employed the empirical models of the CME-driven pressure front propagation,

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which allowed us to assess the early evolution of the shock in a system that does not
possess the symmetries assumed in the MHD model.
Our results show that the efficiency of particle acceleration crucially depends on
the modelled properties of the shock in the corona. Conditions on different field
lines vary very much and while the shock on some field lines is able to produce
a relativistic particle event, it fails to do so on others. The most important factor
governing the acceleration efficiency in our study was the Alfvénic Mach number
of the shock: the higher the Alfvénic Mach number, the more likely the shock to
accelerate protons to relativistic energies (Afanasiev et al. 2017).
In our simulations, we focused on two events that differ in one important aspect:
one of them (2012 May 17) is a GLE and the other one is not. Both of the events
are associated with long-duration  -ray events, which might seem contradictory, but
actually is not. In the light of our simulations, there are two possible explanations
for this. Firstly, as the particle acceleration efficiency at the shock varies a lot from
one flux tube to another, the 1-AU proton event does not necessarily correspond to
the best acceleration conditions on the shock surface. Thus, we may well observe
a long-duration (pion-decay)  -ray event due to shock-accelerated protons without
a clear increase observed at 1 AU at energies required for pion production at the
Sun. The Earth-based observer sees but a small fraction of the complete picture.
The other, more subtle explanation deals with the strength of the turbulence in the
foreshock region of the coronal shock. The CSA simulations show that the foreshock
is extremely turbulent near the Sun, traps a large fraction of particles (almost all) in
its vicinity and allows only a minor fraction to escape. While the SaP model contains
the possibility to use enhanced foreshock turbulence, it is tuned to reproduce the
observations when the shock is detected in situ. Therefore, the source function
deduced from the 1-AU observation represents more the fraction of particles that
can escape upstream than the fraction that can be transported downstream from
the shock. The large discrepancy between the CSA and SaP modelled spectra of
precipitated particles is, thus, partly explained by this effect, as well. Furthermore,
these explanations shed light on the tendency to get lower numbers of precipitated
>300 MeV protons in the SaP+DSP simulations (especially for the 2012 January
23 event), as compared to the observations.
The transport model we employ for the downstream region has several important
simplifications in it. Firstly, it employs a shock completely opaque to protons and,
thus, allows downstream-advected particles to reside in the region between the
shock and the Sun for as long as they get precipitated. The only loss process we
employ is adiabatic cooling of the distribution, when the region between the shock
and the Sun expands. On the other hand, we do not include any downstream reacceleration processes, which could also be important and would act in the opposite
direction, helping particles to overcome adiabatic energy losses. Such processes
include downstream stochastic acceleration (see, e.g., Afanasiev et al. 2014) and
compressive acceleration in the highly-compressed regions close to the CME core
(Kozarev et al. 2013). Therefore, we do not regard our model to be overly optimistic
about the prospect of letting shock-accelerated protons precipitate over large time
scales.

9 Modelling of Shock-Accelerated Gamma-Ray Events

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Regarding the CSA model, one important reservation has to be made: the model
makes a simplification to the quasi-linear resonance condition between particles and
scattering Alfvén waves, kres D 2fres =V D B=.R/, neglecting the dependence
of resonant wave number kres on particle pitch-angle cosine  (R is the particle
rigidity). This simplification, while without proper physical justification, allows
one to build the code using the assumption of isotropic scattering, which speeds
up the running times easily by a factor of ten over times obtained when treating
the resonance condition in full. We have, however, evaluated the effect of this
simplification using a local model (Afanasiev et al. 2015), and shown that in parallel
coronal shocks the difference between the two models yields about a factor of 2 in
the roll-over rigidity obtained from the model. On the other hand, the spectrum in
CSA also cuts off much more rapidly than in the model employing the complete
resonance condition, so we do not regard this to be a very serious problem in the
performed modelling. A more complete global model to be developed in future,
however, should take the full resonance condition into account, also since it affects
the foreshock spatial structure as well (Afanasiev et al. 2015). We will undertake the
development of such a model in future projects.
Another transport process missing from the CSA model is diffusion perpendicular to the mean magnetic field. This process can be implemented in a Monte
Carlo simulation, but its inclusion will require to incorporate at least one more
spatial dimension in the model. Therefore, also the requirement for particle statistics
in CSA will be tremendously increased to avoid statistical noise in the result, as
the number of spatial cells in the model will have to be increased by a factor
30–300, depending on the coarseness of the grid in the perpendicular direction.
This is still beyond the reach of the present computers with reasonable running
times of the code. Fortunately, as perpendicular diffusion cannot occur due to
slab-mode waves, the enhanced Alfvénic turbulence in the upstream region is not
strengthening the perpendicular diffusion of the particles. However, one would
expect the downstream plasma to have much more isotropic turbulence which, then,
would lead to the migration of particles from one flux tube to the other while they are
on the downstream side of the shock. For an opaque shock, like we have assumed,
this is not affecting the acceleration of ions at the shock too much since their fate
(scattered back to the shock or transported to the far downstream region with no
return) would be decided (almost) instantly, giving the particles very little time to
diffuse perpendicular to the mean field. Thus, the first step to take the perpendicular
transport into account would have to be performed on the downstream side of the
shock.
We note that the total number of >500 MeV protons as simulated by the CSA
code is several orders of magnitude larger than the observational value in both of the
simulated events. At first, this might seem to be problematic. However, in addition to
the caveats about the resonance condition and the downstream transport modelling
discussed above, we point out that the CSA model is set up quite favourably for
efficient particle acceleration: we use a seed particle population with a relatively
hard suprathermal distribution ( D 2) in the model, which guarantees an efficient
injection to the acceleration process at all obliquity angles of the shock. Using a

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thermal population, only, would limit the injection efficiency of the shock especially
at obliquity angles greater than 20ı quite substantially: according to Battarbee
et al. (2013), the injection efficiency in an oblique coronal shock would go down
by an order of magnitude if we would use a steeper seed population with  D
15. Given all the possible ways to limit the number of precipitating protons in our
model, we would regard the result of getting more than enough high-energy protons
precipitating at the Sun to be a supporting rather than a countering result for the
shock acceleration scenario.
The final shortcoming in the shock models we have employed is their assumption
of the open topology of the upstream magnetic fields. Especially if the  -ray event
occurs during a period of closely spaced CMEs, the second one may drive a shock
through a set of large closed loop-like or flux-rope structures, which would alter
both the shock acceleration properties and, more importantly, the ability of the
particles to escape upstream from the shock. In fact, developing codes capable of
modelling particle acceleration and transport in more complicated upstream fields
than the radial/Archimedean-spiral fields could be listed as one of the most urgent
things needing improvement on the way towards physical space-weather modelling
capabilities.
One of the most difficult things to estimate is the size of the source of nearrelativistic protons in the event. While the 3-D modelling of the shock front can be
performed in a relatively accurate and detailed manner, high-resolution density and
magnetic-field structure of the corona are crucial for the correct determination of
the shock properties and, thus, the total number of interacting protons in the event.
Therefore, even a fully global 3-D model of coronal shock evolution and particle
acceleration might not capture every detail affecting the total number of relativistic
protons in the CME system. In this work, we resorted to estimating numbers based
on the filling factor of field lines being capable of facilitating proton acceleration
to relativistic energies based on an evaluation of shock properties on a large set of
field lines. We believe that such statistical method to estimate the total number of
interacting protons is the most efficient way to address the problem.
In conclusion, while a number of simplifications have been introduced in the
modelling performed, we have still demonstrated that coronal shock acceleration
and subsequent diffusive downstream particle transport is a viable option to explain
pion-decay  -ray events from the Sun observed by Fermi/LAT. More elaborated
simulation models are needed (especially for the particle transport back to the Sun)
but our results serve as a motivation by indicating that the end result of this vast
modelling effort can be positive.

