Particle Dynamics in the Earth's Radiation Belts: Review

Particle Dynamics in the Earths Radiation Belts Reviewof Current Research and Open QuestionsJ‐F Ripoll1 S G Claudepierre23 A Y Ukhorskiy4 C Colpitts5 X Li6 J F Fennell2 andC Crabtree7

1CEA DAM DIF Arpajon France 2The Aerospace Corporation El Segundo CA USA 3Department of Atmospheric andOceanic Sciences University of California Los Angeles CA USA 4The Johns Hopkins University Applied PhysicsLaboratory Laurel MD USA 5School of Physics and Astronomy University of Minnesota Minneapolis MN USA6LASP University of Colorado Boulder Boulder CO USA 7Naval Research Laboratory Washington DC USA

Abstract The past decade transformed our observational understanding of energetic particle processes innear‐Earth space An unprecedented suite of observational systems was in operation including the VanAllen Probes Arase MagnetosphericMultiscale Time History of Events andMacroscale Interactions duringSubstorms Cluster GPS GOES and Los Alamos National Laboratory‐GEO magnetospheric missionsThey were supported by conjugate low‐altitude measurements on spacecraft balloons and ground‐basedarrays Together these significantly improved our ability to determine and quantify the mechanisms thatcontrol the buildup and subsequent variability of energetic particle intensities in the inner magnetosphereThe high‐quality data from National Aeronautics and Space Administrations Van Allen Probes are the mostcomprehensive in situ measurements ever taken in the near‐Earth space radiation environment Theseobservations coupled with recent advances in radiation belt theory and modeling including dramaticincreases in computational power have ushered in a new era perhaps a ldquogolden erardquo in radiation beltresearch We have edited a Journal of Geophysical Research Space Science Special Collection dedicated toParticle Dynamics in the Earths Radiation Belts in which we gather the most recent scientific findings andunderstanding of this important region of geospace This collection includes the results presented at theAmerican Geophysical Union Chapman International Conference in Cascais Portugal (March 2018) andmany other recent and relevant contributions The present article introduces and review the context currentresearch and main questions that motivate modern radiation belt research divided into the followingtopics (1) particle acceleration and transport (2) particle loss (3) the role of nonlinear processes (4)new radiation belt modeling capabilities and the quantification of model uncertainties and (5) laboratoryplasma experiments

1 Introduction

Earths radiation belts consist of two toroidal belts of energetic charged particles (electrons and ions) sur-rounding Earth The outer belt typically lies at geocentric radial distances between 3 and 7 Earth radii (1Earth radius = 6370 km) in the equatorial plane and consists primarily of highly energetic (01ndash10 MeV)electrons and high‐energy protons (1ndash100 keV) though other ion species and lower‐energy particles are alsopresent The inner belt sits between 1 and 3 Earth radii and contains primarily hundreds of kiloelectron voltselectrons along with extremely energetic (eg hundreds of megaelectron volts) protons This description ishowever an idealized representation of a simplified structure This representation can be valid during quietgeomagnetic times but dynamicdisturbed conditions bring complex dynamic monobelt or multibelt struc-tures (eg Baker Kanekal Hoxie Henderson et al 2013) forming within the inner magnetosphere below~7ndash8 Earth radii Earths radiation belt location is also energy dependent Many competing processes contri-bute to the dynamic formation and depletion of the belts including radial transport local wave accelerationparticle loss to the magnetopause particle precipitation into the atmosphere and others These competingenergization loss and transport mechanisms greatly contribute to generating complex structures far beyondthe ideal two‐belt structure These competing mechanisms typically occur simultaneously (eg Baker et al2019 in this collection) and are energy dependent an accurate description of the radiation belts mustaccount for their combined effects The relative importance of each process is the most fundamental unan-swered question in radiation belt physics This question cannot be answered fully without the combinedeffort of and collaboration between experimentalists theorists and modelers

copy2019 American Geophysical UnionAll Rights Reserved

INTRODUCTION TOA SPECIAL SECTION1010292019JA026735

Special SectionParticle Dynamics in theEarths Radiation Belts

Key Pointsbull We review and discuss current

research and open questions relativeto Earths radiation belts

bull Aspects of modern radiation beltresearch concern particleacceleration and transport particleloss and the role of nonlinearprocesses

bull We also discuss new radiation beltmodeling capabilities thequantification of modeluncertainties and laboratory plasmaexperiments

Correspondence toJ‐F Ripolljean‐francoisripollceafr

CitationRipoll J‐F Claudepierre S GUkhorskiy A Y Colpitts C Li XFennell J amp Crabtree C (2020)Particle Dynamics in the EarthsRadiation Belts Review of CurrentResearch and Open Questions Journalof Geophysical Research Space Physics125 e2019JA026735 httpsdoiorg1010292019JA026735

Received 27 MAR 2019Accepted 20 NOV 2019Accepted article online 26 DEC 2019

RIPOLL ET AL 1 of 48

The motion of a charged particle in the Earths magnetic field was first formulated by Stoumlrmer (2018) andwas subsequently studied by him and several others in connection with auroral phenomena and cosmicrays (Stoumlrmer 2017) The motion and the stability of charged and trapped particles in Earths magneticfield was then well established by 1960 (eg Northrop amp Teller 1960 Dragt 1965 Faumllthammar 1965)and has provided the theoretical basis for the presence of Earths radiation belts discovered by pioneeringspace missions (Van Allen 1959 Vernov et al 1959) It was shown that in the approximately dipolarmagnetic field of the inner magnetosphere including the Earths Van Allen radiation belts charged par-ticles undergo quasiperiodic motion composed of gyro bounce and gradient‐curvature drift motionseach associated with an adiabatic invariant This set of three invariants defines a stable drift shell encir-cling Earth Subsequent experiments revealed that particle intensities across the belts can vary signifi-cantly with time which requires violation of one or more of the adiabatic invariants The theoreticalinterpretation of the variability of radiation belt intensities was largely inspired by the experiments inparticle acceleration by random‐phased electrostatic waves in synchrocyclotron devices and by the subse-quent development of the theory of weak plasma turbulence It was thus suggested that the adiabaticinvariants of trapped particles can be violated by small‐amplitude waves which resonantly interact withthe quasiperiodic particle motion (Balescu 1960 Lenard 1960 Vedenov et al 1961) Since both the den-sity and energy density of radiation belt particles are negligible compared to other plasma populationstheir motion does not affect the fields that govern them (with some exceptions eg chorus waves)Thus it was suggested that the evolution of radiation belt intensities can be described kinetically and sta-tistically as a quasilinear diffusion in the three adiabatic invariants (Northrop amp Teller 1960) under theaction of prescribed wave fields with the diffusion coefficients determined by resonant wave‐particleinteractions (eg Hess 1968 Walt 1970 Schulz amp Lanzerotti 1974) The theoretical framework of quasi-linear diffusion of radiation belt particles developed within the first decade following the discovery ofthe belts has been the backbone of most of the modeling of global variability of radiation belt intensities(see recent reviews eg Hudson et al 2008 Shprits et al 2008a 2008b Thorne 2010 and see discus-sion in section 5) We will see many aspects of this approach treated in this JGR Special Collection Inaddition it is now clear that nonlinear effects must also be considered in radiation belt dynamics andthis will also be addressed specifically (eg section 4)

Understanding the variability of the Van Allen radiation belts to the point of predictability is one of thegreat outstanding questions in heliophysics research In the coupled Sun‐Earth system solar wind energyis transferred into the radiation belts leading to charged particle dynamics over a broad range of timescales(eg seconds to years) Radiation belt enhancements have wide‐ranging implications for the man‐madetechnologies that operate in this region of geospace such as radiation hazards that can affect astronautsor charged particle spacecraft interactions that can damage satellites (eg Lanzerotti 2017) Therefore amore complete understanding of the highly variable dynamics of radiation belt particles is an internationalpriority which has led to many recent missions devoted to exploring the belts The main current mission isNational Aeronautics and Space Administrations (NASA) Van Allen Probes launched in 2012 a two‐space-craft mission devoted to unraveling the mysteries of the dynamics of the particle radiation trapped by theEarths magnetic field (Mauk et al 2013) that has ended in October 2019 In addition low‐altitudeCubesat measurements the Japanese Arase mission (Miyoshi et al 2018) and the suite of other spacecraftsuch as the European Space Agency (ESA) Cluster (eg Pokhotelov et al 2008) the Time History of Eventsand Macroscale Interactions during Substorms (THEMIS) (Angelopoulos 2008) the MagnetosphericMultiscale (MMS) (Burch et al 2016) the Solar Anomalous and Magnetospheric Particle Explorer(SAMPEX) missions (Baker et al 1993) National Oceanic and Atmospheric Administrations (NOAA)GOES the Polar Orbiting Environmental Satellites (POES) composed of multiple National Oceanic andAtmospheric Administration spacecraft and of the European Organisation for the Exploitation ofMeteorological Satellites (EUMETSAT) MetOp satellites High Earth Orbiting (HEO) satellites LosAlamos National Laboratory (LANL) GEO and GPS satellites constellations and the ESA Project for On‐Board Autonomy and Vegetation (Proba‐V) (Borisov amp Cyamukungu 2015 Pierrard et al 2019 in this col-lection) all probing the inner magnetosphere have led to unprecedented coverage of this dynamic andimportant region of geospace Observations of various phenomena in space can be complemented by subor-bital measurements particularly from balloons such as the BARREL balloon campaigns (Millan et al 2013)or ground‐based observations There is a large variety of ground‐based instruments starting with

1010292019JA026735Journal of Geophysical Research Space Physics


magnetometer arrays such as the Canadian Array for Real‐time Investigations of Magnetic Activity(CARISMA) magnetometer array database (eg Mann et al 2008) or the Magnetometers‐IonosphericRadars‐All‐sky Cameras Large Experiment (MIRACLE) instrument network in Finland (Sangalli et al2011) Incoherent scatter radars such as the European Incoherent Scatter (EISCAT) very high frequency(VHF) radar in Tromsoslash in Norway the Arecibo radar in Puerto Rico and the Super Dual Auroral RadarNetwork (superDARN) (eg Fenrich et al 1995) also provide contextual information Broadband high‐frequency ground radio and optical receivers exist in Canada (eg relative ionospheric opacity meters(riometers) All‐Sky Imagers (ASIs) and Meridian Scanning Photometers at the NORSTAR facility(eg Liang et al 2007 Liu et al 2007 Spanswick et al 2007 Zou et al 2012) and in Finland(Grandin et al 2015 2017 McKay‐Bukowski et al 2015) Finally there is a global network of subiono-spheric very low frequency (VLF) radio wave receivers called the Antarctic‐Arctic Radiation‐beltDynamic Deposition VLF Atmospheric Research Konsortia (AARDDVARK) (Clilverd et al 2009)which monitors energetic precipitation (eg Neal et al 2015) and other energy inputs reaching theionospheric D region

This article is a preface written as a comprehensive introduction of the Special Collection of Journal ofGeophysical Research (JGR) Space Science dedicated to Particle Dynamics in the Earths Radiation Beltsin which we review the context the main current research and major open questions in radiation beltphysics without performing a systematic introduction of the main physical concepts or a fully exhaustivereview Monographs on radiation belt particle dynamics such as Northrop (1963) Roederer (1970)Roederer and Zhang (2014) Schulz and Lanzerotti (1974) and Summers et al (2013) introduce all neces-sary physical notions Literature reviews can be found in Schulz (1982) Li and Temerin (2001) Friedelet al (2002) Millan and Thorne (2007) Shprits et al (2008a 2008b) Reeves et al (2009) Thorne et al(2010) Millan and Baker (2012) and Baker et al (2018) We also recommend the discussions inSummers (2011) Baker et al (2011) Liemohn and Chan (2007) Denton et al (2016) Liemohn et al(2016) Lanzerotti and Baker (2017) Tu et al (2019) and Yu et al (2019)

In this Special Collection we gather the latest research works of international experts to explore this com-plex interplay using unprecedented comprehensive data coverage along with recent advances in theoryand state‐of‐the‐art modeling of radiation belt physics These studies use valuable new assets to addressmany outstanding questions and also to open up new and unexpected avenues of research This SpecialCollection is published 6 years after Summers et als monograph (2013) on the dynamics of the Earths radia-tion belts that reviewed the state of the art of this field at the time of the Van Allen Probes launch Both con-tributions demonstrate the scale of the scientific progress made in the intervening time In addition weinclude a focus on laboratory plasma experiments that can help shed light on important aspects of radiationbelt dynamics

However we do not discuss the proton radiation belt since we do not have contributions on this subject in thisSpecial Collection More information on the proton belt can be found in for example Spjeldvik (1977) Beutieret al (1995) Albert et al (1998) Looper et al (2005) Selesnick Looper andMewaldt (2007) Ginet et al (2007)Selesnick Hudson and Kress (2013) Selesnick et al (2014 2016 2018) Mazur et al (2013 2014) Tu Coweeand Liu (2014) and Borovsky et al (2016) In addition we do not discuss any kind of trapped particles that ori-ginate from the nuclear reaction of ultrahigh energy proton (eg Gusev Kohno et al 1996 Gusev Martin etal 1996 Pugacheva et al 2013 Selesnick Looper Mewaldt amp Labrador 2007) suprathermal ionosphericheavy ions (eg Spjeldvik 1979) such as iron ions (Christon et al 2017 Spjeldvik et al 2006) or carbon ions(Spjeldvik 2004) high‐energy solar protons (eg OBrien et al 2018) or cosmic rays (eg Amatoamp Blasi 2018Blake et al 1997 Smart et al 2000 Shea et al 1992 Smart amp Shea 2002)

This Special Collection focuses on five major themes in radiation belt research that are each discussed in fol-lowing (1) particle acceleration and transport (2) particle loss (3) the role of nonlinear processes (4) newradiation belt modeling capabilities and the quantification of model uncertainties and (5) laboratory plasmaexperiments related to radiation belts physics In the following we develop each of these themes discussingthe scientific context of all the articles that compose the Special Collection (with the exception of the articlesthat are currently under review and were not accepted for publication in the collection before the writing ofthis preface)



2 Particle Acceleration and Transport in the Inner and Outer Zones

The radiation belt system from the near‐Earth inner zone to the outer reaches of the geosynchronous envir-ons and beyond (up to L ~ 8ndash10) undergoes significant changes of phase space density (PSD) on a range oftimescales from seconds to decades (ie from timescales ranging from the gyro or bounce or drift motion upto many years for the most stably trapped particles) and over a wide range of magnetic moments or energiesWe will focus on the processes that cause these changes in particle PSD from both observational and theo-retical perspectives and discuss the most fundamental unresolved questions therein This is a voluminoussubject that is only briefly discussed here By nature of the complex interplay between the processes at workin the radiation belts many of the questions raised here overlap with the sections that consider loss model-ing and nonlinear processes (sections 3ndash5)