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Chapter 10

Inversion Methodology of Ground Level
Enhancements
B. Heber, N. Agueda, R. Bütikofer, D. Galsdorf, K. Herbst, P. Kühl,
J. Labrenz, and R. Vainio

Abstract While it is believed that the acceleration of Solar Energetic Particles
(SEPs) is powered by the release of magnetic energy at the Sun, the nature, and
location of the acceleration are uncertain, i.e. the origin of the highest energy
particles is heavily debated. Information about the highest energy SEPs relies
on observations by ground-based Neutron Monitors (NMs). SEPs with energies
above 500 MeV entering the Earth’s atmosphere will lead to an increase of the
intensities recorded by NMs on the ground, also known as Ground Level Event
or Ground Level Enhancement (GLE). A Fokker-Planck equation well describes
the interplanetary transport of near relativistic electrons and protons. An NM is an
integral counter defined by its yield function. From the observations of the NM
network, the additional solar cosmic ray characteristics (intensity, spectrum, and
anisotropy) in the energy range &500 MeV can be assessed. If the interplanetary
magnetic field outside the Earth magnetosphere is known (see Sect. 10.3.2) a
computation chain can be set up in order to calculate the count rate increase of
an NM for a delta injection at the Sun along the magnetic field line that connects
the Sun with the Earth (Sect. 10.3.3). By this computations, we define a set of

B. Heber () • D. Galsdorf • K. Herbst • P. Kühl • J. Labrenz
Christian-Albrechts-Universität zu Kiel, Kiel, Germany
e-mail: heber@physik.uni-kiel.de; galsdorf@physik.uni-kiel.de; herbst@physik.uni-kiel.de;
kuehl@physik.uni-kiel.de; labrenz@physik.uni-kiel.de
N. Agueda
University of Barcelona, Barcelona, Spain
e-mail: agueda@fqa.ub.edu
R. Bütikofer
University of Bern, Physikalisches Institut, Sidlerstrasse 5, CH-3012 Bern, Switzerland
High Altitude Research Stations Jungfraujoch and Gornergrat, Sidlerstrasse 5, CH-3012 Bern,
Switzerland
e-mail: rolf.buetikofer@space.unibe.ch
R. Vainio
Department of Physics and Astronomy, University of Turku, Turku, Finland
e-mail: rami.vainio@utu.fi
© The Author(s) 2018
O.E. Malandraki, N.B. Crosby (eds.), Solar Particle Radiation Storms Forecasting
and Analysis, The HESPERIA HORIZON 2020 Project and Beyond, Astrophysics
and Space Science Library 444, DOI 10.1007/978-3-319-60051-2_10

179

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Green’s functions that can be fitted to an observed GLE to determine the injection
time profile. If the latter is compared to remote sensing measurements like radio
observations, conclusions of the most probable acceleration process can be drawn.

10.1 Introduction
The Earth is constantly bombarded by high-energy particles, also known as cosmic
rays. Those who are not deflected by the geomagnetic field, as discussed in Chap. 5,
enter the atmosphere and undergo interactions with atoms and molecules as well
as with the nuclei of the atmosphere. Low-energy cosmic rays (<500 MeV) are
absorbed in the atmosphere, i.e. no secondary particles can be observed at sea level
from primary particles as described in Chap. 6. Most of the primary particles are
of galactic origin and are known as Galactic Cosmic Rays (GCR). In solar eruptive
events, such as solar flares and Coronal Mass Ejections (CMEs), protons and other
ions can be accelerated to high energies (>30 MeV). The acceleration mechanisms
are thought to be related to magnetic reconnection in solar flares (Aschwanden
2012) and the shock waves generated by CME (Cliver et al. 2004).
According to the review by Reames (1999) impulsive events are small, electron
rich, tend to be enriched in heavy ions and are 3 He-rich (3 He/4 He
1). They are
associated with small magnetic loops in the lower corona with heights smaller than
104 km and have ionization states typical of solar flare temperatures, i.e., 107 K
(Mason 2007). The emission is generated at low altitudes, and fast drift (type III)
radio emission, which reflects the electron escape into the interplanetary medium
(Klein and Trottet 2001), is observed as well.
Gradual SEP events, in contrast, are believed to originate high in the corona from
a CME-driven shock whose extent is consistent with the observations of such SEP
over relatively wide longitudinal ranges (Rouillard et al. 2011; Dresing et al. 2014).
The association of CMEs with type II emission (see Chaps. 1 and 2 for details) also
confirms the conclusion that gradual SEP events are accelerated by large CMEdriven shocks (Reames 1999). These events produce some of the highest intensity
events observed at Earth at energies up to several GeV (Mewaldt et al. 2012; Kühl
et al. 2016).
While this two class picture appears to describe the origin of <50 MeV ions
with some success, the origin of SEPs that cause GLEs is less studied due to the
lack of detailed observations (Moraal and McCracken 2012). It was found that the
GLE spectra tend to be slightly harder than non-GLE spectra and that they are
consistent with double power laws (Mewaldt et al. 2012; Kühl et al. 2016). Also,
the authors found that the composition of GLEs tends to have higher Fe/O ratios,
enrichments in 3 He (Wiedenbeck 2013) and highly-ionized charge-states of heavy
elements such as Fe. This lead to the conclusion that GLE ions may be accelerated
by CME-driven shocks, with quasi-perpendicular shock geometry and the presence
of suprathermal ions from previous flares playing a key role (Tylka et al. 2005).
Moraal and Caballero-Lopez (2014) found different scenarios for different GLEs

10 Inversion Methodology of Ground Level Enhancements

181

having a prompt component from the impulsive phase and a gradual one indicating
shock acceleration. To gain further insight the interplanetary and magnetospheric
transport of high energy charged particles needs modeling (Bieber et al. 2004).
While a Fokker-Planck equation well describes the interplanetary transport of near
relativistic electrons (Dröge 2003; Dröge et al. 2010) the processes that need to be
included at high energies have not been fully explored (Dalla et al. 2013, 2015).
Gradual particle events tend to be larger, typically associated with large 105 km
X-ray emitting structures, last much longer than impulsive events, are protonrich without significant enrichment in 3 He/4 He, electron poor, and have elemental
abundances and charge states representative of solar coronal or solar wind material
and temperatures, i.e., 106 K (Klecker 2013).
However, the relative roles of both components and how we can discriminate
them remains a key problem in solar and solar-terrestrial physics, especially
regarding the diverse interest in GLEs. There is a practical interest in GLEs owing
to their significance for space weather. Solar cosmic rays can damage spacecraft
electronic components and are a significant radiation hazard to astronauts. To
quantify these risks, the full particle distribution in energy and pitch angle as a
function of time needs to be determined from the NM observations. A method to
derive the “physical quantities” is based on forward-modeling of SEP transport
(Sects. 10.3.1 and 10.3.2) in interplanetary space and the Earth’s magnetosphere (see
also Chaps. 4 and 5) by utilizing a power law spectrum in rigidity at the injection
point of the Sun (see Chap. 3) and the response/yield function of the NM (see
Sect. 10.3.2 and Chap. 6). The forward modeling is utilized in Sect. 10.4 to derive an
inversion methodology that is applied to observations in Sect. 10.5. To validate our
model chain, results are compared to spacecraft measurements that are described in
Sect. 10.2.

10.2 Space and Ground Based Measurements of GLEs
SEP events, where protons are accelerated to energies above 500 MeV, occur a few
times per solar cycle. Protons with such energies penetrate the Earth’s atmosphere
and produce secondary particle showers which can increase the intensities recorded
by NMs on the ground. Such intense SEP events are also known as Ground
Level Events or GLEs. Initially designed by Simpson (1948), NMs are used for
precise monitoring of spectral and directional variations in the cosmic-ray flux. The
detection of a GLE event by an NM on average occurs a few times per solar cycle.
The first GLE was observed on February 28, 1942 and the first GLE observed by
NMs was the one on February 23, 1956 (see gle.oulu.fi).
Since 1942 until the end of 2015 a total of about 70 GLEs have been observed, i.e.
one GLE per year. Each GLE has its typical characteristics (amplitude, spectrum,
duration, spatial distribution of flux, etc.). During a GLE the measurements of the
ground-based NM network show an increase in the count rate within typically a
few minutes and decreasing intensities to background levels within hours. In some

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cases, GLEs show a double-peaked time structure, with an initial fast rise and an
anisotropic particle population—called “prompt component”—followed by a more
gradual and less anisotropic “delayed component” (McCracken et al. 2012).
SEP events causing GLEs are restricted to events that accelerate ions to energies
above 500 MeV/nucleon. Experiments on board spacecraft located close to
Earth such as the Geostationary Operational Environmental Satellites (GOES), the
Solar and Heliospheric Observatory (SOHO), the Payload for Antimatter Matter
Exploration and Light-nuclei Astrophysics (PAMELA) and the Alpha Magnetic
Spectrometer 02 (AMS-02) aboard the International Space Station (ISS) can observe
protons below and above this threshold in differential energy channels. These data
serve to fill an observational gap between the few hundred MeV and less, typically
monitored by other satellite instruments on board e.g. the Advanced Composition
Explorer (ACE) (Gold et al. 1998) and Wind (Lin et al. 1995). This latter spacecraft
allows us to determine the chemical and isotope abundance (Mewaldt et al. 2007;
Nitta et al. 2015), the charge states (Mason et al. 1995; Kartavykh et al. 2007) and
to study the lepton component i.e. electrons (Dröge 2000; Dresing et al. 2012, 2014;
Agueda et al. 2014) during SEP events. As discussed in Chap. 4 it is important to
know not only the intensity-time profiles but also the evolution of the PAD. The
pitch angle is defined as the angle between the magnetic field and the velocity
vector ˇ. A particle instrument with a limited opening angle and a pointing direction
n in interplanetary space is sensitive to a pitch angle range around cos.#/ D  Bn
B
with B the interplanetary magnetic field vector. Spacecraft like ACE, Wind, and
the International Monitoring Platform (IMP) 8 outside the Earth’s magnetosphere
provide us with measurements of the interplanetary magnetic field vector B near the
first Lagrangian point L1. Contrary to IMP 8 neither GOES nor SOHO measures
B. The OMNI dataset1 maintained by the US National Space Science Data Center
provides us with the magnetic field, and plasma data sets from ACE, Wind and the
IMP-8 shifted to the Earth’s bow shock nose. For an observer in the magnetosphere,
(PAMELA and AMS-02) the viewing direction n is the asymptotic direction that
has to be calculated as described in Chap. 5.

10.2.1 dE/dx-dE/dx-Method
This method is utilized by EPHIN aboard SOHO and is based on the energy loss
in two detectors. Figure 10.1 right illustrates the measurement principle of the
EPHIN instrument (Müller-Mellin et al. 1995). Plotting the energy loss in two

1

http://omniweb.gsfc.nasa.gov/owmin.html.

10 Inversion Methodology of Ground Level Enhancements

183

83°

Kapton foil
Titanium foil
A

Photomultiplier
G

G
B
C
D
E

Detectors A, B:
5
4

1
0

2

3

F

Fig. 10.1 The left and right panels display a sketch of the Electron Proton Helium INstrument
(EPHIN) aboard SOHO (Müller-Mellin et al. 1995) and the dE/dx-dE/dx measurement principle
applied to it, respectively

adjacent detectors against each other, the mean energy losses of H and He follow
the characteristic tracks. This is used to identify the particle species in certain areas
of the two-dimensional pulse height plane. In these regions, the energy loss in both
detectors is attributed to the incoming energy of the particle. Both Goddard Medium
Energy (GME) experiment and the Medium Energy Detector (MED) (Meyer and
Evenson 1978) utilize this technique.
EPHIN is a multi-element array of solid state detectors with anticoincidence to
measure energy spectra of electrons in the range 250 keV to >8.7 MeV, and of
hydrogen and helium isotopes in the range 4 MeV/n to >53 MeV/n. The instrument
is sketched in Fig. 10.1 left and consists of a stack of silicon solid state detectors
(A-F) surrounded by an anticoincidence (scintillator, G). The method to derive
energy spectra for penetrating particles with energies above 50 MeV/nucleon is
described in detail by Kühl et al. (2015). Since relativistic protons and electrons have
the same energy loss dE=dx in matter, electrons with energies above 10 MeV are
leading to too high fluxes at energies above
700 MeV for protons when utilizing
the dE=dx  dE=dx-method.
The second instrument utilizing this method is the GME aboard IMP-8 that was
launched by NASA in 1973 into a 35 RE geocentric orbit with a 12 days period.
The spacecraft was in the solar wind for 7–8 days of every 12-day orbit, where it
measured the magnetic fields, plasma, and energetic charged particles (e.g., cosmic
rays). The spacecraft spin axis was normal to the ecliptic plane, and the spin rate
was 23 rpm. PAD information was obtained in eight angular sectors.
In contrast to EPHIN, the MED design consisted of three pulse-height analyzed
CsI detectors with thicknesses of 1 mm, 2 cm and 1 mm, respectively, and a
cylindrical plastic scintillator anticoincidence shield. Penetrating particles have an
energy above 80 MeV and a geometry factor of nearly 5.0 cm2 sr (for details see
http://spdf.gsfc.nasa.gov/imp8_GME/GME_instrument.html).

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10.2.2 dE/dx - C
This method is used for penetrating particles. This method is based on charged
particles completely penetrating the Solid State Detector (SSD) and a Cerenkov
detector (C), which is placed underneath. If the particles penetrate C faster than
with the speed of light in this medium, i.e., with a speed of ˇ > 1n where
n is the refractive index of the material, they produce a measurable light flash
(Cerenkov radiation). Plotting the Cerenkov detector signal against the energy-loss
by ionization,  E in the SSD results in characteristic curves for protons and helium,
clearly separated with their slopes depending on particle speed. Thus, the method
allows an identification of the penetrating particles and gives their energy above a
threshold speed. This method is utilized by the HEPAD assembly (Rinehart 1978)
aboard a series of GOES satellites in geosynchronous orbit maintained by National
Oceanic and Atmospheric Administration (NOAA), which provides differential
fluxes in three channels between 350 MeV and 700 MeV, and integral flux above
700 MeV (Sauer 1993). HEPAD consists of two 500 m thick silicon detectors and
a silica radiator. The two surface barrier silicon detectors have an area of 3 cm2 and
define an effective acceptance aperture of 24ı half-angle.
Charged particles, which completely penetrate the two semiconductor detectors,
can be studied with the help of the Cerenkov-detector (McDonald 1956; Linsley
1955), which is placed underneath the semiconductor detectors. The use of a
different detector is necessary since, with energy-loss-measurements alone, the
energy determination is only possible in a narrow energy range above the maximum
energy for stopping particles. The official archive for GOES Energetic Particle data,
including proton flux data, can be found at the National Geophysical Data Center.2