The current paradigms for particle acceleration and transport in the outer radiation belt (L ~ 3ndash7 where Lrefers to the equatorial crossing of a dipole magnetic field line measured in Earth radii) include the effectsof numerous processes such as convective transport particle injections either by shocks associated with tra-veling interplanetary disturbances or by inductive electric and magnetic fields generated during magneto-spheric substorms in situ acceleration by wave‐particle interactions radial transport by interactions withlow‐frequency field fluctuations and interactions with electrostatic structures We need to determine quan-titatively which of these processes are dominant in the radiation belts (eg Reeves et al 2013 Turner et al2014) both statistically and for specific external conditions such as storms driven by coronal mass ejectionsor corotating interaction regions and at both local and global spatial scales

21 Source and Seed Populations

Many theoretical observational and modeling studies have concluded that the internal process of gyroreso-nant wave‐particle interactions are an important cause of rapid electron energization to relativistic energiesoutside of the plasmasphere (Thorne 2010) However these internal ldquolocal accelerationrdquo processes arethemselves complicated and require a specific chain of events to occur on the proper timescales in orderto be effective The current proposed global scheme is that there exist two distinct electron populationsresulting from magnetospheric substorm activity that are crucial elements for electron acceleration in theouter belt the electron source population (tens of keV) which is directly injected by substorm processes inthe magnetotail and gives rise to local VLF wave growth in the vicinity of the outer belt and the seed popula-tion (hundreds of kiloelectron volts) which penetrates the outer belt and drifts inward becoming in turnaccelerated to much higher energies (up to megaelectron volts) through VLF wave resonant interactionsgenerated by the electron source population (eg Jaynes et al 2015 Rodger et al 2016) Relativistic energi-zation in the outer radiation belt by such wave‐particle interactions (essentially energy diffusion) requiresthat the seed population of electrons of order hundreds of kiloelectron volts be present while plasma wavessuch as lower band chorus are generated and subsequently act on this seed population The waves in ques-tion must be generated by nonlinear instabilities in yet another part of the plasma regime identified as thelower‐energy source population (generally tens of kiloelectron volts) Generally it has been assumed thatthe seed population is injected simultaneously with the source population This crucial assumption has tobe tested and examined Bingham et al (2018) in this collection show the importance of the timing andthe level of the seed electron enhancements in radiation belt dynamics through a superposed epoch analysisof the chorus wave activity the seed electron development and the outer radiation belt electron responsebetween L = 25 and L = 55 for 25 coronal mass ejection and 35 corotating interaction region storms usingVan Allen Probes observations (see also Bingham et al 2019) Khoo et al (2018) in this collection show thatthe initial enhancement of tens of kiloelectron volt electrons was observed before the initial enhancement ofhundreds of kiloelectron volt electrons for five intense storm periods observed with the the MagneticElectron Ion Spectrometer (MagEIS) instrument on board the Van Allen Probes (Blake et al 2013) Thisand a further study (Khoo et al 2019) indicate that the initial enhancement from 30 keV to 2 MeV alwaysoccurs outside of the innermost plasmapause itself computed with two plasmapause models (the Liu et al2015 model and the Plasmapause Test Particle simulation of Goldstein et al 2014) Tang et al (2018) in thiscollection investigate the role of the transient and intense substorm electric fields the convection electricfield and drift resonance with ultralow frequency (ULF) waves for understanding the dynamics of the seedpopulations in the heart of the outer radiation belt



22 Reaching Relativistic Energies

If any of the components in this process chain are missing this wave‐particle explanation for generatingrelativistic electrons may fail Recent work (Jaynes et al 2015) has shown that such failure resulted whenthe seed population was present but neither the source population nor the associated waves were presentThis raises the crucial question howwhen is the seed population generated if not through a substorm injec-tion Is there a high‐latitude zone of the Earths atmosphere that plays the role of a source or are there exter-nal injections Generally there is a loss of nearly all particles at the onset of a geomagnetic storm (seesections 3 and 5) Does that loss always include the seed population Is the seed population part of a conti-nuum of electron acceleration wherein it is generated from the source population as opposed to beingdirectly injected (cf sections 4 and 5) This highlights the question of how often such enhancement failuresoccur because of missing elements and candoes the process ever still succeed in producing enhanced PSD inspite of a break in the sequence of processes How do these loss and source processes end up affecting thetotal electron content of the radiation belts (eg Forsyth et al 2016 Murphy et al 2018) These questionsform some of the core elements of the theme on acceleration and transport and cross over into other themesas noted above

23 Radial Transport

In addition to local acceleration the radial transport of electrons by interaction with field fluctuations andwaves at ULFs (in the Pc3 to Pc5 frequency range approximately millihertz eg Mann et al 2012) canincrease the electron PSD over a wide range of energies while preserving the first and second adiabaticinvariants (Hudson et al 2008 Mann et al 2013) Recently Jaynes et al (2018) found that ultrarelativisticelectrons up tosim8MeV are accelerated primarily or entirely by ULF wave‐driven diffusion in the absence oflocal acceleration Zhao et al (2019) in this collection analyze the solar wind conditions during moderateand intense storms that produce ultrarelativistic electron (2ndash8 MeV) flux enhancements We note howeverthat if this radial transport is diffusive then acceleration requires that the PSD is sufficiently large at thehigher L values in order to be effective and operates on longer timescales than local acceleration During sud-den injections coherent ULF waves can produce a local peak in PSD into the heart of the outer belt (egDegeling et al 2008) In that case acceleration timescales can be comparable to local acceleration (whis-tler‐driven) timescales (eg Ukhorskiy et al 2006) Many analyses and models have used the radial trans-port paradigm to explain the observed PSD profiles in much of the radiation Often the models combinethe radial transport with magnetopause shadowing and wave‐particle losses to obtain a realistic spatiotem-poral PSD distribution (eg Mann et al 2016 Ozeke et al 2018) This is even more complicated when con-sidering the complex PSD structures that arise during storms (eg Turner et al 2012 2013) Recent electronPSD compilations measured from both the Relativistic Electron‐Proton Telescope (REPT Baker KanekalHoxie Batiste et al 2013) and the MagEIS instruments on board the Van Allen Probes can be found forinstance in Zhao et al (2019) and Boyd et al (2018) Analytic solutions are possible only in simple config-uration for example Degeling et al (2019) in this collection calculate analytically ULF wave fields and drift-ing electron fluxes near a poloidal mode field line resonance in a dipole field

When the transport is diffusive the question of which radial diffusion coefficients apply remains today a sub-ject of debate A large choice of model is available and the main statistical radial diffusion coefficientsinclude Brautigam and Albert (2000) (including the electrostatic and the electromagnetic components)Ozeke et al (2014 equations (20) and (23)) the electric radial diffusion coefficient obtained by Liu et al(2016 equation (2)) derived from 7 years of in situ electric field measurements by the THEMIS and Ali et al(2016 equations (14) and (15)) derived from 3 years of the magnetic field data and the electric field datarespectively measured by EMFISIS and by the EFW instrument on board the Van Allen Probes These fourmodels are compared together at all energies for all L‐shells (L lt 6) for a quiet event in Ripoll et al (2017)with some noticeable differences found among them Additional radial diffusion coefficient models can befound in Selesnick et al (1997) Ukhorskiy and Sitnov (2008) Ozeke et al (2012) and Ali et al (2016) Allof these models depend on the theoretical expressions derived by either Faumllthammar 1965 Faumllthammar1968) or Fei et al (2006) as discussed in Lejosne (2019) Faumllthammar assumes a backgroundmagnetic dipolefield and equatorial (Faumllthammar 1965) or not (Faumllthammar 1968) trapped particles that are radially drivenby both magnetic field fluctuations including the effect of the induced electric fields and electric potentialfluctuations Fei et al (2006) assume a slightly asymmetric background magnetic field for equatorial trapped



particles radially driven by both magnetic field fluctuations in the absence of electric field fluctuation anduncorrelated electric field fluctuations For instance the models of Ali et al (2016) Liu et al (2016) andOzeke et al (2012 2014) rely on the decomposition proposed by Fei et al (2006) Lejosne (2019) demon-strates that Fei et als formulas for computing radial diffusion coefficients are erroneous in the presenceof magnetic field fluctuations underestimating radial diffusion by a factor of 2 Lejosne (2019) proposes anew general method based on the rate of change of the third adiabatic invariant (see also Lejosne et al2012) without any assumption regarding the topology of the background magnetic field and without anyartificial uncorrelation between the magnetic and electric fluctuations driving cross drift shell motion (thelatter assumption causing the error in Fei et al 2006) Olifer et al (2019) in this collection compute radialdiffusion coefficients derived from Pc4 and Pc5 ULF wave power during the intense geomagnetic stormon 17ndash18 March 2015 They show the radial diffusion coefficients do not correspond to statistical estimatesduring storm main phase (while they confirm it does during storm recovery) and do not behave as expectedsince the electric component is reduced and the magnetic component increases becoming nonnegligible

24 Magnetic Field

Accounting for the complexity of the magnetic field during storm times is also a key component that directlyinfluences the PSD profile (Green amp Kivelson 2004 Selesnick amp Blake 2000) The representation of the PSDprofile in the physical space with respect to either the McIlwains L value McIlwain (1961) or L pitch angleand energy relie on both a thoroughly tested magnetic field model and an accurate field line tracer and isessential in order to differentiate adiabatic from nonadiabatic effects (Roederer amp Lejosne 2018) Loridanet al (2019) and Ozeke et al (2019) both in this collection show how dramatic the effect of the magneticfield is when one generates PSD profile from observations Both of these articles question the systematicattribution of PSD local peaks to wave‐particle interactions associated with chorus waves and show it canbe erroneous Furthermore in situ measurements have shown that there can be drift resonant interactionswith corresponding PSD enhancement of particles by these low‐frequency waves For instance Hao et al(2019) in this collection show the outer belt ultrarelativistic electron enhancement (from RelativisticElectron‐Proton Telescope (REPT) measurements) associated with the storm sudden commencement ofthe 16 July 2017 geomagnetic storm These authors explain and reproduce the prompt electron accelerationresponse (from 2 to 34 MeV in less than 1 hr) to the shock‐induced ULF wave in the Pc5 frequency rangeusing a generalized drift resonance theory One of the primary questions is whether these radial transportprocesses ever become dominant in the core of the radiation belts (defined here as the high flux regions sur-rounding the Earth below L ~ 8) There are hints that this may be the case in the outer edge of the slot regionwhere the outer radiation belt electrons have been observed to diffuse inward slowly to lower L There is alsoevidence that the PSD radial profiles from the slot region into the inner zone are consistent with such radialtransport When the magnetic field is disrupted or deviates from a dipole field (eg in the South AtlanticAnomaly (SAA) cf Jones et al 2017) transport can also occur in an anomalous diffusive (Roederer et al1973) form that has been found to play an important role in both the outer belt (OBrien 2014) and the innerbelt (Cunningham et al 2018) In addition it was recently recognized that Cosmic Ray Albedo NeutronDecay is a dominant source of quasi‐trapped energetic electrons at the inner edge of the inner belt up to782 keV (Li Selesnick et al 2017 Xiang et al 2019 Zhang Li et al 2019) (Quasi‐trapped electrons aredefined as having a lifetime greater than a bounce time period but less than a drift time period because theyare precipitated due to the change of pitch angle associated to the change of the magnetic field in the SouthAtlantic Anomaly (SAA) Finally there are also injection like signatures that directly transport and energizeelectrons in these same regions Determining which of these are the dominant processes for maintaining theinner and outer zone electron fluxes is thus another important element of the research studies

25 Deep Low‐Energy Injections

The electron PSD in hundreds of kiloelectron volt energy regime waxes and wanes in the outer zonethroughout the slot region (L lt 35) and even in the outer region of the inner zone A number of open ques-tions remain surrounding the dynamics of these numerous seed electrons what are the processes that con-trol these PSD changes How deeply can electrons be directly injected Observationally the tens to hundredsof kiloelectron volt electrons appear rapidly (within hours) in the slot region and even in the inner zone dur-ing storms (eg Reeves et al 2016 Turner et al 2015 Zhao et al 2016) (These electrons have quite lowmagnetic moments compared to the electrons in the peak of the outer radiation belt) For instance



Lejosne et al (2018) showed some of the injections occurring deep into the inner magnetosphere could bedue to a potential drop associated with subauroral polarization stream (SAPS) (eg Lejosne amp Mozer2017) Are these electrons locally accelerated Is this a result of inductive electric fields acting on the elec-tronsWhat fraction is convected inwardWhat is the electric field at these low L values during such eventsDo the processes require that the plasmasphere boundary be eroded to the lowest L value where the elec-trons quickly appear What is the real timing of their appearance relative to storm onset These major unre-solved questions regarding the radiation belt seedsource population dynamics will be addressed in thisSpecial Collection

3 Particle Loss in the Inner and Outer Zones

As described above the overall state of the radiation belts is controlled by several major processes includingparticle acceleration and transport (addressed in both the first and third sections) and particle loss Particletransport can act as both a source and loss of particles Particle acceleration can also be perceived as both asource and loss of particles of different energies considering the number of particles being locally constantThis section is fully dedicated to particle loss processes addressing the loss of trapped particles from obser-vational theoretical and computational view points for radiation belt particles (electrons and ions) fromclose to the Earth (L ~ 11) to geostationary orbit and beyond (L gt 6)

The loss of electrons from the radiation belts occurs primarily by either precipitation into the atmosphere orby escape through the magnetopause boundary (Millan amp Thorne 2007 and references therein) Withinthese two paradigms there are numerous subprocesses that contribute to the overall loss of radiation beltparticles and this section concerns all of them except those associated with nonlinear mechanisms (cfsection 4) We aim to address Coulomb collisions and wave‐particle interactions causing scattering intothe atmosphere as well as adiabatic effects and loss due to electron drift orbits intersectingthe magnetopause

31 On Coulomb Collision

In the closest vicinity of the Earth (L ~ lt15) pitch angle diffusion is induced by the process of elasticCoulomb collisions of radiation belt electrons with themolecules of the dense ambient air of the upper atmo-sphere (eg Walt amp MacDonald 1964 Walt 1966) rather than by interactions with VLF waves at higher L‐shells Scalar momentum p is nearly conserved during an elastic collision between a light electron and themuch heavier neutrals and ions of the atmosphere ionosphere and plasmasphere However energy lossoccurs through inelastic collisions with free and bound electrons (Walt and Farley 1976 Selesnick 2012)and contributes to a change in the spectrum of the radiation belt electrons These electrons will ultimatelydiffuse into the loss cone and scatter in the atmosphere and sometimes backscatter according to the energyand the zenith angle at which the electron strikes the atmosphere (Davidson amp Walt 1977 Selesnick et al2004) The Coulomb collision formalism has been recently revisited (Selesnick 2012) and used in modernMonte Carlo and Fokker‐Planck codes (Selesnick 2016) While these effects are known in generalCunningham et al (2018) recently showed evidence that Coulomb collisions can cause radial transportdue to the asymmetry of the Earths magnetic field (due to the South Atlantic Anomaly) which requiresone to keep all cross terms in the Fokker‐Planck equation (usually they are neglected for simplicity andor computational resources) Such an effect was suggested over 40 years ago (Roederer et al 1973) Thiswork opens the path to revisit Coulomb interactions within the general complexity of the magnetic fieldand to confirm its effects importance timescales etc