10.2.3 Magnet Spectrometer
In addition we utilize data from the Russian-Italian PAMELA mission (Picozza
et al. 2007) and the AMS-02 aboard the ISS (Aguilar et al. 2013; Kounine 2012).
PAMELA as well as AMS-02 are magnetic spectrometers in Low Earth Orbit,
providing extremely high-quality observations of electrons and ions, which we have
used for validation and cross-calibration purposes. Because the orbits of PAMELA
and AMS are within the Earth’s magnetic field, the two spacecraft do not have
a 100% duty cycle for observing low-energy cosmic rays (Adriani et al. 2011).
Therefore our approach is to use their observations to validate measurements e.g.
from EPHIN.

2

http://www.ngdc.noaa.gov/stp/satellite/goes/.

10 Inversion Methodology of Ground Level Enhancements

185

10.3 Forward Modeling from the Sun to the Observer
at Ground
The project HESPERIA gathered experts in different fields to take into account
interconnections between the solar, heliospheric and NM communities and to
advance our knowledge of GLEs further. The group developed a model chain
allowing to infer the solar release time profile of relativistic SEPs and their
interplanetary transport parameters directly from NM observations. The process
chain starts with the propagation of SEPs from the Sun to the Earth. Utilizing
the local interplanetary field in Geocentric Solar Ecliptic (GSE) coordinates, the
PAD outside the magnetosphere can be converted to an angular distribution in
GSE coordinates. Computing the energetic particle transport in the geomagnetic
field and taking into account the NM yield function the count rate variation of
all NMs that have measured the event can be predicted. Although the physics of
the underlying processes is discussed in detail in Chap. 4 (interplanetary transport),
Chap. 5 (transport through the magnetosphere) and Chap. 6 (ground-based measurements by NMs) we will show in a compact way how the different models need to be
interlinked.

10.3.1 Interplanetary Particle Transport: From the Sun
to the Magnetosphere
Here we give a summary of Chap. 4 in which we model the particle transport
from the Sun (ri D 2 rSun ) in an unperturbed solar wind with constant velocity
v. The Interplanetary Magnetic Field (IMF) can be described as a smooth average
field, represented by an Archimedean spiral, with superposed magnetic fluctuations.
The quantitative treatment of the evolution of the particle’s phase space density,
f .z; ; t/, can be described by the focused transport equation (Roelof 1969):


@f
1  2
@f
@
@f
@f
C ˇc  C
ˇc

D
D q.z; ; t/
@t
@z
2L
@ @
@

(10.1)

Here z is the distance along the magnetic field line that depends on the solar
wind velocity v,  D cos ˛, is the cosine of the particle pitch angle, ˛, and t
is the time. The systematic force is characterized by the focusing length, L.z/ D
B.z/=.@B=@z/, in the diverging magnetic field B, while the stochastic forces are
described by the pitch-angle diffusion coefficient D ./. As discussed in detail in
Chap. 4 the pitch-angle diffusion coefficient has the same form as in Agueda et al.
(2008).
Another approximation was introduced by Hasselmann and Wibberenz (1970). If
we take the particle radial mean free path, r , to be spatially constant, then the mean
free path parallel to the IMF line is given by jj D r sec2 , where is the angle

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B. Heber et al.

between the field line and the radial direction. As shown in Chap. 4 it is sufficient
to compute a database of “Green’s-functions” for particles moving with the speed
of light (ˇ D 1). The database consists of 30 different values of the radial mean free
path, from r D 0:1 to r D 2:0 AU and for solar wind velocities ranging from
300 to 700 km/s. The intensity spectra at the source are given by the solar spectrum
that is typically a power-law with N.R/ / R , where  is the spectral index of the
solar source. Results of this modeling have been discussed in Chap. 4 and (Agueda
2008). There the results could be directly compared to spacecraft measurements.
However, observations in the magnetosphere and ground-based measurements need
to take into account the geomagnetic filter as described in Chap. 5 and the shielding
by the atmosphere and the specific response of the NM (Chap. 6).

If we assume for each energy interval a number of delta injections in time at
the source region the phase space density f .z; ; t/ can be calculated for any
time t at 1 AU corresponding to a distance z.v/ depending on the solar wind
velocity v for every  if the mean free path r , the solar wind speed v and the
direction of the interplanetary magnetic field are known. Acceleration theories
(see Chap. 3), as well as measurements, suggests that the source spectrum is
given by a power law described by the spectral index  . Thus three free
parameters describe the temporal evolution of a SEP event caused by a
single ı-injection at the Sun.

10.3.2 From the Interplanetary Particle Distribution to
Neutron Monitor Measurements - Magneto- and
Atmospheric Transport of Charged Energetic Particles
The transport of cosmic ray particles in the geomagnetic field and in the Earth’s
atmosphere are described in detail in the Chaps. 5 and 6. Here we refer to the objects
that are relevant to the investigations of NM data during solar cosmic ray events.
The asymptotic viewing directions for each NM station are often computed only
for primary cosmic ray particles that penetrate into the Earth’s atmosphere from a
vertical direction. The contribution of obliquely incident particles is often neglected
in GLE analysis as their contribution to the counting rate is assumed to be small
because of the soft spectrum of the solar cosmic rays.
The minimum rigidity that a charged energetic particle must have to reach
a location within the magnetosphere and from a given direction of incidence is
expressed by the geomagnetic cutoff rigidity RC . This cutoff rigidity varies from
a minimum at the magnetic poles (RC
0 GV) to a value of about 15 GV in
equatorial regions. The asymptotic direction for a NM, for a given direction of
incidence into the Earth’s atmosphere above the location of the NM and a selected

10 Inversion Methodology of Ground Level Enhancements

187

particle rigidity, is defined as the direction of motion of the primary cosmic ray
particle before penetrating the Earth’s magnetosphere. In contrast to previous work
by e.g. Bieber et al. (2004), neither the shape of the PAD nor the incoming direction
is a free parameter in the High Energy Solar Particle Events forecasting and Analysis
(HESPERIA) approach. The PAD of SEPs outside the Earth’s magnetosphere is
calculated as described in Sect. 10.3.1. To assign for each rigidity the pitch angle
range of a NM we need to know the Interplanetary Magnetic Field (IMF) direction
close to the Earth magnetopause and the asymptotic direction in GSE coordinates.
In HESPERIA, we make use of the 5-min averaged OMNI data to prepare a set of
magnetic field directions outside the magnetosphere, to be used as the directions
of the symmetry axis of the directional relativistic proton distribution. The field to
which the distribution tends to become gyro-tropic is not the momentarily measured
field at the particle position but rather the field it averages over. Although the
timescales of the gyro motion are relatively small, the spatial ones are not. A first
order estimation, rL =.uSW t/  1, leads to t D 1670 s for the averaging time of
the fluctuating field for a 1-GV particle in a 5 nT field and a solar wind speed of
400 km/s. However, it should be noted that particles would need a rigidity-dependent
averaging time of the field direction. As an example, Fig. 10.2 displays on the left the
rigidity-dependent vertical asymptotic directions for a stationary observer in Kiel
from 1:30 to 3:00 UT on May 17, 2012. The colored triangles show the direction of
the interplanetary field for each period. From these two directions, the pitch angle
for each rigidity and time can be calculated. The right panel of Fig. 10.2 displays
the corresponding results.

Fig. 10.2 Left: Calculations of the asymptotic direction at different rigidities during the onset of
the May 17, 2012 SEP event as function of time for an observer at Kiel. The triangles indicate the
direction of the interplanetary magnetic field. The right panel shows the pitch angle coverage for
the same period. For details see text

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B. Heber et al.

If we assume that only protons are accelerated in a SEP event to sufficient
rigidities R that NMs can measure, then the count rate N caused by solar cosmic
ray protons at the NM station x and at time t can be expressed by:
Z
Nx .t/ D

Ru

I.R; ˛; t/  Sx .R; h/  dR;

(10.2)

Rc

where Rc and Ru are the cutoff and upper (Ru D 20 GV) rigidities, ˛ the pitch
angle of the incoming proton, Sx .R; h/ the yield function of the NM station x at
the atmospheric depth, h (for details see Chap. 6). Here Eq. (10.2) is approximated
by the sum of discrete values covering the full rigidity and pitch angle range. The
upper value of Ru D 20 GV was chosen because there is no observational evidence
for SEP protons with rigidities above 20 GV.

Given the IMF vector B in GSE coordinates and the asymptotic directions n
in the same coordinate system, we compute the pitch angle, ˛ coverage, for
each NM. Together with the yield function described in Chap. 6 the count rate
increase for each NM is computed.

10.3.3 Combined Greens-Function
As part of HESPERIA, the two models described in the previous two sections were
combined. The first step is to compute the additional count rate, N, caused by
SEPs for a given NM station with cutoff rigidity RC at the time t1 , based on the
computed rigidity and cosine of the pitch angle () dependent intensity I1 .; t1 ; r/
of relativistic protons at time t1 . This spectrum I1 results from an energy spectrum
I0 / R injected as a ı-function at a time t0 before t1 . The two parameters
determining the injection function are the power-law index  and the number of
particles injected at a rigidity R D 1 GV. The particle transport in the IMF is
described by Eq. (10.1) using 0 as the only free parameter. The path length of the
particles is determined by the solar wind speed measured at 1 AU (see Sect. 10.3.1).
The IMF outside the Earth’s magnetosphere together with the asymptotic direction
calculated for t1 gives the pitch angle coverage for the NM. Within HESPERIA
the Green’s function Gˇ .t; z; ; v/ are derived from the ones Gc .t; z; ; c/ that
are available from SEPServer (http://server.sepserver.eu) for relativistic protons
(ˇ D 1). For near relativistic particles the energy loss in the IMF can be neglected
and therefore the Green’s function for a lower velocity ˇ is given by:

Gˇ

1
t; z; ; ˇ
ˇ


D ˇGc .t; z; ; c/ :

(10.3)

10 Inversion Methodology of Ground Level Enhancements

189

We consider near relativistic protons with rigidities from 0.5 to 20 GV (kinetic
energies from 0.12 to 19 GeV) and following a power law in rigidity I.R/ D I0  R
with the spectral index  .
The proton mean-free path is taken to increase with rigidity following the
standard model. The resulting pitch angle dependent energy spectra at 1 AU are
transported through the magnetosphere and atmosphere as described above.

10.4 Inversion Methodology
The previous two sections are describing the forward modeling of energetic particles
from the Sun through the inner helio-, magneto- and atmosphere. Up to now, the
inversion has only been attempted in two separate steps:
Inversion of NM data: The standard analysis of GLE events is based on solving
an inverse problem where data by the worldwide network of NMs is used to
determine the spectral and angular characteristics of SEPs near Earth but outside
the magnetosphere causing the GLE.
Inversion of spacecraft data: The injection time profile of SEPs at the Sun and the
characteristics (mean free path) of their transport in the interplanetary medium is
inverted from 1 AU spacecraft measurements.
In what follows we review first the two inversion approaches used so far and then
describe the HESPERIA approach.

10.4.1 Inversion of Spacecraft Data to the Sun
Numerical simulations of the propagation of SEPs along the IMF are a useful tool
to understand SEP events and their sources. We currently have a good theoretical
understanding of the transport processes that affect SEPs in the interplanetary
medium (see Chap. 4). In Sect. 10.3.1 we discussed a model that simulates the
processes undergone by SEPs during their propagation from their source to the
observer with the critical parameters summarized in the gray box on page 186.
The approach introduced by Agueda et al. (2008) is to utilize the computed
response of the “system” to an impulsive (delta) injection at the Sun, i.e. the Green’s
function of particle transport. A convolution of some delta injections allows us to
compute different pitch angle dependent proton intensity time profiles that are used
as input to the second step in the chain (see Sect. 10.3.2).
Given a system impulse response, g.t/, and the input injection profile q.t/, the
output, I.t/, is the convolution of g.t/ and q.t/:
Z

1

I.t/ D
0

g.t0 /q.t  t0 /dt0

(10.4)

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B. Heber et al.

1RUPDOL]HG ,QWHQVLW\



SOPO MCMU APTY ATHN





model (γ = 5.5, λ0 = 0.1 AU)



  
8QLYHUVDO 7LPH



Fig. 10.3 Convolution of different ı-injections close to the Sun on April 15, 2001 (GLE60) from
13:45 h to 14:15 h (left panel) with a set of ı injection  D 5:5 at the Sun, and a mean free path
 D 0:1 AU in interplanetary space leads to intensity increases at the Apatity, Athens, McMurdo
and South Pole NM (right panel)

i.e., I.t/ is the sum of responses resulting from a series of impulses at the Sun,
weighted and shifted in time according to q.t/. For simplicity, here we assumed that
the response is only time-dependent, but the same holds if one includes the energetic
and directional dependence in the Green’s function.
Particle intensities measured in the heliosphere as a function of time, energy and
direction, are obtained as a temporal convolution of the source function (particle
injection profile) and the Green’s function of particle transport at the spacecraft
location. The origin of SEP events can be unfolded by solving the inverse problem
(deconvolving the in-situ measurements). The measurements are used to infer the
values of the model parameters. It is a deductive approach, and it has the advantage
that a systematic exploration of the parameters’ space is possible. A simulated GLE
time profile with a proton injection from 13:45 h to 14:15 h at the Sun as displayed
in the left panel of Fig 10.3 leads to a proton event observable close to Earth by
intensity increases at Apatity, Athens, McMurdo and the South Pole displayed in
the right panel. A convolution of a ı-injection with  D 5:5, and a mean free path
0 D 0:1 AU has been used.
Let’s consider an arbitrary function q.t/—to be determined—that represents the
injection function of SEPs close to the Sun. The modeled directional intensities, Mjk ,
resulting from a series of impulse solar injections can be written as
Z
Mjk .tI / D

T2

T1

dt0 gkj .t; t0 I / q.t0 /;

(10.5)

where gkj .t; t0 I / represents the impulse response in a given direction j and energy
interval k, at a given time t, when particle injection took place at time t0 and assuming
an interplanetary mean free path . The duration of the injection function, t0 2
ŒT1 ; T2 , is determined by the SEP event time interval selected for fitting, t 2 Œt1 ; t2 ,
that is, T1 D t1  t and T2 D t2  t, where t is the transit time of the first
arriving particles at the spacecraft location, assuming a given value of the scattering