32 On Magnetopause Losses and Radiation Belt Dropouts

Flux dropouts due to magnetopause shadowing occur over a broad range in energy equatorial pitch angleand radial distance (eg Lotoaniu et al 2010 Shprits et al 2012 Sorathia et al 2018 Turner et al 2012Ukhorskiy et al 2015 Xiang et al 2017 2018) These spatial energy and pitch angle‐dependent character-istics can be exploited to differentiate and quantify the various loss processes Both loss types can substan-tially decrease the trapped electron flux over short timescales (eg a few hours) Extreme depletions ofthe belts during disturbed times such as interplanetary shocks (Xiang et al 2017) substorms or storms willbe considered in addition to quiet time losses from the belts



Particle loss to the magnetopause occurs when the magnetopause is suddenly pushed Earthward usually inresponse to increased solar wind dynamic pressure allowing particles to drift from the magnetosphere intointerplanetary space This loss process generally acts in the outer regions of the radiation belts but can reachlower L shells (eg L lt 4) where both an adiabatic inflation of the electron drift orbits caused by ring cur-rent growth andor outward radial transport can enhance the losses A dedicated review to magnetopauselosses is available in Turner and Ukhorskiy (2020) On the other hand wave particle interactions occurthroughout the radiation belts and are particularly prevalent inside the plasmasphere

33 Waves Causing Loss in the Radiation Belts

Radiation belt particle loss into the atmosphere by wave‐particle interactions is governed by cyclotron reso-nance and operates for a given wave over a specific energy and pitch angle range of particles located at agiven L‐shell (eg Roberts 1969 Lyons et al 1972 Horne amp Thorne 1998 Summers et al 1998 Albert2005 Glauert ampHorne 2005) A general review of themagnetospheric waves that contribute to wave particleinteractions is given in Thorne et al (2010) Hospodarsky et al (2016) also review waves observed in theradiation belts by the Van Allen Probes We review and discuss in the following the main waves that driveloss from wave‐particle acceleration with a focus on main and recent findings (omitting ULF waves thatwere discussed in the previous section and are associated with electron transport and loss but through trans-port to the magnetopause)

In the plasmasphere VLF waves from ground‐based transmitters (eg Sauvaud et al 2008) lightning‐gen-erated whistler waves (eg Voss et al 1998) and whistler mode hiss (Dunckel and Helliwell 1969 Thorneet al 1973) are the three main whistler mode waves that can interact with trapped electrons

331 VLF Waves From Ground‐Based Transmitters

Wave‐particle interactions that cause pitch angle diffusion and ultimately radiation belt electron precipita-tion have been reported as being induced by VLF waves from various ground‐based transmitters (eg Imhofet al 1983) This includes for instance the 214‐kHz NPM transmitter in Hawaii with precipitation reportedby subionospheric VLF remote sensing (Inan et al 2007) the 164‐kHz JXN transmitter in Norway withprecipitation detected optically from cameras on the ground (Denton et al 2014) two US Navy transmit-ters on the US East Coast operating at frequencies of 178 and 214 kHz (with nominal radiated powers of1000 and 265 kW respectively) with precipitation reported from space (Imhof et al 1986) and the powerful198‐kHz NWC transmitter (1‐MW radiated power) in Australia at L = 145 with precipitation observedfrom the French microsatellites DEMETER (Gamble et al 2008 2009) Computer simulations support theprecipitation observations (eg Inan et al 1984 Marshall et al 2010a 2010b) Meredith et al (2019) com-piledsim5 years of plasma wave data from the Van Allen Probes to construct newmodels of the observed wavepower from VLF transmitters These authors show that the total average wave power from all VLF transmit-ters lies in the range 3ndash9 pT2 in the region 13 lt L lt 30 with approximately 50 of this power emanatingfrom three VLF transmitters NWC (W Australia) NAA (Maine USA) and DHO38 (Germany) UsingMeredith et als (2019) VLF wave power Ross et al (2019) show the VLF transmitters reduce electron life-times of 500‐keV electrons by a factor of ~10 down to the order of 200 days near the outer edge of the innerradiation belt (L ~ 18) However VLF transmitter waves are ineffective at removing multindashmegaelectronvolt electrons (gt~2 MeV) from either the inner radiation belt or slot region

332 Lightning‐Generated Whistlers

Cloud‐to‐ground lightning flashes strongly emit electromagnetic radiation in the VLF band This radiationpropagates with low attenuation inside the Earth‐ionosphere waveguide (Crombie 1964) for thousands ofkilometers These lightning‐generated whistlers can escape the waveguide to the magnetosphere in ductedmodes along magnetic field lines or in unducted modes (eg Carpenter 1968 Clilverd et al 2008Helliwell 1969 Inan amp Bell 1977) Lightning‐generated whistlers are impulsive electromagnetic radiationevents with a frequency bandwidth (~2ndash12 kHz) (eg Meredith et al 2007) that allows resonant interactionsat the energy of trapped electrons eventually leading to electron loss in the inner belt (eg Rodger et al2003) These plasmaspheric waves have been associated to electron precipitation using DEMETER observa-tions (eg Gemelos et al 2009 Graf et al 2009) or seen from Trimpi effects (Helliwell et al 1973) on VLFtransmitter signals (eg Clilverd et al 2004 Inan et al 1988 Peter amp Inan 2005) Computer simulationsbased on ray tracing techniques (eg Bortnik et al 2006 Lauben et al 2001) have been carried out to repro-duce observed precipitation similar to the simulation of VLF‐transmitter waves induced precipitation



Analysis of lightning‐generated whistlers occurrence andor effects is often also supported by lightning data-bases established from ground VLF stations For instance Peter and Inan (2005) use the US NationalLightning Detection Network (Cummins et al 1998) and Zheng et al (2016) Ripoll Farges et al (2019)and Zaacutehlava et al (2019) use the World‐Wide Lightning Location Network (eg Holzworth et al 2011Hutchins Holzworth Brundell amp Rodger 2012 Hutchins Holzworth Rodger amp Brundell 2012 Rodgeret al 2009) In turn Colman and Starks (2013) use sensors from space such as the Optical TransientDetector (OTD) and its follow‐on the Lightning Imaging Sensor (LIS) (eg Cecil 2001 Cecil et al 2014Christian et al 2003)

333 Whistler Mode Hiss WavesWhistler mode hiss waves are the third main wave of the plasmasphere (eg Thorne et al 1979) actingbroadband from (~50 Hz to ~2 kHz) from L ~ 2 up to the plasmapause (Li et al 2015 Meredith et al2004 Meredith Horne Clilverd et al 2006 Meredith et al 2018 Tsurutani et al 2015) These wavesare right hand polarized with ellipticity above ~02 or more according to the authors (eg ellipticity gt05and polarization gt05 in Hartley Kletzing Santoliacutek et al 2018) Higher‐frequency hiss (2ndash10 kHz) havealso been reported (He et al 2019) Whistler mode hiss waves occur independently of the geomagneticactivity being present in the plasmasphere during geomagnetic quiet times during substorms and duringmagnetic storms The origin of hiss waves has been debated for decades Bortnik Thorne and Meredith(2008) proposed that plasmaspheric hiss originates from chorus emissions which are generated outsidethe plasmasphere and are able to propagate into the plasmasphere where they become trapped Ray tracingstudies support this scenario (eg Chen Li et al 2012 Chen Reeves et al 2012 Chen et al 2012b2012c) This thesis is also supported by global statistical evidence based on chorus waves measurementsfrom 6 different satellites (Meredith Horne Glauert et al 2013) Simultaneous appearance and disappear-ance of hiss and chorus waves could support this theory (Liu et al 2017) Nevertheless the origin or theorigins of plasmaspheric hiss remain an open question Hartley et al (2019) used Van Allen Probes obser-vations coupled to ray tracing simulation and found a spatial limitation of the wave vector orientation thatindicates that chorus waves may only contribute to a small fraction of the plasmaspheric hiss wave powerInternal generation is a plausible alternative For instance Falkowski et al (2017) explained that a secondsource for plasmaspheric hiss could be the midnight injection of energetic electrons from substorm or smallinjection event (nonstorm events) Moreover plasmaspheric hiss has been widely regarded as a broadbandstructureless and incoherent emission Summers et al (2014) showed evidence that plasmaspheric hisscould be a coherent emission with complex fine structure Some coherence in the structure was in turnobserved with polar in plumes during solar minimum conditions (Tsurutani et al 2015) and in triggeredplasmaspheric hiss above 1 kHz (Zhu Liu amp Chen 2019) A better understanding of the nonlinearmechanism of generation and growth of hiss waves may help to reveal their origin and to better understandtheir internal structure (eg Omura Nakamura et al 2015 Nakamura et al 2016) Whistler mode hisswaves are also observed in high‐density plumes outside the plasmasphere (Chan amp Holzer 1976Summers et al 2008) and the characterization of their properties and their effect outside the plasmasphereis ongoing (Woodroffe et al 2017 Su et al 2018 Shi et al 2019 Li et al 2019 Zhang et al 2018 ZhangNi et al 2019)

Whistler mode hiss waves are powerful waves and the main driver of the slot formation and the well‐knownenergy dependent two‐belt structure of the radiation belts (Lyons amp Thorne 1973) principally during quiettimes (eg Meredith Horne Glauert et al 2006 Ripoll et al 2017) (see discussions below) Their powercan be locally high (gt502 pT2) but their important effects come from their continuous existence (often witha power gt ~102 pT2) in a broad domain (L gt ~2 up to the plasmapause location) There is strong visiblecoherence between the hiss amplitude (1 to 4 days after a storm) and electron loss observed in the form ofbremsstrahlung X‐rays measured from a BARREL balloons flying at altitudes of ~35 km over Antarcticawith modulations correlated with the variation of the plasma density and the magnetic field (Brenemanet al 2015) (see also discussion below about the results of Turner et al 2019 and Ripoll et al 2019 bothin this collection) Due to their great contribution to particle scattering the statistical distribution of hisswave properties needs to be well characterized in magnetic local time (MLT) L‐shell and geomagnetic activ-ity Themost recent distributions available are the those generated by Li et al (2015) Malaspina et al (2017)Hartley Kletzing Santolik et al (2018) and Shi et al (2017 2019) based on the Van Allen Probes Tsurutaniet al (2015) based on Polar Kim et al (2015) based on THEMIS and Meredith et al (2018) based on DE1



Cluster THEMIS and the Van Allen Probes An MLT‐dependent model of hiss amplitude is given inSpasojevic et al (2015) Knowledge of the hiss wave normal angle is important for wave particle interactions(eg Yu Li et al 2017) although Ripoll Albert and Cunningham (2014) showed pitch angle diffusion coef-ficients and electron lifetimes are not strongly dependent on the wave normal angle unless the hiss wavenormal angle becomes higher than ~60deg which drastically reduces pitch angle diffusion and increases theelectron lifetime Numerous studies have been devoted to hiss‐driven loss (eg Li Ni et al 2014 Niet al 2013 2014 2017 Orlova et al 2014 Hardman et al 2015 Gao et al 2015 Hua et al 2019 Liet al 2019 Reeves et al 2016 Ripoll et al 2017)

334 Plasmaspheric Wave‐Induced Precipitation

Plasmaspheric wave‐induced precipitation (eg Imhof et al 1986 Meredith Horne Glauert et al2006) which combines all three whistler waves is theoretically supported by global Fokker‐Plancksimulations of radiation belt electrons within the plasmasphere (eg Abel amp Thorne 1998a 1998b1999 Meredith et al 2007 Meredith Horne Glauert Baker et al 2009 Kim et al 2011 SelesnickAlbert amp Starks 2013 Ripoll Chen et al 2014 Glauert et al 2014a) (see more discussions insection 5) In all cases these predictions rely on a firm knowledge of the plasmasphere itself (see reviewin Darrouzet et al 2009 Darrouzet amp De Keyser 2013) Outstanding questions concern the structure ofthe plasmasphere its extent its boundaries and its filamentary and outlying regions The characteriza-tion (both timewise and statistically) of the plasmasphere remains a problem of fundamental interestStatistical models of the plasmasphere density have existed for years (eg Carpenter amp Anderson1992 Albert 1999 Sheeley et al 2001 Moldwin et al 2002 OBrien amp Moldwin 2003 Denton et al2004 2006 Ozhogin et al 2006) as well as dynamic simulations of the plasmasphere (De Pascualeet al 2018 Goldstein et al 2005 2014 2016) Plasmaspheric density is currently inferred from theupper hybrid resonance line (Kurth et al 2015) from the spacecraft potential (Thaller et al 2015)and from hiss waves (Hartley Kletzing De Pascuale et al 2018) taken from measurements made withthe EMFISIS instrument (Kletzing et al 2013) and the EFW instrument (Wygant et al 2013) on boardthe Van Allen Probes In the absence of data a modeling alternative is to use neural network methodsto provide plasma density estimates at any location and geomagnetic activity level (eg Zhelavskayaet al 2016 2017 Chu et al 2017)

335 Electromagnetic Ion Cyclotron Waves

Electromagnetic ion cyclotron (EMIC) waves (eg Fraser et al 2006) can be found either inside or outsidethe plasmasphere These waves drive considerable contemporary scientific interest particularly during therecent Van Allen Probes mission Many recent studies are dedicated to the loss they cause to ultrarelativisticelectrons (eg Thorne amp Kennel 1971 Albert 2003 Jordanova et al 2008 Miyoshi et al 2008 Rodgeret al 2008 Rodger et al 2015 Li et al 2013 2014 Usanova et al 2014 2016 Kersten et al 2014 Blumet al 2015 Clilverd et al 2015 Woodger et al 2015 2018 Colpitts et al 2016 Shprits et al 2008a2013 2016 2017 Hendry et al 2016 2019 Zhang et al 2016 Aseev et al 2017 Drozdov ShpritsUsanova et al 2017 Capannolo et al 2018 2019 Denton et al 2019 Qin et al 2019) themselves relatedto the complex location and duration of these waves EMIC waves are discrete electromagnetic emissions inmultiple frequency bands (eg Saikin et al 2015) which are observed across a large region of geospace (egSaikin et al 2016) including the ring current and the plasmasphere dayside plumes and the outer daysidemagnetosphere (Engebretson et al 2015 Engebretson et al 2018 Engebretson et al 2018 Tetrick et al2017) When EMIC emissions occur they often spread over one (or a few) MLT sectors which limits theireffect On the other hand EMIC waves can be extremelly powerful (gt~12 nT2) but they do not necessarilylast long and the question of their duration remains open and fundamental for the characterization of theireffect The effect of EMIC waves is also highly dependent on the local ion plasma composition (H+ O+ andHe+) which is important to accurately compute the wave‐particle interactions for instance based on mea-sured local properties such as measured by the HOPE instrument (Funsten et al 2013 Spence et al 2013) ofthe Van Allen Probes Knowledge of duration spatial spread and ion density is thus necessary to computeEMIC effects EMIC wave scattering causes relativistic electron precipitation but how important is it forradiation belt losses on the whole For example loss due to EMIC wave scattering appears to be localizedspatially from an observational standpoint Do we understand quantitatively why that is the case Thisaspect of EMICwave loss thus makes it difficult to parameterize in radiation belt modeling an issue that willbe taken up in conjunction with section 5 Do EMIC waves only act on ultrarelativistic electrons (cf Denton



et al 2019 in this collection and discussion in section 5) Another question that warrants deeper investiga-tion is whether EMIC scattering occurs significantly or not in the plasmasphere and inner zone Finallywave‐particle interactions are based on Doppler‐shifted local cyclotron (and Landau) resonance (Schulz ampLanzerotti 1974) butone may want to also assess the effect of all possible types of resonance phenomenaBlum et al (2019) in this collection discuss the possible role of bounce resonance that is a current researchinterest (Cao et al 2017 Cao et al 2017 Shprits 2016)

336 Whistler Mode Chorus Waves

Whistler mode chorus waves are electromagnetic right‐hand polarized whistler mode waves that areobserved in two distinct frequency bands outside the plasmasphere up to geostationary orbits and beyond(eg Allcock 1957 Bunch et al 2013 LeDocq et al 1998 Meredith et al 2012 Meredith Horne Li etal 2014 Tsurutani amp Smith 1974) Chorus lower band ranges from about 01 to 05 of the electron cyclotronfrequency (fce) and the upper band from about 05 to 08 fce They have a coherent fine temporal structuremade of chorus elements with rising‐tone and falling‐tone frequency as well as short impulsive bursts allwith timescales lower than a second (eg Cully et al 2011 Santoliacutek et al 2004 Santoliacutek Gurnett et al2003 Yu et al 2018) The origin and growth of the chorus fine structure is a current complex subject ofresearch that involves nonlinear wave‐particle interactions (eg Omura et al 2009 Tao et al 2012Omura et al 2019) (cf sections 4 and 5)

Whistler mode chorus waves have been the subject of a multitude of research studies as these powerfulwaves are responsible for intense and extreme electron acceleration from a few tens of kiloelectron voltsup to several megaelectron volts (eg Horne amp Thorne 1999 Horne et al 2003 Horne et al 2005Horne et al 2005 Shprits Thorne Horne et al 2006 Summers et al 2007 Bortnik Thorne amp Inan2008 Tao amp Bortnik 2010 Thorne et al 2013 Su et al 2014 Ma et al 2018 Allison et al 2019 Omuraet al 2019) Chorus emissions are also essential because of their strong interaction with electrons in theouter radiation belt which leads to nonadiabatic scattering causing precipitation into the atmosphere anda net removal of energetic electrons from the outer radiation zone This is a dominant scattering process out-side of the plasmasphere leading to diffuse auroral precipitation (eg Johnstone et al 1993 Miyoshi et al2010 2015 Ni et al 2011 Nishimura et al 2010 Oyama et al 2017 Thorne et al 2010) We note the sta-tistical databases of chorus wave properties generated from the Van Allen Probes (Li et al 2016) fromCluster (Agapitov et al 2013) and the compilation from multiple satellites (DE1 Combined Release andRadiation Effects Satellite [CRRES] Cluster Double Star TC1 and THEMIS) by Meredith et al (2012Meredith Horne Li et al 2014) Wang et al (2019) in this collection provide an analytical model of bothamplitude and frequency for upper‐ and lower‐band chorus waves based on Van Allen Probes data (see alsoZhu Shprits et al 2019 and Agapitov et al 2018)

337 Microbursts

The inherently bursty nature of chorus waves also causes lower‐energy electron microbursts that are short‐timescale (tens of milliseconds) intense precipitation events with energies of tens to hundreds of kiloelectronvolts (Fennell et al 2014 Lorentzen et al 2001 Mozer et al 2018) One major question is whether micro-bursts are actually significant at relativistic (eg Blum Li et al 2015 Breneman et al 2017) or ultrarelati-vistic energies or not and whether they can be caused by waves other than whistler mode chorus wavessuch as EMIC waves Douma et al (2018) in this collection used combined space and ground based observa-tion to show that chorus waves are most likely the primary drivers of relativistic microbursts but presentsome case studies that confirm the potential of EMIC waves as an occasional driver of relativistic micro-bursts Additional questions regarding microbursts concern How do microbursts contribute to the globalflux decay of the outer belt during storms How do they correlate with loss of outer belt electronsGreeley et al (2019) in this collection find that the microburst to global loss coupling is predominant inthe quasi‐trapped population of radiation belt electrons (ie electrons performing less than one full driftbefore being precipitated) while having negligible influence on the untrapped and stably trapped popula-tions Previous estimates of microburst flux levels are not well constrained and further studies are neededto refine these estimates which can then be incorporated more accurately into radiation belt models(section 5)

338 Magnetosonic and Electrostatic Cyclotron Harmonic Waves

Finally magnetosonic waves (Russell et al 1970) are extremely oblique waves (mean wave normal angle~89deg) with a relative effect in terms of loss that is rather small compared with other waves with pitch



angle diffusion concentrated around a narrow range of intermediate to high pitch angles at energies above100 keV (eg Albert et al 2016) and with some events responsible for particle acceleration (eg Horne et al2007) These waves were originally referred as magnetosonic equatorial noise (see also Perraut et al 1982Santoliacutek et al 2004 Thomsen et al 2011) Wave particle interactions with magnetosonic waves viaLandau resonance have been recently suggested to cause the so‐called ldquopeculiarrdquo pitch angle distributions(Li et al 2016 Ni et al 2016) with enhanced PSD at intermediate pitch angles and an abrupt decayaround ~90deg observed in the slot region and in the inner zone (Zhao et al 2014a) But the competingprocess of cross diffusion (pitch angle and energy) involving chorus and hiss interactions could alsoexplain such ldquopeculiarrdquo angular distributions (Albert et al 2016) Lessard et al (2019) in this collectionpropose EMIC waves as another contributor to the development of butterfly distributions Researchstudies are ongoing to confirm the mechanism that forms such ldquopeculiarrdquo pitch angle distribution as itmay become a direct way to measure or sense particular wave effects

For the sake of completeness we list the electrostatic electron cyclotron harmonic waves for minor resonantinteractions with radiation belt electrons and a contribution to diffuse aurora at L gt 8 (Liu et al 2018Meredith et al 2000 Meredith Horne Thorne amp Anderson 2009 Shaw amp Gurnett 1975 Zhanget al 2015)

34 Determining Loss Processes

From the great variety of electromagnetic waves aforementioned one understands how important it is todetermine quantitatively the relative contributions to relativistic electron loss from precipitation into theatmosphere due to wave‐particle interactions and from magnetopause shadowing either statistically or ina given electron loss event and over a variety of distinct energy and L‐shell ranges

341 The Importance of the Plasmasphere

In addition to the wave environment we seek to understand the local plasma conditions (eg Thaller et al2019 Hwang amp Yoon 2018 in this collection) that lead to the enhancement or suppression of these variouswave modes and the consequences therein for the precipitation of the trapped populations For instanceGreeley et al (2019) in this collection have found that the plasmapause is likely a better indicator of micro-burst location than L‐shell Their results complement the study by Douma et al (2017) in which it wasshown that microbursts primarily occur outside of the plasmapause and follow the inward movement ofthe plasmapause with increasing geomagnetic activity The density level becomes then the relevant spatialmarker since wave particle interactions are very sensitive to the density This thesis is supported by strongcorrelations that have also been found between plasma density and hiss wave amplitudes (Malaspinaet al 2018) or similarly with the plasmapause location (Malaspina et al 2016)

342 Energy‐Dependent Structure of the Belts

Measurements from the MagEIS instruments on board the Van Allen Probes show the flux level of electronsof energy above 1 MeV in the inner belt is below the instrument background level (Fennell et al 2015) Thissuggests that the inner belt is devoid of megaelctron volt electrons and more generally reveals the absence ofmultindashmegaelectron volt electrons below L = 28 (Baker et al 2014) except for rare events (egClaudepierre et al 2019 in this collection) This discovery has changed our understanding of the inner beltand led us to revisit older flux measurements of inner belt electrons made with different instruments(Selesnick 2015) Thus the ideal two‐belt structure that we sketched in our introduction is itself energydependent and the morphological structure of these two belts has also been shown to be highly energydependent Thus we seek to investigate if this energy‐dependent innerouter belt structure is due to dimin-ishing radial transport as electrons migrate inward losses due to wave‐particle interactions some combina-tion of both or other processes altogether either for quiet times or for storm times During storm timesTurner et al (2019) in this collection provide a statistical characterization of the energy‐dependent evolutionof the radiation belts during 4 days after and before the storm For quiet times Ripoll et al (2019) in this col-lection provide a complementary analysis (though not statistical) of the energy dependence of the radiationbelts based on MagEIS electron flux observations EMFISIS whistler hiss waves observations and Fokker‐Planck simulations 4 days after the storm and lasting 12 days These authors show excellent agreementbetween the energy dependence of quasi‐linear hiss‐driven scattering and the energy dependence of theradiations belts during quiet times from L = 13 to L = 55 It is important to globally investigate whistler



mode hiss wave interactions with electrons as it determines the energy‐dependent slot structure and radia-tion belt boundaries (Reeves et al 2016 Ripoll Reeves et al 2016)

Since VLF waves can resonate with ~01‐ to 2‐MeV electrons between L = 17 and L = 3 how do Earthground‐based VLF transmitters affect energetic electron populations at low L What is the relative impor-tance of VLF transmitter waves and lightning‐generated whistlers compared with whistler mode hiss wavesall three responsible for radiation belt electron precipitation Are these waves responsible for some of theslot region formation or connected in any way to the lack of megaelectron volt electrons observed at lowL‐shells If so then how can that be reconciled with the observed energy dependence of the location ofthe inner edge of the slot region All of these questions regarding the energy‐dependent structure of theradiation belts and the role that the various loss processes play therein should be more thoroughly investi-gated In addition among all of the plasma waves noted above we seek to understand which ones contributethe most to the scattering of trapped particles for both the kiloelectron volt and megaelectron volt popula-tions and where in near‐Earth space (inside the plasmasphere at the plasmapause outside the plasma-sphere at GEO orbits etc) they are most effective

343 Inner Belt Dynamics and Active Experiments

Acknowledging the absence of electrons above 1MeV in the inner zone how do we explain possible losses ofthe relativistic electrons from this region Aside fromVan Allen Probes what other reliable observations canbe brought to bear on the subject of electron loss from the inner zone or more generally at low L‐shellsGiven observed interplanetary shock injections of multindashmegaelectron volt electrons to low L such as dur-ing the March 1991 event (Li et al 1993) what processes would contribute to electron loss in the inner zoneand at low L‐shells Which mechanisms are responsible for large and sudden particle depletions at low L‐shells Can active experiments produce particle depletion and help to answer these questions There havebeen various anthropogenic manners to influence the ionosphere and the space environment as presentedin the review of Gombosi et al (2017) Chang et al (2018) in this collection address this aspect in investigat-ing electron diffusion from the effect of controlled heating of the ionosphere More generally theDemonstration and Science Experiments mission (Adler et al 2006 Fennelly 2009 Moldwin 2010) thatwas launched in May 2019 will use antennas to drive electromagnetic waves in the radiation belts and mea-sure the propagation of these waves and any resulting pitch angle diffusion of the trapped particles In addi-tion there is an upcoming sounding rocket experiment named SMART (Space Measurement of RocketReleased Turbulence) to be launched in 2021 that will inject high‐speed Barium in the upper ionosphere thatis unstable to lower‐hybrid waves that undergo a turbulent conversion to electromagnetic whistler wavesthat will propagate into the radiation belts and interact with trapped particles (Ganguli et al 2015) Waveemission from pulsed electron beams either on board of a rocket or spacecraft is a third alternative that iscurrently under investiguation (eg Delzanno amp Roytershteyn 2019) Pulsed electron beams fired from aspacecraft and spotted at its magnetic footpoint in the ionosphere can also be used to follow the magneticfield lines and connect and map the magnetosphere to the ionosphere (eg Delzanno et al 2015 2016Lucco Castello et al 1968) What can we also learn from the systematic appearance of structured flux peaksand valleys called zebra stripes (Ukhorskiy et al 2012 Lejosne amp Roederer 2016) that are observed in thespectrograms of energetic electrons and ions trapped in the inner belt below L ~ 3 and could be modifiedby active experiments

344 Loss Observations

An important topic concerns the observations and measurements of losses independent of the associatedprocesses Specifically we need to better identify the definitive observational signatures of atmosphericandmagnetopause losses For example it is possible that loss signatures are misidentified since as we knownot every decrease in flux is a real loss Thus it is crucial to take full advantage of multipoint observationscombining those in space and onnear the ground as in the research contained in this collectionExample measurements include NASAs Van Allen Probes THEMIS Magnetospheric Multiscale andSAMPEX NOAAs GOES and Polar Orbiting Environmental Satellites constellations LANLs GPS andGEO constellations Japan Aerospace Exploration Agencys Arase mission ESAs Cluster and Project forOn‐Board Autonomy and Vegetation missions the BARREL balloon campaigns low‐altitude CubeSatsand ground‐based observatories such as magnetometer arrays broadband high‐frequency and VLF radiowaves receivers (eg riometers in Canada and Finland AARDDVARK) and radars Small satellite missionswill play a key role in the future (Millan et al 2019)



4 The Role of Nonlinear Processes in the Global Variability of theRadiation Belts

The development of nonlinear dynamics and plasma theory dramatic increase in computational power andnumerical simulation capability and most importantly highly accurate in situ field and plasma measure-ments collected in the radiation belts since the Combined Release and Radiation Effects Satellite (CRRES)mission 30 years ago (eg Anderson et al 1992 Vampola et al 1992) have revealed a number of nonlinearacceleration and loss processes that cannot be described in the quasilinear diffusion approximation Thuswe seek to advance our theoretical and experimental understanding of the role of the nonlinear processesin the global variability of the inner and the outer belt (see Sorathia et al 2018 in this collection) We broadlyclassify these investigations into three categories nonlinear particle dynamics nonlinear particle interactionwith quasi‐monochromatic waves and weak‐turbulence effects In the following we list some of the out-standing science questions in each category

41 Nonlinear Particle Dynamics

Is radial diffusion appropriate for modeling radial transport in the outer belt slot and the inner belt regionThe results of test‐particle simulations of radial transport in broadband ULF turbulence in Pc4 to Pc5 fre-quency range suggest that persistent phase correlations cause large deviation of the transport from the radialdiffusion approximation It is important to determine whether these deviations become less prominent inthe slot region and the inner belt

What is the role of drift orbit bifurcations in radial transport in the outer belt In the outer regions of the beltwhere the magnetic field becomes sufficiently compressed such that two local minima of the magnetic fieldintensity are formed above the equatorial plane electron drift orbits exhibit bifurcations associated with sec-ond adiabatic invariant violation producing rapid nondiffusive transport and strong enhancement of mag-netopause losses (Ukhorskiy et al 2011) Multispacecraft measurement analyses are required to address theoverall importance of drift orbit bifurcations to radial transport and magnetopause losses