10 Inversion Methodology of Ground Level Enhancements

191

mean free path. The number of time points in the event time interval selected for
fitting is equal to nt D .t2  t1 /=ıt C 2, where ıt is the time resolution of the data.
Taking discrete values of time, we have
Mjk .th I / D

nt
X

gkj .th ; tl0 I / q.tl0 /

(10.6)

lD1

where j D 1; 2; : : : ; ns are numbers representing the directions (sectors or bins)
observed by the telescope, k D 1; 2; : : : ; nc numbers for the energy channels and
h D 1; 2; : : : :; nt numbers of the time intervals.
Equation (10.6) can be written as
Mjk .th I /  Mi ./ D

nt
X

gil ./ ql D .g  q/i

(10.7)

lD1

where i D k C . j  1/  nt D 1; 2; : : : ; nT numbers the total number of observational
points and nT D nt ns gives the total number of observational points in all sectors; g
is an nT  nt matrix with .g/il D gil ./.
In matrix form,
0

1

0

g11 g12
C B g21 g22
B
C B
B
CDB :
B
::
A @ ::
@
:
gnT 1 gnT 2
MnT
M1
M2
::
:

1 0 1
q1
   g1nt
B
C
   g2nt C B q2 C
C
:: C  B :: C
::
@
A
: :
: A
   gnT nt
qnt

(10.8)

The goal is to compare the modeled intensities with the observations. Let Ji be
the observations (background subtracted). We want to derive the nt -vector q that
minimizes the length of the vector J  M, that means minimizing the value of
jjJ  Mjj  jjJ  g  qjj;

(10.9)

subject to the constraint that ql 0 8l D 1; 2; : : : ; nt . Thus, the best-fit
q D .q1 ; q2 ; : : : ; qnt / corresponds to a combination of delta-function injection
amplitudes. To obtain the best-fit values, we use the NNLS method developed by
Lawson and Hanson (1974), which always converges to a solution.
Note, that if each energy channel is fitted separately, the total number of
observational points considered in the fit is nt ns and the total number of independent
fitting parameters (injection amplitudes) is nt . Since nt ns  nt , the number of
degrees of freedom is clearly much larger than the number of model parameters
and the inversion problem is well constrained. If one instead neglects the directional
information in the data and uses the modeled omnidirectional intensities to fit the
omnidirectional event, then the number of observational points and the number of
independent fitting parameters is equal, and the problem is not well constrained
(multiple injections and transport scenarios can provide an explanation for the data).

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B. Heber et al.

The goodness of fit describes how well the model predictions fit a set of
observations. One way to evaluate the goodness of the fit, in case the measurement
errors are known, is to construct a weighted sum of squared residuals (for details see
Agueda 2008). The 2 estimator does not work very well for SEP events because
during impulsive events the maximum intensities can be several orders of magnitude
higher than the intensities observed during the decay phase, thus emphasizing the
peak period. Therefore a better goodness-of-fit estimator is provided by the sum
of the squared logarithmic differences between the observational and the modeled
data. This estimator gives an equal weight of all relative residuals instead of just
emphasizing the goodness of fit at the time of maximum. By evaluating the goodness
of the fit under different interplanetary transport conditions (different values of ),
one can objectively discern the “best fit” scenario (-value and associated injection
profile) by minimizing the values of the goodness-of-fit estimator.

10.4.2 Inversion of NM Data to the Border of the Earth’s
Magnetosphere
In general, the standard analysis of GLE events is based on an inverse problem,
where data by the worldwide network of NMs is used to determine the spectral and
angular characteristics of SEPs near Earth causing GLEs for selected times (Shea
and Smart 1982; Mishev et al. 2014). Analysis of the characteristics of the primary
solar particles causing GLEs from ground-based data records is a serious challenge
(Bütikofer and Flückiger 2013). Data from stations with different cutoff rigidities
(geomagnetic latitudes) provide information necessary to determine the spectral
characteristics. Responses of stations over a wide range of geographical locations
are required to determine the axis of symmetry. Data are fitted to directional
distributions that are rotationally symmetric about one direction in space. This,
in principle, is close but not exactly the direction of the instantaneous magnetic
field measured close to the Earth but outside the Earth’s magnetosphere (Bieber
et al. 2013). Therefore, axis-symmetry is assumed, but the direction of the axis of
symmetry is optimized to fit the data.
The PADs of relativistic solar protons in space are assumed to follow a given
functionality. A variety of functions has been used in the literature. These include
a linear form, an exponential plus a constant, a parabola, two Gaussians, and two
exponentials plus constant. The latter three are expected to provide better fits to
bidirectional fluxes, if present (Bieber et al. 2013; Mishev et al. 2014).
Similarly, the spectra of relativistic solar protons during a GLE are assumed to
follow a power law in rigidity, or energy with extensions that describe the softening
of the spectrum at higher energies by multiplying a power law with an exponential
cutoff.

10 Inversion Methodology of Ground Level Enhancements

193

The parameters of the rigidity spectrum, the PAD and the direction of symmetry
are determined by minimizing the sum of squared differences between the modeled
relative
in the NM count rate at the station x
 change

Nx
and
Nx mod.
the
observed relative count rate change
 corresponding

Nx
Nx

obs.

FD


m 
X
Nx
xD1

Nx

mod.




Nx
Nx



2
(10.10)

obs.

for the set of selected NM data. The Levenberg-Marquardt algorithm (LMA)
(Marquardt 1963) provides a numerical solution to the problem of minimizing a
nonlinear function over the space of parameters of the function. The goodness of the
fit is commonly expressed by a weighted sum of squared residuals or by computing
a correlation coefficient, between measurements and the model.

10.4.3 The HESPERIA Approach
For the first time, models of the transport of SEPs in the interplanetary medium,
the Earth’s magnetosphere and atmosphere, and the response of NMs are linked
to each other. The first goal is to compute the expected additional count rate, N,
caused by SEP for a given NM station, based on the intensities of the primary cosmic
rays near Earth, I.R; ˛; t/, as function of rigidity, R, pitch angle, ˛, and time, t. As
detailed above the interplanetary transport is described by Green’s functions representing characteristics of the SEP interplanetary transport conditions. To ascribe the
magnetospheric transport, the magnetic field direction outside the magnetosphere
is computed from interplanetary measurements, and the asymptotic directions are
calculated utilizing the PLANETOCOSMICS code in GSE coordinates. The latter
can be found at the HESPERIA webpage during each GLE in the past and for the
NMs of the worldwide network.
Since the parameters are the same than the ones used by Agueda et al. (2008)
the differences lie in the indirect measurement of the pitch angle dependent count
rate and the integration over wide energy ranges: For all NM stations, the counting
rate increases can then be computed for a series of delta injections from the Sun
and for selected times. Note that the hardness of the source spectra described by
 is assumed to be constant in the HESPERIA approach for all ı-injections. The
amplitudes of the source components, for a given scenario, are inferred by fitting
the NM observations with the modeled NM counting rate increases. The NNLS
algorithm described in Sect. 10.4.1 is used to determine the best set of parameters.
Regularized inversion approaches will be explored for refinements. The goodness
of the fit will be evaluated by computing a weighted sum of the squared residuals.

194

B. Heber et al.

The result of the inversion problem is a detailed time profile of the injection process
at the Sun. The shape of this profile is presumably determined by details of the
acceleration process and possible transport processes in the corona (see Chap. 3 for
details).