What role do kinetic Alfveacuten waves play in energetic particle acceleration and loss in the inner magnetosphereRecent measurements from the Van Allen Probes have revealed that kinetic Alfveacuten waves (eg Chastonet al 2015) can be commonly produced in the inner magnetosphere in association with injections fromthe magnetotail For instance Chaston et al (2018) showed the simultaneous occurrence of broadbandAlfveacutenic fluctuations observed by the Van Allen Probes and the multitimescale modulation of enhancedatmospheric X‐ray bremsstrahlung emission in the BARREL data Pitch angle diffusion in the Alfveacutenic fluc-tuations that are time stationary on the electron timescale could cause the transport of electrons into the losscone over an energy range from hundreds of kiloelectron volts to multindashmegaelectron volts on diffusivetimescales on the order of hours which would constitute a significant loss process for the radiation beltsIt was previously suggested that the ion gyroradii‐scale electric fields that they carry may be sufficient todemagnetize ion motion and allow stochastic acceleration in the waves perpendicular electric fieldDetailed numerical modeling and data analysis are required to determine what role kinetic Alfveacuten wavesplay in ion heating in the inner magnetosphere and whether these processes are significant at radiationbelt energies

Finally the role that nonlinear wave structures commonly referred to as ldquotime domain structuresrdquo (TDSs)play in relativistic electron dynamics in the outer zone is important to understand One of the surprisingresults from the Van Allen Probes is the ubiquity of TDS observed in the inner magnetosphere (Mozeret al 2015 2017) Given the novelty of these radiation belt observations the role of TDSs in radiation beltdynamics is underexplored and is rife for investigation and potential discovery

42 Nonlinear Wave‐Particle Interactions

What is the relative importance of nonlinear wave‐particle interactions of electrons with quasi‐coherent whistlermode waves in radiation belt acceleration and loss and how do the inhomogeneities in the local environmentaffect them Are the numerical simulation models used representative of reality How does it compare with lin-ear and quasilinear theoryMultiple theoretical analyses and numerical simulations (see reviews Shklyar ampMatsumoto 2009 Nunn amp Omura 2015) show that phase trapping of electrons in large‐amplitude obliquewhistler mode waves in an inhomogeneous magnetic field can result in rapid acceleration as well as atmo-spheric loss of radiation belt electrons on bounce timescales (few seconds) Recently very large amplitude



whistler mode waves have been observed propagating obliquely at the equator (Cattell et al 2008)Statistical analysis of large‐amplitude whistler mode waves at different magnetospheric conditionsis required to assess the global effects on acceleration and loss Recent progress toward this goal has beenmade by the use of a numerical ldquoGreens functionrdquo (Omura Miyashita et al 2015 Kubota amp Omura2018) that gives the nonlinear test‐particle response to a given subpacket of chorus and demonstrates thatrapid acceleration to megaelectron volt energies is possible A subpacket of chorus (Foster et al 2017 andSantoliacutek et al 2014) is a burst of chorus power within a chorus element where the amplitude varies drama-tically on a timescale of the order of 5ndash10 wave periods and may itself be due to a higher‐order nonlinearresonance between the whistler mode wave and the electrons that generate the wave (Crabtree et al2017a 2017b)

What role do rising tone EMIC emissions play in radiation belt losses and ring current acceleration Recentanalysis (Kubota et al 2015 Shoji amp Omura 2014) showed that rising tone EMIC emission can producerapid heating of energetic protons around the equator because of the stable trapping as well as the atmo-spheric losses of relativistic electrons inside the plasmasphere Nakamura et al (2019) presented directVan Allen Probes observations of an event of rapid precipitation of relativistic electrons in timescale shorterthan 1 min and in lt1 hr of MLT possibly through nonlinear trapping by EMIC rising tones Quantitativeassessment of the occurrence rates of EMIC rising tones is required to establish their importance to the ringcurrent and radiation belts

43 Nonlinear Weak‐Turbulence Effects

Recent theoretical analysis (Crabtree et al 2012) has shown that inside the plasmasphere the threshold forthe nonlinear scattering of plasma waves with frequencies between the ion and the electron gyrofrequenciescan be reached by waves with amplitudes as low as 50 pT in the magnetic field perturbation which can bereached by powerful plasmaspheric whistler mode waves (Breneman et al 2011 Cattell et al 2008) Thenonlinear scattering of these waves can lead to a preference for wave properties that can produce anenhanced precipitation rate Can this effect be observed Are weak turbulence effects important to innerradiation belt dynamics Can this effect be incorporated into current models for example by incorporatingthe dependence of the statistical wave normal angle of waves with the amplitude Are there other instanceswhere wavendashwave coupling needs to be incorporated for accurate understanding of radiation belt dynamics

Can weak turbulence effects compete with quasi‐coherent nonlinear wave particle interactions in the radiationbelts Current theories of chorus generation mechanisms assume a coherent parallel‐propagating planewave which allows for the analytical solution to the nonlinear current and feedback mechanisms Recentdetailed analysis of wave data from EMFISIS (Crabtree et al 2017) indicates that these assumptions maynot be met and that chorus as it grows in amplitude may give rise to new secondary instabilities similarto weak turbulence interactions Nonlinear wave growth and saturation (eg Summers et al 2011) isexpected to differ from the linear Kennel‐Petschek limit (Kennel amp Petschek 1966) but by how muchRecent laboratory experimental evidence demonstrates that nonlinear induced scattering and nonlinearthree‐wave decay plays a role in saturating the nonlinear amplification process in triggered emissions(Tejero et al 2016) Thus this question will be addressed in conjunction with the fifth research theme

5 New Radiation Belt Modeling Capabilities and the Quantification ofModel Uncertainties

Modeling is necessary to fully understand the physical mechanisms responsible for the observed dynamics ofradiation belt particles Nearly 20 years ago the first detailed computer simulations of radiation beltdynamics were undertaken modeling pitch angle andor radial diffusion (see for instance review inShprits et al 2008a 2008b) In order to model specific observed events such modeling often relied onCRRES measurements of electromagnetic waves and plasma conditions or CRRES andor LANL GEOfluxes for providing the boundary conditions Many of the codes in use then which were developed intothe end of the 1990s were not particularly elaborate but they ultimately proved to be useful in future stu-dies once the physical properties of the space environment were more fully understood In those timesmany of the physical parameters required for the initial and boundary conditions that are needed to run suchmodels were sparse often averaged and sometimes relied on empirical models while others were simplynot known Detailed observations for model validation were also sparse available only over a limited



energypitch angle range and usually available over limited periods of time Data from the CRRES satellitewas typically regarded as the gold standard at the time but unfortunately CRRES survived only 14 monthsbefore suffering a fatal anomaly In that time it did not precess even one full revolution in MLT hence leav-ing the prenoon sector unsampled

Nevertheless since the CRRES era the radiation belt community has developed new code capabilities inmany aspects of radiation belt physics For example many research groups now develop and run codes thatmodel multiple wave particle interactions (eg energy and pitch angle diffusion) dynamic magnetic fieldconfigurations coupled ring current codes coupling between radial diffusion and pitch angle diffusionand other cross term effects coupling with global magnetohydrodynamic (MHD eg Sorathia et al 2018in this collection) and 2‐D and 3‐D particle‐in‐cell (PIC) simulations (eg Chang et al 2018 in this collec-tion) We briefly review in the following paragraphs the state of the art of modern computational tools forsolving the radiation belts and their environment

51 Modern Computational Tools511 The Fokker‐Planck FormalismThe primary radiation belt models currently use a Fokker‐Planck formalism based on quasilinear diffusionof radiation belt particles These codes have tremendously improved over the last 15 years thanks to two par-allel efforts relative to theory and model validation

First the theory of quasilinear pitch angle diffusion of the 1970s (eg Roberts 1969 Lyons et al 1971 1972Lyons 1974a Schulz amp Lanzerotti 1974) has been deeply revisited rederived and modernized to be moreeasily understood and implemented in modern codes (eg Albert 2005 2007 2010 2012 Glauert ampHorne 2005 Summers 2005) Such a task was needed and difficult as illustrated by the various missing fac-tors of 2 that were tracked within the various formalisms from 2005 to 2012 (eg Albert 2012 Summers2005 Tu et al 2013) Theoretical understanding also made great progress thanks to the derivation of simpli-fied models whose accuracy turned out to be sufficient to understand the main physical drivers and to allowthe derivation of scaling laws Among them there is the parallel approximation (Summers 2005) the meanvalue approximation (Albert 2007 Albert 2008a) the analytical approximation of lifetime (Albert ampShprits 2009) and various other analytical approximations of pitch angle diffusion and lifetime (egMourenas amp Ripoll 2012 Albert 2017) The solidity of the theoretical framework directly benefitted theFokker‐Planck numerical codes that were developed simultaneously by numerous research groups aroundthe world These codes are all based on an equation that takes the form of a linear diffusion equation andon bounce and drift averaging procedures well adapted to the dynamics of the particles trapped into theradiation belts making use of the periodic motion of trapped particles Bounce and drift averaging helpsby reducing the dimension to three (radial distance energy and pitch angle or equivalently three adiabaticinvariants associated to the three phases of the periodic motions of the particle) instead of the six dimen-sions of the nonlinear Vlasov equation However the Fokker‐Planck equation relies on the prerequisite cal-culation of various diffusion coefficients that represent the effect of small‐amplitude waves (from millihertzto kilohertz frequency range) on the particle distribution function All the effects induced by the electromag-netic waves are included in these diffusion coefficients which are calculated in the framework of quasilineartheory (eg Faumllthammar 1965 Kennel amp Petschek 1966 Lerche 1968 Lyons et al 1971 1972 Lyons1974a 1974b) This means that all the electromagnetic waves must be specified prior to the Fokker‐Planck simulations and that they are not calculated by the code itself like in MHD or PIC simulationsQuasilinear theory nevertheless requires that the waves have random phases and small amplitudes andare based on cold plasma linear theory (Stix 2006) (ie neglecting thermal effects) and that the particlesare in (cyclotron and Landau) resonance with the wave spectrum Tao et al (2012) have for instance ver-ified the breakdown of the quasi‐linear theory when the wave amplitude becomes too large

While the full Fokker‐Planck formalism was already available in early text books (eg Schulz amp Lanzerotti1974) most early formulations were based on the unidimensional Fokker‐Planck equation that solves forradial diffusion and approximates pitch angle diffusion (or any other diffusion phenomenae) thanks to lossterms (that do not involve partial derivatives) Derivation and limitation of this method are for instance dis-cussed in Ripoll Loridan et al (2016) A well‐known result obtained with this formulation is the reproduc-tion of the electron radiation belts energy structure by Lyons and Thorne in 1973 The 1‐D Fokker‐Planckformulation has been commonly used since the 1970s for Earths (and other planets) radiation belts (eg



Spjeldvik amp Thorne 1975 1976 Spjeldvik amp Lyons 2013 Brautigam amp Albert 2000 Shprits et al 2005Shprits Thorne Horne et al 2006 Tu et al 2009 Ozeke et al 2014 Li Millan et al 2014 RipollLoridan et al 2016 Ripoll Reeves et al 2016 Schiller et al 2017 Loridan et al 2019) There exist tract-able analytical solutions of this equation according to the form of the diffusion coefficient andor the lifetimemodel for the steady problem (Haerendel 1968 Hood 1983 Jentsch 1984 Thomsen et al 1977a 1977b)and for the general (unsteady) problem (Loridan et al 2017 Schulz 1986 Schulz amp Newman 1988 Walt1970) Tridimensional full Fokker‐Planck codes only became readily available and operational in a commonmanner in the years 2005ndash2010 (eg Albert et al 2009 Subbotin amp Shprits 2009 Varotsou et al 20052008) This is due to the complexity of different technical aspects such as the coupling between radial diffu-sion (solved in the invariant space) and the other diffusion processes (solved in the physical space) cross dif-fusion (such as mixed pitch angle and energy diffusion terms) the lack of knowledge of the wave and plasmaproperties that serve for the diffusion coefficients as well as for the initial and boundary conditions and thecomputational cost For instance cross diffusion is still nowadays not necessarily included in all 3‐D simula-tions (eg Glauert et al 2018) and there are debates on the appropriate numerical schemes that should beused (Albert 2013 Albert amp Young 2005 Camporeale et al 2013a 2013b) We also emphasize that no mod-ern model is free running based only on knowledge of the Suns behavior all the current models require theimposition of preverified outer boundary conditions With a full Fokker‐Planck code one can solve todaysimultaneously the following processes radial diffusion pitch angle diffusion energy diffusion cross energyand pitch angle diffusion Coulomb collision and anomalous diffusion Among the most well‐establishedFokker‐Planck codes are the ONERA Salammbocirc code (eg Beutier amp Boscher 1995 Bourdarie et al1996 2000 2005 Pugacheva et al 2000 Beutier et al 2005 Varotsou et al 2005 2008 Maget et al2015 Herrera et al 2016) the British Antarctic Survey (BAS) Radiation Belt Code (eg Glauert et al2014a 2014b Glauert amp Horne 2005 Horne et al 2013 Meredith et al 2016 2018) the VERB 3‐D code(eg Subbotin amp Shprits 2009 Shprits et al 2009 Subbotin et al 2010 2011 Kim et al 2011 Kim et al2012 Drozdov et al 2015) recently extended to a 4‐D version (eg Aseev et al 2016 Shprits et al 2015)to soon incorporate models of nonlinear wave‐particle interactions the University of California LosAngeles (UCLA) 3‐D diffusion code (eg Tao et al 2011 Li et al 2014 Li Ma et al 2016 Ma et al2015 2016 2016 Ma et al 2017 that incorporates the (UCLA) Full Diffusion Code (eg Ni et al 2008 Niet al 2011 Shprits amp Ni 2009) in order to compute diffusion coefficients (similarly to VERB 3‐D4‐D)the radiation belt code of the Space Vehicles Directorate of the US Air Force Research Laboratory (AFRL)(eg Albert 2005 2008b Albert et al 2009 Albert amp Young 2005 Selesnick Albert amp Starks 2013) theLANL Dynamic Radiation Environment Assimilation Model (DREAM) 1‐D (eg Tu et al 2009 Reeveset al 2012 Welling et al 2013) and 3‐D codes (Camporeale et al 2013a 2013b Cunningham 2016Cunningham et al 2018 Tu et al 2013) the Commissariat agrave lEnergie Atomique (CEA) CEVA code(Reacuteveilleacute 1997 Ripoll amp Mourenas 2012 Ripoll Chen et al 2014 Ripoll Reeves et al 2016 Ripollet al 2017 2019) and the STEERB code developed in China (eg Su et al 2010 Su Zheng et al 2011Su et al 1984)

The second effort made to develop Fokker‐Planck codes is the successive tests and validations of thesecodes that have been carried along the years against various types of events such as fast dropout andstrong enhancement of megaelectron volt electrons during storms with DREAM 3‐D (eg TuCunningham et al 2014) local acceleration by chorus waves with the UCLA diffusion code (LiThorne et al 2014 Li Millan et al 2014 Thorne et al 2013) electron radiation belt dropout eventduring storms with the US AFRL (eg Albert et al 2009) STEERB (Su et al 2001) and the CEVA(Loridan et al 2019 in this collection) codes rapid loss of radiation belt relativistic electrons by EMICwaves with STEERB (Su et al 2017) and VERB 3‐D (Drozdov Shprits Usanova et al 2017) nonstormtime and quiet dynamics of electron radiation belts with STEERB (eg Su et al 2014) UCLA (Ma et al2015 Ma Li Thorne Bortnik et al 2016) and the CEVA (Ripoll et al 2019 Ripoll Chen et al 2014)codes nonstorm time dropout of radiation belt electron fluxes with STEERB (Su et al 2016) internalacceleration and continuous losses with the BAS code (Glauert et al 2014b) early storm recovery phaseswith the UCLA code (Ma Li Thorne Nishimura et al 2016) flux enhancements during both the stormand the nonstorm times with the UCLA code (Ma et al 2018) deep injection of ~1‐MeV electrons intothe slot region with VERB 3‐D (Kim et al 2016) the atmospheric scattering and decay of inner radia-tion belt electrons (Selesnick 2012) and inner radiation belt dynamics (Selesnick Albert amp Starks 2013)



with the US AFRL code and the DREAM (Cunningham et al 2018) codes Long periods of radiationbelts dynamics that combine successively various types of events with the complexity of cumulating theerror as time increases have been simulated for 6 months with DREAM 3‐D (Tu Cunningham et al2014) 1 year with VERB 3‐D (Drozdov Shprits Usanova et al 2017) 3 years with DREAM(Cunningham et al 2018) and 4 years (and up to 30 years) with the BAS code (Glauert et al 2018)All these studies are encouraging and successful with regards to the formalisms and the methods butalso often reveal lacking pieces and the need to continue the effort of validation

Radiation belt particles are tied to the Earths magnetic field itself responding to both external and internalforces The ring current dominates the plasma influence on the near‐Earth electric and magnetic fields andis therefore a strong internal driver of the variation of the Earths magnetic field Rather than solving theradiation belt particle dynamics within a modeled and prescribed inner magnetosphere an alternative isto model the dynamics of the inner magnetosphere magnetic and electric fields and to include the trappedradiation belt particles within the inner magnetosphere model Such an approach is favored by the fact thatthe ring current and its interactions (cf review in Daglis et al 1999 Liemohn 2006 Ganushkina et al 2017and references within) can also be computed similarly with a bounce‐averaged kinetic Fokker‐Planck equa-tion that describes the evolution of the PSD as an advectionndashdiffusion process in coordinates consisting ofradial distance kinetic energy cosine of the equatorial pitch angle and as fourth variable driving advectionthe geomagnetic longitude For example the LANL Ring Current‐Atmosphere Interactions Model (RAM)computes ion distribution functions for the ring current plasma When coupled with a Self‐ConsistentMagnetic Field model RAM provides the anisotropic pressure that calculates self‐consistently the magneticfield topology for the ring current (RAM) plasma (Jordanova et al 1996 1997 2006 Zaharia et al 20062010 Jordanova amp Miyoshi 2005 Miyoshi et al 2006 Jordanova et al 2010 Welling et al 2011 Yuet al 2011 Yu Jordanova et al 2017) Recent extensions of RAM‐SCB include the generalization to rela-tivistic energies and radial diffusion such that the radiation belt electrons can now be included and wellsolved (Jordanova et al 2014 2016) Similarly the Comprehensive Inner Magnetosphere‐Ionosphere(CIMI) model considers the effects of the ring current the plasmasphere and the radiation belts particlesThe CIMI model (Fok et al 2014) was developed by merging the Comprehensive Ring Current Model(Fok et al 2001 Fok amp Moore 1997) and the Radiation Belt Environment (Fok et al 2008 2011 Gloceret al 2011 Kang et al 2016) models CIMI solves for both ion and electron distributions in the ring currentand radiation belts electron precipitation in the ionosphere plasmaspheric density subauroral convectionfields convection potential and Region 2 field‐aligned currents These global and self‐consistent approachesare highly promising in particular for storm times (and at L gt 3) that are vastly driven by the strongly vari-able and non dipolar magnetic field These models however usually lack a full resolution of wave particleinteractions that focus first on a correct resolution of the inner magnetosphere itself whose dynamics isindependent of radiation belts particles Recently the CIMI model incorporated pitch angle energy andcross diffusion of electrons due to EMIC waves (Kang et al 2016) and chorus and plasmaspheric hiss waves(Aryan et al 2017) to obtain a more realistic dynamics of radiation belt particles Global validation is there-fore only just now starting and sparse for that reason although encouraged by successful simulations ofstorm time dynamics with RAM‐SCB (eg Jordanova et al 2016) of rapid dropout event for highly relati-vistic electrons with Radiation Belt Environment (Kang et al 2016) of drift‐resonant interaction withULF waves (Komar et al 2017) and of electron flux dropout due to magnetopause shadowing with CIMI(Kang et al 2018) We note also the Geospace Environment Modeling System for Integrated Studies(GEMSIS) developed at Nagoya University that combines a ring current model (Amano et al 2011)(GEMSIS‐RC) a radiation belt model (Saito et al 2010 Saito et al 2012 Kamiya et al 2018) (GEMSIS‐RB and GEMSIS‐RBW) and a MHD model (Matsumoto amp Seki 2010) In a similar effort to account forthe variability of the magnetic field or for the inclusion of nonlinear effects or again for describing the azi-muthal dynamics of trapped particles advection terms have begun to be added into regular radiation beltsFokker‐Planck codes this is the case of the VERB 3‐D code evolving into VERB 4‐D (eg Aseev et al2016 Shprits et al 2015)

A limitation inherent to inner magnetosphere models when computing the dynamics of radiation belts par-ticles and also to the all radiation belt Fokker‐Planck models is that the treatment of wave particle interac-tions (through quasilinear diffusion coefficients) will unlikely be made consistently with the evolving



magnetic field because that would require dynamically computing diffusion coefficients as the nondipolarmagnetic field changes Not only is such computation highly computer time‐consuming but also a robusttheory and its associated numerical recipe are currently lacking to compute diffusion coefficients in the caseof a general non dipole magnetic field which may experience drift‐orbit bifurcations andor complexShabansky orbits (Shabansky 1971) To the authors knowledge only Orlova and Shprits (2010) have suc-ceeded in accounting for the Kp‐variable T89 magnetic field (Tsyganenko 1989) into the computation ofpitch angle diffusion coefficients that were based on CRRES data A similar effort was made in Kang et al(2015) who computed pitch angle diffusion coefficients but with the simpler parallel approximation ofSummers (2005) and the Tsyganenko 04 (T04) magnetic field model (Tsyganenko amp Sitnov 2005) Withthe samemotivation Cunningham (2016) has proposed a new theoretical formalism this time for radial dif-fusion coefficients that accounts for the variability of the magnetic field yet this is very new and complexand has yet to be broadly tested or used Thus today the full coupling between a disturbed and dynamicmagnetic field and wave‐particle interactions remains yet unsolved (independently of what transport codeis used) How does that matterWill the variability of themagnetic field soon be included in the computationof wave‐particle interactions The availability of magnetic field models and software as for instanceLANLGeoMag (httpsgithubcomdrsteveLANLGeoMag) as well as the availability of supercomputerpower that allows the computation of event‐driven diffusion coefficients over thousands of processors (cfRipoll et al 2019 in this collection) shows we are now ready to make better couplings between wave‐par-ticle interactions and the magnetic field To which extent will we try to conserve this coupling Would itbe enough to use a Kp‐variable T89 magnetic field as in Orlova and Shprits (2014) Or can we eliminatethe problem and assume the variability of the magnetic field is already accounted for in wave‐particle inter-actions through the wave properties that are measured within a dynamic magnetic field What level of con-sistency should we try to maintain between wave and plasma density properties that do require a magneticfield when these properties are generated (as for instance the Olson‐Pfitzer quiet time field model of Olsonamp Pfitzer 2009 in Malaspina et al 2018) and the magnetic field model that is used within the computationof the diffusion coefficients orand within the (diffusion or advectionndashdiffusion) Fokker‐Planck model Atwhich L‐shell and energy could these effects become important In conclusions there remain a greatamount of physical and technical questions for including a dynamic magnetic field in wave‐particle interactions

512 Test Particle PIC Hybrid and Full Vlasov Formalisms

A third class of kinetic codes uses a test particle approach These trace a large number of test particles inglobal Earth electric and magnetic fields that are generated from MHD codes (eg Elkington et al 20022004 Ukhorskiy et al 2008 Ukhorskiy amp Sitnov 2012 Kress et al 2012 Sorathia et al 2018) Theyrely on solving for the Full Liouvilles equation and Hamiltonian theory of the guiding‐center motion(eg Cary amp Brizard 2009) The formulation can be gyroaveraged for instance for limiting the compu-tational cost for electrons For instance since the variation of the gyroradius among the particle speciesvaries as 1∶40∶160 (eminusH+O+) it is necessary to keep the gyrotrajectory when computing particle lossof heavy ions through the magnetopause (eg Sorathia et al 2015) Global coupled MHDtest particlecodes are well adapted for instance for azimuthal transport that is solving for particle gradient‐curva-ture drift motion for rapid particle energization occurring during interplanetary shocks on the front endof coronal mass ejections (eg Hudson et al 1997 Kress et al 2007 2008) for drift‐orbit bifurcationtrajectory (Ukhorskiy et al 2011) for acceleration at dipolarization fronts (Ukhorskiy et al 2018 in thiscollection) for solar wind ion entering the magnetosphere (Sorathia et al 2000) for energetic particleinjections in the inner magnetosphere during substorms (eg Gkioulidou et al 2015) or O+ ion out-flow directly injected within the radiation belts (Gkioulidou et al 2019) or for the sudden depletion(eg Ukhorskiy et al 2015) and rapid recovery of the outer belt (eg Sorathia et al 2018 in this col-lection) These codes can also be used to generate diffusion coefficients (eg Ukhorskiy amp Sitnov 2008)The main drawback of global test‐particle codes is their high computational cost in 3‐D and the currentlack of inclusion of wave‐particle interactions such as pitch angle or energy diffusion in particular ener-gization from wave‐particle interaction with chorus waves that competes with the adiabatic energizationfrom the magnetic field Both of these currently limit the usability of these codes for studying radiationbelts electron dynamics during long time periods (eg gt2 days) Test‐particle codes are used to investi-gate the self‐consistent nonlinear mechanism of wave generation and growth in the radiation belts (eg



Omura et al 2009 Hikishima et al 2009 Omura amp Zhao 2012 2013 Chen et al 2016 Katoh et al2018 Omura et al 2019) Nevertheless wave particle interaction in this context is at the forefront ofthe field with for instance Omura et al (2019) using test particle simulation for studying energetic elec-trons acceleration in resonant interaction with a chorus wave packet

Particle‐in‐cell (PIC) codes (Dawson 1983) and hybrid codes which include the feedback from plasma tofields (eg Camporeale 2015 Delzanno et al 2013 Meierbachtol et al 2017) allow the self‐consistent gen-eration of the wave spectrum and no further assumption is required PIC codes are used to investigate theself‐consistent mechanism of wave generation and growth in the radiation belts such as chorus generationand enhancement (Fu et al 2014 2017 Lu et al 2019) whistler instability effects (Fan et al 2019 Yoonet al 2019) and saturation (Wu et al 2019) and magnetosonic wave excitation (Chen et al 2018) and pro-pagation (Min et al 2019) PIC codes are also used to test the validity of the quasilinear theory (egCamporeale 2015 Tao et al 2017) and for computing spacecraft charging in the radiation belts(Delzanno et al 2015 Lucco Castello et al 1968) Hybrid codes in which the dense cold electrons are treatedas a fluid while the resonant electrons are treated as super particles (PIC based) For instance Omura et al(2009) provide the comparison between a hybrid and a full computation in which the energetic and coldcomponents of electrons are treated as particles Hybrid codes are used to investigate the self‐consistent gen-eration of whistler waves in the inner magnetosphere such as the nonlinear generation and growthmechan-isms of chorus waves (eg Katoh amp Omura 2004 2006 2007 2013 Wu et al 2015 da Silva et al 2017) andEMIC waves (eg Hu amp Denton 2009 Hu et al 2010 Denton et al 2019 in this collection) These methodshave significant potential For instance Denton et al (2019) in this collection showed that nonlinear inter-actions with EMIC waves can cause precipitation of subndashmegaelectron volt electrons while the generalassumption based on quasi‐linear resonant interactions is that the dominant interactions occur for gt~2‐MeV electrons (eg Kersten et al 2014 and references within) Recent multi‐instrument observationsfrom Hendry et al (2019) corroborate this finding showing one event of nonlinear EMIC‐driven electronprecipitation at subndashmegealectron volt energies The comparative role of resonant and nonresonant interac-tions is still a widely open subject (eg Camporeale 2015 Chen et al 2016 Denton et al 2019 Hendryet al 2019) Full Vlasov simulations are generally not carried out for radiation belt dynamics due to theirprohibitive computational cost and this type of simulation is for instance restricted to the Earths foreshockupstream of the terrestrial bow shock (eg Kempf et al 2015 Palmroth et al 2015) or to reconnection ratesat the magnetopause (Hoilijoki et al 2017) Preliminary results of modeling of electron precipitation com-puted with the full Vlasov Vlasiator code are presented in Palmroth and the Vlasiator team (2019) inthis collection

513 MHD

As an alternative to kinetic theory the MHD approach consists of neglecting all single particle aspectsand focus on the whole collective behavior of the magnetospheric plasma that is treated as a conductingfluid being described through its macroscopic variables that are the moments of the distribution func-tion MHD simulations have the ability to give a description of the dynamics over large spatiotemporalscales for example the interaction of the solar wind with the bow shock and the impact on the entiremagnetosphere over many days The American Block‐Adaptive‐Tree‐Solarwind‐Roe‐Upwind‐Schemecode (Powell et al 1999 De Zeeuw et al 2000 Gombosi et al 2004) today embedded within theSpace Weather Modeling Framework (Ellington et al 2016 Glocer et al 2013 Haiducek et al 2017Morley Welling amp Woodroffe 2018 Toacuteth et al 2005 2012) the Open Geospace General CirculationModel (Raeder et al 2001) and the Coupled Magnetosphere‐Ionosphere‐Thermosphere model alsoreferred to by the magnetospheric Lyon‐Fedder‐Mobarry component (Lyon et al 2004 Wiltbergeret al 2015) and most recently GAMERA (Zhang et al 2018) models are all four state‐of‐the‐artMHD codes made for the computation of the dynamics of the magnetosphere and magnetospheresolarwind interaction At high spatial resolution they can solve for fine filamentary structure of the electricfield in the nightside that dynamically changes with a turbulent nature These codes can generate MHDlow‐frequency waves (mHz) (eg Claudepierre et al 2016) and can be used to generate radial diffusioncoefficients (eg Tu et al 2012) but fail to treat higher‐frequency waves (kHz) that would be neededfor computing consistently the wave‐particle interactions that play a fundamental role in radiation beltdynamics MHD models are commonly used to provide the magnetic and electric fields in the magneto-sphere and on the ground and are also used to compute geomagnetic indices such as Dst (eg