In contrast to a classical approach with a total number of at least 10 fit
parameters to derive the injection function at the Sun (see Sect. 10.4.2) the
HESPERIA approach relies on several well-documented assumptions (see
Chaps. 3, 4, and 5) reducing the number of free parameters. Assuming for
each rigidity a number of delta injection at the source region the phase
space density f .z; ; t/ close to Earth can be calculated for any given time
t corresponding to the distance z.v/ that depends on the measured solar wind
velocity v. The mean free path 0 , the number of particles, the injection time
profile and its rigidity spectrum described by a power law with index  are
utilized to derive f .z; ; t/. The cosmic ray particle trajectories through the
Earth’s magnetosphere are computed for selected rigidities Rc , Rc C 0:1 GV
. . . 20 GV as a function of GSE coordinates of the NM station, for a selected
time. Applying the Tsyganenko 1989 (Tsy89) model and the yield function
for each NM we can ascribe the SEP time profiles for the NM network by a
minimum of free parameters.

10.5 Results and Validation
Since the HESPERIA approach depends on the knowledge of the IMF outside the
Earth’s magnetosphere that is provided by OMNI since November 4, 1973, our
investigation is restricted to GLEs with numbers larger than number 26 occurring on
April 30, 1976. To validate the results, pitch angle dependent intensity time profiles
of protons with energies above 500 MeV are needed. Here we utilize SOHO/EPHIN
and Wind 3DP measurements. The latter are needed in order to estimate the pitch
angle coverage of SOHO/EPHIN.
Since SOHO was launched in December 1995, we restrict our validation to GLEs
with numbers 55 (GLE55 occurred on November 6, 1997). Kühl et al. (2015,
2016) showed that EPHIN is capable of measuring the proton spectra in the range
from 100 MeV to above 1 GeV. Since no magnetic field measurements are available
on SOHO, we compare the intensity-time-profiles of near relativistic electrons
measured by EPHIN and Wind 3DP with each other. In Fig. 10.4 different colored
curves show the pitch angle dependent time-profiles for Wind 3DP with energies
between 230 and 646 keV. Three thick black lines show the EPHIN measurements
with energies between 0.25 and 0.7 MeV multiplied by different factors (0.05,
0.08, and 0.1 as solid, dashed, and dashed-dotted lines) to take into account cross

10 Inversion Methodology of Ground Level Enhancements
GLE 60 2001–04–15

105
Intensity
((cm2s sr MeV)–1)

195

104
103
0.25–0.7 MeV *0.05
0.25–0.7 MeV *0.08
0.25–0.7 MeV *0.1
Wind sectors 230–646 KeV

102

Pitch
Angle (°)

101
180
160
140
120
100
80
60
40
20
0

105.58

105.60

105.62

105.64

105.66

105.68

Doy in 2001

Fig. 10.4 From top to bottom: Hourly averaged intensity time profiles of 234–646 keV electrons
measured by Wind 3DP. The different colors give the pitch angle coverage for the WIND
observations shown in the bottom panels. Also the solid, dashed and dashed-dotted lines represent
the 0.25–0.7 MeV EPHIN electron measurements multiplied by a factor 0.05, 0.08, and 0.1
respectively

calibration. Only the dashed-dotted line agrees with all Wind sectors when the flux
becomes isotropic. Thus we assume that the curve that agrees best with the dasheddotted line ascribes the viewing direction of EPHIN. In our example, the purple
curve describing the measurements at a pitch angle of 120ı fulfills this criteria best.
Figure 10.5 is an extension of Fig. 10.3 that only showed predicted intensity time
profiles close to Earth and by different NMs. It compares the results computed
with the GLE inversion software with measurements of other facilities as radio
telescopes, NMs and particle detectors in space. The parameters used in the
prediction were derived by the inversion of the NM data for GLE 60. The middle
panel of Fig. 10.5 compares the simulated and measured intensity time profiles of
the Apatity, Athens, McMurdo and South Pole NMs with each other showing a good
agreement between measurements and the model. The injection profile close to the
Sun is shown in the left panel together with the micro wave profile measured by the
Radio Solar Telescope Network (RSTN) showing a good agreement between the
particle component injected into interplanetary space and towards the lower corona.
Note, that the injection profile is in very good agreement with the one derived by
Bieber et al. (2004). For details on micro waves and their importance, the reader is
referred to Chap. 2.
The middle bottom panel displays the energy spectrum between 100 MeV and
1 GeV predicted by the model (red curve) and measured by EPHIN (black curve).
Note, that the prediction was scaled down by a factor of 20. From the figure, it
is evident that the model predicts the same spectral index when taking into account
the contribution of electrons at 900 and 700 MeV, respectively (for details see Kühl
et al. 2017).

196

B. Heber et al.

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6*05  0+]

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measured increases
model (γ = 5.5, λ0 = 0.1 AU)






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Fig. 10.5 Predicted ı-injections (upper left panel), NM increases (upper right panel) and differential intensity spectrum (lower panel) for GLE60 (see also Fig. 10.3) in comparison to actual
measurements (for details see text)

10.6 Concluding Remarks
A new approach has been presented here that allows computing the injection
function of SEP close to the Sun based on the data of the worldwide NM network
during a GLE. This injection function is described by a power law in rigidity R with
two parameters that are the intensity at R0 D 1 GV and the spectral index  . For the
interplanetary transport, we utilize a 1-dimensional model with the mean free path
r as free parameter. The solar wind speed taken from interplanetary measurements
determines the length of the magnetic field line connecting the Earth back to
the Sun. The IMF direction is taken from the OMNI data set using appropriate
accumulation periods. The transport through the Earth’s magnetosphere is computed
with the PLANETOCOSMICS software using the Tsy89 model for the outer
Earth’s magnetic field. The NM yield function describes the passage of the cosmic
ray particles through the atmosphere and the detection of the secondary nucleon
component by the NMs. Using this model chain GLE 60 could be reproduced very
well. A discrepancy between the prediction and the measurements in interplanetary
space exists that needs further investigations. Especially the whole number of
observed GLEs should be analyzed and validated by using GOES HEPAD data that

10 Inversion Methodology of Ground Level Enhancements

197

go back to the 1970s. Further improvements like utilizing more sophisticated models
of the magnetosphere and the interplanetary transport, as well as different NM yield
functions, should be taken into account in order to improve the model presented
here.

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Index

A
Abundance ratios, 8, 46, 149, 150, 151, 152
Asymptotic directions, 79, 80, 91, 187, 188,
193
Atmospheric effects, 100, 105–106

B
Bremsstrahlung, 27, 28, 31, 32, 34, 36, 40,
115, 135, 136, 137, 139, 140

D
ıinjections, 186, 189, 190, 193, 196
Differential intensity spectrum, 196
Diffusive shock acceleration (DSA), 15, 41,
53–58
Diffusive transport, 71–72, 161
Discontinuity, 91, 92, 159
Downstream propagation (DSP) model, 159,
161–164, 169, 170, 173
Dynamo, 79

C
Charged particles, 17, 18, 36, 37, 38, 40, 41,
50, 51, 63, 67–69, 79, 80, 81, 89,
181, 183, 184
Charged particle transport, 63–76
Chromosphere, 29, 32, 35, 135, 145, 157, 158
CME-driven shock, 3, 5, 14, 16, 46, 144, 148,
152, 157, 158, 180
Collapsing magnetic trap, 57–58
Combined Greens-function, 188–189
Compressional acceleration, 46, 57–58
Convolution, 189, 190
Coronal mass ejection, 1, 27, 37–42, 45, 63,
96, 117, 180
Coronal shock acceleration, 9, 159–161, 176
Cosmic ray particle transport, 79–93
Cutoff rigidities, 80, 91–93, 192
Cyclotron resonance, 51, 52
Cyclotron waves, 52, 59

E
Earth’s atmosphere, 95, 97–100, 103, 105, 106,
181, 186
Earth’s Magnetic field, 79–83, 86–88, 90, 92,
97, 100, 107, 184, 196
Earth’s magnetosphere, 19, 66, 79–93, 114,
182, 187, 188, 192, 193, 194, 196
Electric field acceleration, 47–49
Electrodynamic coupling, 29
Electromagnetic fields, 45, 47, 48, 69, 80
Electromagnetic waves, 33, 52, 69–70
Electron beams, 33–34, 36
Electron intensities, 120, 121, 122
Energetic particles, 1–23, 41, 63–64, 69, 98,
114, 134, 159, 185–189
Energy spectra, 4, 11, 12, 13, 19, 22, 118–120,
149, 150, 167, 168, 169, 173, 183,
189
Eruptive activity, 27–41

© The Author(s) 2018
O.E. Malandraki, N.B. Crosby (eds.), Solar Particle Radiation Storms Forecasting
and Analysis, The HESPERIA HORIZON 2020 Project and Beyond, Astrophysics
and Space Science Library 444, DOI 10.1007/978-3-319-60051-2

201

202
F
First adiabatic invariant, 67–69
Focused transport, 70–71, 185
Forecasting tools, 23, 113–130
Forward modeling, 181, 185–189

G
Gamma-ray, 28, 31, 34, 38, 133–151, 157–173
Gamma(/-ray emission, 27, 34, 134–138,
140–145, 149, 169
Geomagnetic field, 80, 82, 84, 85, 87, 88, 89,
92, 95, 96, 104, 180, 186
Geomagnetosphere, 79, 80, 81, 82, 83, 87, 88,
89, 91, 92, 93, 96
Gradual SEP events, 2, 3, 5–11, 46, 60, 64,
180
Ground-based measurements, 95–109
Ground level enhancement, 11–12, 97, 114,
124, 158, 179–196
Gyrosynchrotron, 31–33, 39, 115
Gyrosynchrotron radiation, 31–33, 115

H
Hard X-ray, 28, 30, 31, 32, 35, 36, 38, 115,
135, 137, 138, 139, 140, 141, 142,
143, 148, 151, 152
Hazard assessment, 20–22
Heliosphere, 6, 9, 12–16, 38, 40, 64, 71, 190
Historical microwave data, 115–118
Human health, 19–20
Human health effects, 19–20

I
Impulsive flare, 3, 29, 40, 134, 137, 138, 139,
140
Impulsive SEP events, 2, 3, 151
Intensity time-profiles, 13, 171, 194
Interplanetary magnetic field, 3, 14, 64–66, 69,
87, 89, 166, 182, 185, 186, 187
Interplanetary medium, 63–76, 180, 189, 193
Interplanetary particle distribution, 186–188
Interplanetary transport, 72, 77, 181, 185, 192,
193
Inversion methodology, 179–196
Inversion model, 72, 75, 76
Ionosphere, 19, 83, 86, 87, 114

L
Langmuir waves, 33, 34
Large gradual SEP events, 5–11, 60

Index
Long duration -ray events, 136, 141–143,
145, 158, 173, 174
Lorentz force, 36, 38, 47, 49, 67, 68, 80–81, 97

M
Magnetic flux rope, 38, 39
Magnetic polarities, 39
Magnetic structuring, 28
Magnetohydrodynamic, 2, 41, 56, 159
Magnetospheric electric currents, 86–87
Mean free path, 57, 71, 74, 99, 102, 162, 185,
186, 189, 190, 191, 194, 196
Microwave flux density, 114, 116, 117, 119,
120, 129
Mitigation procedures, 20, 22–23
Mitigation strategies, 17, 22
Multi-spacecraft observations, 12–14

N
Neutron monitor data, 105, 108
Neutron monitor detector, 100–106
Neutron monitors, 2, 22, 91, 95–109
Neutron monitor station, 96, 97, 98, 100, 104,
106, 107, 108, 109
Neutron monitor yield function, 103–104
Nuclear gamma-ray emission, 27
Numerical techniques, 72

P
Parallel diffusion coefficient, 9
Particle acceleration, 2, 10, 14–15, 27–37,
40–42, 45–60, 115, 129, 152, 169,
173, 174, 175, 176
Particle cascade, 99–100
Particle effects, 18
Particle transport equations, 69–70
Peak proton intensity, 6, 11
Perpendicular diffusion coefficient, 9
Photon energies, 31, 134–136, 141
Photosphere, 28, 29, 36, 38, 39, 41, 145
Pion-decay, 34, 134, 135, 136, 137, 139, 140,
142, 151, 152, 158, 174, 176
Plasma emission, 31, 33–34, 39
Propagation, 13, 19, 54, 63, 64, 68, 74, 79,
89–91, 114, 159–165, 170, 173, 185,
189
Proton acceleration, 158, 167–168, 172–173,
176
Proton differential intensity, 73
Proton fluxes, 116, 117, 146
Proton injection rate, 165, 166, 167, 171, 172

Index
Proton intensity, 5, 6, 11, 12, 116, 117, 120,
171, 189
Proton spectra, 4, 119, 129, 139, 164, 169, 173,
194
Proton transport, 159, 161, 169–170, 173

R
Real-time predictions, 23, 130
Real-time tools, 113
Relativistic gamma-ray events, 133–152
Remote sensing, 16, 22, 180
Reservoir region, 12, 13
Resonant wave acceleration, 50–53

S
SEP effects, 17–19
Shock-accelerated particles, 9, 56, 71, 75, 141
Shock acceleration, 7, 9, 11, 15, 41, 46, 47,
53–57, 152, 158–161, 176, 181
Shock drift acceleration, 40, 53
Shock modelling, 168
Shock passage, 12, 13, 73, 74, 165
Shock surfing acceleration, 53
Shock waves, 2, 7, 27, 28, 36, 37, 40–42, 54,
70, 141, 144–145, 158, 180
Simulation model, 159, 161, 176
Snowstorm effect, 18

203
Soft X-ray, 7, 29, 30, 31, 114, 129, 140, 141,
142, 143, 146, 147, 149, 151, 152
Solar activity, 27, 42, 66, 87, 100, 106, 124
Solar atmosphere, 28, 31, 32, 34, 40, 115, 134,
137, 141, 144, 145, 151, 152, 158
Solar corona, 16, 28, 33, 36, 37, 39, 42, 45, 53,
143, 181
Solar cosmic ray, 96, 97, 105, 106, 181, 186
Solar cycle 23, 11, 12
Solar energetic particle events, 27–42, 63–64,
72–76, 100, 114, 134, 137, 145–151
Solar energetic particles, 1–23, 45, 124, 134
Solar flare, 1, 2, 3, 7, 16, 22, 29–36, 40, 53, 63,
135, 137, 138, 158, 180
Source plasma temperature, 12
Space weather, 1–23, 96, 118, 130, 176, 181
Spectrometer, 96, 98, 102, 107–108, 134, 182,
184
Stochastic acceleration, 46, 58–60, 158, 174
Suprathermal seed populations, 8
Sustained emission events, 137–141

T
Tsyganenko model, 88, 89

V
Validation, 184, 194–196