Liemohn McCollough et al 2018 Liemohn Ganushkina et al 2018) They are mandatory for realistictest‐particle simulations that use these fields MHD models can also be coupled to a Fokker‐Planckradiation belt code (eg Glocer et al 2009 2011)

514 Empirical ModelsExtensive empirical models of the radiation belts have also been developed over the years fromAE4 (Singleyamp Vette 1972) to AE8 (Fung 1996 Vette 1991) and IRENEAE9AP9 (Ginet et al 2013) incorporatingsatellite measurements that date back into the 1960s from many orbital regimes (eg LEO MEO HEOand GEO) We note also the IGE‐2006 model for electrons of 1 keV to 52 MeV (Sicard‐Piet et al 2008)the two‐Maxwellian ATS‐6 model for electrons of less than 50 keV for charging spacecraft surfaces (Purviset al 1984) and the empirical Low‐Earth‐Orbit Electron Environment Model of radiation belt electronbelow ~600 km (Chen et al 2012) Precomputed empirical models for electron pitch angle distributioncan be useful for initial and boundary conditions analytical estimates etc PSD models are legion in the lit-erature (eg Vampola 1997 Horne Meredith et al 2003 Gannon et al 2007 Xudong et al 2011 Zhaoet al 2014a 2014b Chen et al 2014 Ni et al 2015 Shi et al 2016 Allison et al 2018 2019) For instanceDenton et al (2015 Denton et al 2016) derived an empirical model of particle fluxes in the energy range~1 eV to ~40 keV at geosynchronous orbit based on a total of 82 satellite years of observations (between1990 and 2007) made by LANLGEO data These empirical models are an invaluable tool for both the scien-tific and spacecraft engineering communities

52 Accuracy Uncertainty Quantification and Forecasting

Today with the Van Allen Probes we have entered a new era for which we now have at our disposalnearly full coverage of the waves and plasma properties precise measurements of particle fluxes by multi-ple instruments very fine energy resolution and simultaneous measurements of magnetic and electricfields Other satellite missions deliver relevant measurements for both model validation and model bound-ary conditions The amount of information now available is considerable and allows for realistic simula-tions over long time intervals (eg years) detailed simulations dedicated to specific events such asquiet time decays or strong magnetic storms and performing real‐time computations that can be usedfor space weather predictions and situational awareness We are indeed at a golden era in radiation beltmodeling owing to the convergence of both the dramatic increase in computational power and numericalsimulation capability along with the highly accurate in situ field and plasma measurements collected inthe radiation belts

Thus radiation belt modelers are now faced with new challenges such as addressing the important physicaleffects that are still missing from the various models along with constructing quantitative metrics to evalu-ate and track model predictions and uncertainties We highlight three specific areas in which modeling cap-abilities should be enhanced described in greater detail below

521 Accurate Modeling of Acceleration Transport and Loss ProcessesAs described above in section 2 in the radiation belts the two primary sources of new outer radiation beltelectrons are less energetic electrons from larger L‐shells energized by inward radial transport as they enterthe inner magnetosphere or less energetic electrons on the same L‐shell energized locally by wave‐particleinteractions In both cases lower‐energy electrons usually have a substantially larger PSD and thus can be asource of the more energetic electrons However the relative contribution of these two accelerationmechan-isms is unclear A priority is to differentiate between these (and other) acceleration mechanisms Radiationbelt models are in a unique position to address this question as they provide a natural testbed to artificiallyturn on and turn off contributions from the relevant wave modes For instance distinguishing accelerationdue to ULF waves from acceleration due to chorus waves is essential (eg debate in Loridan et al 2019 andin Ozeke et al 2019 both in this collection) This is something that is not entirely possible in observationalstudies because both mechanisms often operate at the same time and in conjunction with the various lossprocesses and thus are difficult to distinguish from one another

The modeling of trapped electron dynamics is also strongly dependent on the loss processes and thus on theloss physics incorporated into ones model Similar to the questions surrounding the acceleration and trans-port processes our current understanding of the relative contributions between loss due to precipitation intothe atmosphere and loss to the magnetopause is still lacking (see section 3) In particular it is important tounderstand if our theoretical modeling of particle precipitation matches observational reality and if not by



how much it differs This quantitative comparison between observed and modeled particle precipitationusually requires both space and ground measurements and accurate numerical simulations themselves rely-ing on an accurate description of both the space and the atmospheric environment The complexity of such atask explains why there exist only a few studies that have been capable to tackle this hard subject (egClilverd et al 2017 Woodger et al 2018) We also continue further refining our models such that loss asso-ciated with EMIC wave scattering is incorporated in a realistic and quantitative manner Furthermorerecent work has clearly shown that global MHD test particle simulations do produce the large‐scale dropoutevents over the wide range of L shells that is typically observed (Ukhorskiy et al 2015 Sorathia et al 2018in this collection) Thus we try to identify what is incorrectmissing with either our representation of radialdiffusion (eg ULF enhanced outward transport) or the local magnetopause loss models As noted above aquantitative understanding of magnetopause particle loss is required for a quantitative understanding of theparticle acceleration because the measured electron flux is the net result of a dynamic competition betweenloss and acceleration Thus advances in our modeling of loss processes are crucial for accurate radiation beltmodeling on the whole

522 Quantification of Model Uncertainties

Quantitative assessments made with dedicated metrics allow us to understand the input conditions andexpected output values for which a model has high or low performance capabilities Doing so revealsstrengths and weaknesses of the underlying methodology (Jolliffe amp Stephenson 2012 LiemohnMcCollough et al 2018) According to the accuracy of the numerical model a specific physical processcan be confirmed or disproved Operational metrics are generally specifically designed for certain forecasttypes or user communities (Eastwood et al 2017) The proper choice of metrics is also important for com-parisons with the measurements made on a moving spacecraft (Gordeev et al 2015) Different statisticalmetrics have been used through the field of the radiation belt physics and applied to radiation belts electronfluxes (unidirectional or omnidirectional) These metrics can be based on the forecast error (differencebetween the model and the reference) on a relative forecast error (normalized difference between the modeland the reference) or on an accuracy ratio (ratio of the model with the reference) Mean or median of thesequantities are made in a linear or (Base 10) logarithmic scale Advantages and drawbacks of error metrics ofthis type are given in Morley Brito and Welling (2018) (see also Liemohn McCollough et al 2018) Amongthe main radiation belt flux metrics we note the normalized forecast error (eg Subbotin et al 2010Subbotin amp Shprits 2009 Subbotin amp Shprits 2001) the mean absolute percentage error (eg Kim et al2012 Ripoll et al 2017 Tu et al 2013) the prediction efficiency (eg Pulkkinen et al 2011 Tu et al2013) and the median symmetric accuracy percent and the median accuracy ratio (eg Glauert et al2018 and Ripoll et al 2019 in this collection)

However there is currently not an overarching framework for evaluating and tracking radiation belt modelpredictions and uncertainties For example a typical modeling effort focuses on a specific event and oftenone looks for which correction of the main parameters (eg the wave amplitude or the lifetime or diffusioncoefficients of any kind and MLT dependence) is required for the model to reach a good agreement withobservations delivering a corrective factor for that event The correction that is brought can be seen as a tun-ing or a calibration of the model would need to be validated onto that event For instance the importance ofthe MLT dependence of whistler hiss mode amplitudes measured by Radiation Belt Storm Probes is dis-cussed in Ripoll Reeves et al (2016) in which these authors showed the lacking MLT dependence in theirevent‐driven approach accounted for a factor ranging from ~1 for L in (15 3) up to ~4 for L in (4 55) Orsimilarly one tries among all the various models available for one quantity to determine which one leads tothe most accurate results For instance Ozeke et al (2017) tested commonly used radial diffusion coefficientmodels during long‐lasting depletions of ultrarelativistic electrons in the outer radiation belt (see alsoDrozdov Shprits Aseev et al 2017) The need of calibration required for operational tools is always justi-fied by one argument the lack of good knowledge of the parameter or of the model that is proposed to becorrected Because even if we have at disposal high‐quality in situ measurements this is most often froma limited number of locations at any one time which therefore obliges modelers to introduce at best sta-tistical models to describe the entire system (in MLT and L) or at worst when statistics are incomplete (ortoo inaccurate) empirical correction factors Both ways are source of errors that are often hard to estimateThis also begs the question if the same model and modeling parameters are applied to different events how



good would be the agreement Still more observations we have at our disposal and less calibration isrequired as confirmed by the availability of the Van Allen Probes data

Do current validation metrics really tell us which physical processes have been captured accurately Whichmetrics should we use Is one metric enough or should we use simultaneously many We tend to run mod-els compare with observations and try to conclude whether the model captures the dynamics reasonablywell or not As we improve and change our models in order to better reproduce the missing phenomenawe rarely come back to older models and to the former agreement that was found So what does that sayabout the ldquogood agreementrdquowe got with old models There is a need to construct a community‐wide frame-work of metrics to enable unbiased and quantitative assessments of the various radiation belt models in usetoday How can we establish a baseline set of statistical analysis metrics for benchmarking Aware of thesequestions and needs the research community is making progress for instance with the recent effortthrough the ldquoQuantitative Assessment of Radiation Belt Modelingrdquo focus group organized at the GeospaceEnvironment Modeling workshop sponsored by the National Science Foundation Division ofAtmospheric and Geospace Sciences from 2014 to 2018 (Tu et al 2019) This group selected four distinctradiation belt dropout and buildup events with the goal of quantitatively assessing the relative importanceof various acceleration transport and loss processes through rigorous validation against contemporaryradiation belt measurements To avoid calibration andor have the least dependence on statistical modelsgreat coordinated efforts have been put into the development of event‐specific and global model inputs ofwave plasma and magnetic field conditions for each of the challenge events As discussed above the orga-nization of quantitative comparisons has been made possible nowadays since radiation belt codes havereached amature and robust stage Another effort made by the space weather community is the organizationof working groups to address the issue of metrics for space weather models This community work led tostandardizing assessment metrics for geomagnetic indices (Liemohn McCollough et al 2018)Nevertheless more studies including and reproducing important geospace features are still needed to helpimprove the models and reveal their intrinsic limitations These efforts are encouraged and can take placethrough space weather research plans or organizations themselves inspired by governmental policies (cfthe National Space Weather Strategy and Action Plan in 2015 and in 2019 followed by US PresidentialExecutive Orders) For instance the Committee on Space Research contributes to coordinated actions onspace weather research and has recently issued a plan for the development of small‐size satellites that willbe key for future scientific missions related to the radiation belts (Millan et al 2019) All the current researchstudies support the conclusion that more validation efforts will be needed for the next 5 to 10 years beforeradiation belt codes reach a good level of predictability

523 Space Weather Forecasting and the Extrapolation to Other Solar Cycles

The Van Allen Probes mission has been in operation during a rather quiet period of the solar cycle and veryfew extreme cases in terms of solar wind properties and geomagnetic indices have been observed thus farIn comparison mission like SAMPEX lasted two decades covering two solar cycles with periods of extremeactivity such as the Halloween storms (eg Baker et al 2004 Lopez et al 2004) We know that energeticradiation belt electrons typically penetrate to lower L with more negative Dst The low level of geomagneticactivity is thus certainly related to the fact that Van Allen Probes has not measured gt1‐MeV electrons in theinner belt (Fennell et al 2015) until 2015 (Claudepierre et al 2017 Pierrard et al 2019) However we knowfrom CRRES that such events do occur for example the extreme March 1991 event (eg Baker et al 2004Blake et al 1992 Li et al 1993) which depositedmultindashmegaelectron volt electrons deep into the inner beltThus we must carefully consider how we extrapolate or generalize Van Allen Probes results to other solarcycles or other parts of the solar cycle (Li Baker et al 2017) We also need to anticipate what could bethe next extreme events (eg Horne et al 2018) and characterize the highest flux that could occur at LEO(eg Meredith et al 2016) and at GEO (eg Meredith et al 2015 2017) In particular it is important tounderstand these implications for empirical models of the radiation environment (eg AE9 in Ginetet al 2013) which are used heavily in the spacecraft engineering and design communities (eg Handset al 2018) Furthermore Van Allen Probes data will eventually be ingested into these empirical modelsand will be considered the gold standard data set for such models Which techniques andor data sets canthus be used to appropriately tie missions together into a climatological description of changing spaceweather Another related question is how well can we forecast the inner and outer electron radiation beltswithout using Van Allen Probes as an input (Van Allen Probes measurements are vital for driving current



operational space weather models but these observations just ended) These are challenges that spaceweather and space climate modeling communities will face in the future and now is the time to beginaddressing them Furthermore recent works have started to incorporate radiation belt electron precipitationinto climate modeling (eg Matthes et al 2017) for instance for multidecadal climate simulations (eg vande Kamp et al 2018 2016) addressing the questions of the impact of radiation belt electrons on the upperstratospheric and mesospheric composition (eg on the polar stratospheric NOx in Newnham et al 2013)and ozone variability and destruction (Turunen et al 2016) or on the HOx and ozone production) at a timeat which climate change is one of the most important scientific issues

6 What Can We Learn About Radiation Belt Dynamics From LaboratoryPlasma Experiments

Much of our current understanding of radiation belt dynamics comes from comparing models with observedin situ plasma wave and particle measurements These analyses are confounded by a lack of repeatability(the radiation belts are never quite in the same circumstances) and controllability (nature gives us the beltsand we observe) This forces assumptions to be made about initial conditions and boundary conditions of themodels and even applicability of the physics underlying the models

In laboratory plasma experiments on the other hand repeatability and controllability are powerful toolsthat can be combined to lead to a detailed knowledge of the spatiotemporal structure of the entire experi-ment and thus can lead to a rigorous understanding of the physical processes under investigationRepeatability allows one to overcome the stochastic nature of many of these processes and observe theunderlying physics This brings an accurate spatial as well as temporal resolution of the processControllability allows for a specific perturbation to be applied and the response to be observed a powerfultool to test hypotheses These abilities lead to rigorous testing of the underlying hypotheses of any given phy-sical radiation belt model

In the past laboratory plasmas have been underutilized in the study of the radiation belts but recently thishas begun to change Modern computer controlled laboratory plasma devices (Amatucci et al 2011Blackwell et al 2010 Gekelman et al 2016) can routinely create and accurately diagnose plasmas withparameters (such as wavelengths to skin depths or gyroradii) that are equivalent to radiation belt plasmasLaboratory experiments investigating the physics of the global scale of the radiation belts are difficult how-ever there are several laboratory magnetic dipole configurations in operation (LDX CTX and RT‐1) thatcan test some hypothesis on a more global scale (Garnier et al 2006 Warren amp Mauel 1995) Most labora-tory experiments focus on investigating the microphysics of plasmas such as wave‐particle interactions thatform the foundation of current global radiation belt models In this regard we describe four areas of specificfocus each elaborated on below

61 Understanding Nonlinear‐Wave Particle Interactions in the Radiation Belts

Recent laboratory experiments have successfully generated whistler mode waves with frequencies thatchirp analogous to chorus emissions in the radiation belts by injecting helical electron beams into a back-ground plasma (Tejero et al 2016 Van Compernolle et al 2015) Triggered emissions and nonlinear ampli-fication have also been demonstrated in the laboratory (Tejero et al 2016) This allows for the possibility ofrigorously testing the predictions of different theories of chorus (Omura et al 2008 Trakhtengerts 1999)Thus we may soon be able to answer the question of the fundamental physics behind nonlinear chirpingwhistler mode waves in radiation belt plasmas Several related questions that have already been consideredare as follows What is the precise role of magnetic field inhomogeneity in chorus wave generation and pro-pagation What is the physics behind the fine structure of both chorus (eg Santoliacutek et al 2014) and hiss(eg Summers et al 2014 Zhu Liu amp Chen 2019) waves that has recently been highlighted by EMFISISobservations from the Van Allen Probes Is it related to the saturation of the nonlinear amplification ofchorus Can laboratory plasmas be used to investigate the role of particle energization and pitch angle scat-tering loss that is seen in association with chorus How can we use laboratory plasmas to understand othernonlinear wave structures that are observed (eg EMIC rising tones in Nakamura et al 2015) and TDSs(Mozer et al 2015) Another way to look at the problem is that the radiation belts are fantastic examplesof wave‐particle interactions Can we use measurements of radiation belt plasmas in conjunction with



laboratory measurements (Doveil amp Macor 2006 Fasoli et al 1994) to investigate nonlinear wave‐particleinteractions in general

62 Understanding Weak Turbulence Processes in the Radiation Belts

The framework of quasilinear diffusion of radiation belt particles has been the backbone of most of the mod-eling of global variability of radiation belt intensities However theoretical plasma physics and laboratoryplasma experiments have long studied nonlinear interactions between waves and particles for examplethree‐wave decay and coalescence and nonlinear Landau damping as the logical next step beyond the quasi-linear picture into the nonlinear regime Many of these phenomena have been investigated (and are beinginvestigated) in the laboratory (Tejero et al 2015a 2015b Dorfman amp Carter 2013) How can this rich heri-tage be applied to radiation belt dynamics What is the role of these processes in different radiation belt phe-nomena What are the important nonlinear wavendashwave and wave‐particle processes in the radiation beltsUnder what conditions do they become indispensable to Van Allen Probe data analysis Can laboratoryexperiments elucidate the plasma microprocesses and identify their measurable signatures in the insitu data

63 Developing New Measurement Techniques for Radiation Belt Plasmas

Another area with a long and important history is the development and testing of new radiation belt sensingdevices and algorithms in laboratory plasmas An example that has seen recent development is the labora-tory verification of methods of determining the wave‐vector direction from single point measurements Inmagnetospheric plasma wave measurements by the Means method (Means 1972) and the Singular ValueDecomposition (SVD) method (Santoliacutek Parrot amp Lefeuvre 2003) have seen widespread use howeverthere are many cases where the assumptions of a single coherent plane wave are violated andmore advancedtechniques must be used One is the wave distribution function technique (Storey amp Lefeuvre 1979 Santoliacutekamp Parrot 2000) which was recently verified in laboratory experiments where results of the wave distribu-tion function technique could be directly compared to cross‐correlation measurements frommultiple probesand its accuracy confirmed (Tejero et al 2015b)

64 Understanding the Origin of Waves and Dynamics in Dipolarization Fronts

Van Allen Probe observations show dipolarization fronts that move earthward and interact with the radia-tion belts where there is plasma energization along with intense broadband electrostatic and electromag-netic wave activity The dipolarization front is the boundary between the low‐pressure plasma of the lobeand the high‐pressure plasma of the plasmasheet and constitutes a layer (eg Fletcher et al 2019 in thiscollection) which is characterized by strong inhomogeneity over a small‐scale size and includes highly loca-lized static electric fields (eg Ukhorskiy et al 2018 in this collection) Because the inhomogeneities arelocalized over very small‐scale sizes that can be easily scaled in a laboratory device the dipolarization frontis well suited for replication in the laboratory for detailed characterization of the physical process that lead tothe observed broadband waves and particle energization This is not easily and unambiguously accom-plished by in situ data The strong inhomogeneities of a stationary boundary layer between the plasmasheetand the lobe have been studied both theoretically (Romero et al 1990 Romero amp Ganguli 1994) and experi-mentally (Amatucci et al 2003 DuBois et al 2013 DuBois et al 2014) Thus laboratory experiments couldsignificantly improve our understanding of the dynamics of dipolarization fronts and their interaction withthe radiation belt plasma

7 Summary and Perspectives

With the NASAs Van Allen Probes coupled with other satellite observations and recent advances in radia-tion belt theory and modeling associated increases in computational power and numerical simulation cap-abilities we are perhaps in a ldquogolden erardquo in radiation belt research In following of this introductive articlewe gather in this Special Collection of Journal of Geophysical Research (JGR) Space Physics a series of state‐of‐the‐art scientific articles dedicated to the physics of Particle Dynamics in the Earths Radiation BeltsThese articles are related to current research questions and studies discussed in this introduction and allrelative to five main aspects of modern radiation belt research (1) particle acceleration and transport (2)particle loss (3) the role of nonlinear processes (4) new radiation belt modeling capabilities and the quan-tification of model uncertainties and (5) laboratory plasma experiments



With the end of the Van Allen Probes mission we enter a new era during which the scientific communitywill have the opportunity to look further into the considerable amount of high‐quality observations thathas been gathered along this 7‐year mission The scientific measurements are available for many moreevent‐based studies or statistical studies of the near Earth space that will reveal in depth both the commonand the rare behaviors of the radiation belts Models will benefit from these data and progress either fromvalidation that will become more and more systematic or from the increasing availability of more reliableambient properties of plasma and waves generated from the Van Allen Probes observations ldquoBig datardquoand artificial intelligence methods should soon allow us to fully take advantage of all Van Allen Probesobservations All progress made will converge toward new advances in the hardening of electronic spacecraftsystems in the coming years The success of this mission certainly shows the human capability to put forth aset of modern reliable long‐life and complementary particle and field sensors in a hostile environment Onthe other hand with the end of the Van Allen Probes mission we will have a limited view of the response ofthe radiation belts to new magnetospheric storms impacting the Earth for times that may be more activethan the rather quiet Van Allen Probes time period The last questions ending our record are certainly aboutwhat the future will be made of regarding the observation of the radiation belts that feed space weather stu-dies and space science The number of satellites launched has doubled over the last 2 years (~400 satellitesper year in 2018) and it is expected that thousands of small satellites will be launched by commercial indus-try connecting people and machines but always sensitive to the radiation environment that remains athreat Severe space weather is today recognized as a global threat that requires a coordinated globalresponse and expanded international collaboration at the governmental policy level (Mann et al 2018)Our preface and the following articles of this Special Collection of Journal of Geophysical Research showhow numerous complex and open remain the main scientific problems on radiation effects in the nearEarth space What will then be the next generation of scientific space observers that will both allow physicsto progress and provide space weather awareness information satellites cubesats microsatellites or nano-satellites Constellations of these spacecraft Or can we imagine probing technological systems embedded incommercial or institutional satellites What observational coverage of the near Earth space do we needWhat will be the main societal goals that the scientific community will be capable to put forward to justifythe economical investment needed for such scientific missions both from civilian and defenserelated perspectives

ReferencesAbel B amp Thorne R M (1998a) Electron scattering loss in Earths inner magnetosphere 1 Dominant physical processes Journal of

Geophysical Research 103 2385ndash2396 httpsdoiorg10102997JA02919Abel B amp Thorne R M (1998b) Electron scattering loss in Earths inner magnetosphere 2 Sensitivity to model parameters Journal of

Geophysical Research 103 2397ndash2408 httpsdoiorg10102997JA02920Abel B amp Thorne R M (1999) Correction to ldquoElectron scattering loss in the Earths inner magnetosphere 1 Dominant physical pro-

cessesrdquo and ldquoElectron scattering loss in the Earths inner magnetosphere 2 Sensitivity to model parametersrdquo Journal of GeophysicalResearch 104(A3) 4627ndash4628 httpsdoiorg1010291998JA900121

Adler A J Guarnieri G Spanjers J Winter G Ginet B Dichter et al (2006) Overview of the AFRLs Demonstration and ScienceExperiments (DSX) Program American Institute of Aeronautics and Astronautics AIAA 2006‐7509 Space 2006 19 ‐ 21 September 2006San Jose California

Agapitov O Artemyev A Krasnoselskikh V Khotyaintsev Y V Mourenas D Breuillard H et al (2013) Statistics of whistler modewaves in the outer radiation belt Cluster STAFF‐SA measurements Journal of Geophysical Research Space Physics 118 3407ndash3420httpsdoiorg101002jgra50312

Agapitov O V Mourenas D Artemyev A V Mozer F S Hospodarsky G Bonnell J amp Krasnoselskikh V (2018) Synthetic empiricalchorus wavemodel from combined Van Allen Probes and Cluster statistics Journal of Geophysical Research Space Physics 123 297ndash314httpsdoiorg1010022017JA024843

Albert J M (1999) Analysis of quasi‐linear diffusion coefficients Journal of Geophysical Research 104 2419ndash2441 httpsdoiorg1010291998JA900113

Albert J M (2003) Evaluation of quasi‐linear diffusion coefficients for EMIC waves in a multispecies plasma Journal of GeophysicalResearch 108(A6) 1249 httpsdoiorg1010292002JA009792

Albert J M (2005) Evaluation of quasi‐linear diffusion coefficients for whistler mode waves in a plasma with arbitrary density ratioJournal of Geophysical Research 110 A03218 httpsdoiorg1010292004JA010844

Albert J M (2007) Simple approximations of quasi‐linear diffusion coefficients Journal of Geophysical Research 112 A12202 httpsdoiorg1010292007JA012551

Albert J M (2008a) Efficient approximations of quasi‐linear diffusion coefficients in the radiation belts Journal of Geophysical Research113 A06208 httpsdoiorg1010292007JA012936

Albert J M (2008b) The coupling of quasi‐linear pitch angle and energy diffusion Journal of Atmospheric and Solar ‐ Terrestrial Physics71 1664 httpsdoiorg101016jastp200811014

Albert J M (2010) Diffusion by one wave and by many waves Journal of Geophysical Research 115 A00F05 httpsdoiorg1010292009JA014732



Albert J M (2012) Dependence of quasi‐linear diffusion coefficients on wave parameters Journal of Geophysical Research 117 A09224httpsdoiorg1010292012JA017718

Albert J M (2013) Comment on ldquoOn the numerical simulation of particle dynamics in the radiation belt Part I Implicit and semi‐implicitschemesrdquo and ldquoOn the numerical simulation of particle dynamics in the radiation belt Part II Procedure based on the diagonalization ofthe diffusion tensorrdquo by E Camporeale et al Journal of Geophysical Research Space Physics 118 7762ndash7764 httpsdoiorg1010022013JA019126

Albert J M (2017) Quasi‐linear diffusion coefficients for highly oblique whistler mode waves Journal of Geophysical Research SpacePhysics 122 5339ndash5354 httpsdoiorg1010022017JA024124

Albert J M Ginet G P amp Gussenhoven M S (1998) CRRES observations of radiation belt protons Journal of Geophysical Research103(AS) 9261ndash9273

Albert J M Meredith N P amp Horne R B (2009) Three‐dimensional diffusion simulation of outer radiation belt electrons during the 9October 1990 magnetic storm Journal of Geophysical Research 114 A09214 httpsdoiorg1010292009JA014336

Albert J M amp Shprits Y Y (2009) Estimates of lifetimes against pitch‐angle diffusion Journal of Atmospheric and Solar ‐ TerrestrialPhysics 71 1647ndash1652

Albert J M Starks M J Horne R B Meredith N P amp Glauert S A (2016) Quasi‐linear simulations of inner radiation belt electronpitch angle and energy distributions Geophysical Research Letters 43 2381ndash2388 httpsdoiorg1010022016GL067938

Albert J M amp Young S L (2005) Multidimensional quasi‐linear diffusion of radiation belt electrons Geophysical Research Letters 32L14110 httpsdoiorg1010292005GL023191

Ali A F Malaspina D M Elkington S R Jaynes A N Chan A A Wygant J amp Kletzing C A (2016) Electric and magnetic radialdiffusion coefficients using the Van Allen probes data Journal of Geophysical Research Space Physics 121 9586ndash9607 httpsdoiorg1010022016JA023002

Allcock G M (1957) A study of the audio‐frequency radio phenomenon known as ldquodawn chorusrdquo Australian Journal of Physics 10(2)286 httpsdoiorg101071PH570286

Allison H J Horne R B Glauert S A amp Del Zanna G (2018) Determination of the equatorial electron differential flux from obser-vations at low Earth orbit Journal of Geophysical Research Space Physics 123 9574ndash9596 httpsdoiorg1010292018JA025786

Allison H J Horne R B Glauert S A amp Del Zanna G (2019) On the importance of gradients in the low‐energy electron phase spacedensity for relativistic electron acceler‐ ation Journal of Geophysical Research Space Physics 124 2628ndash2642 httpsdoiorg1010292019JA026516

Amano T Seki K Miyoshi Y Umeda T Matsumoto Y Ebihara Y amp Saito S (2011) Self‐consistent kinetic numerical simulationmodel for ring current particles in the Earths inner magnetosphere Journal of Geophysical Research 116 A02216 httpsdoiorg1010292010JA015682

Amato E amp Blasi P (2018) Cosmic ray transport in the Galaxy A review Advances in Space Research 62 2731ndash2749 httpsdoiorg101016jasr201704019

Amatucci W E Blackwell D D Tejero E M Cothran C D Rudakov L Ganguli G I amp Walker D N (2011) Whistler waveresonances in laboratory plasma IEEE Transactions on Plasma Science 39(2) 637ndash643

Amatucci W E Ganguli G Walker D N Gatling G Balkey M amp McCulloch T (2003) Laboratory investigation of boundary layerprocesses due to strong spatial inhomogeneity Physics of Plasmas 10(5) 1963ndash1968

Anderson R R Gurnett D A amp Odem D L (1992) CRRES plasma wave experiment Journal of Spacecraft and Rockets 29(4) 570ndash573httpsdoiorg102514325501

Angelopoulos V (2008) The THEMIS mission Space Science Reviews 141(1‐4) 5ndash34 httpsdoiorg101007s11214‐008‐9336‐1Aryan H Sibeck D G Kang S‐B Balikhin M A Fok M‐C Agapitov O et al (2017) CIMI simulations with newly developed

multiparameter chorus and plasmaspheric hiss wave models Journal of Geophysical Research Space Physics 122 9344ndash9357 httpsdoiorg1010022017JA024159

Aseev N A Shprits Y Y Drozdov A Y amp Kellerman A C (2016) Numerical applications of the advective‐diffusive codes for the innermagnetosphere Space Weather 14 993ndash1010 httpsdoiorg1010022016SW001484

Aseev N A Shprits Y Y Drozdov A Y Kellerman A C Usanova M E Wang D amp Zhelavskaya I S (2017) Signatures of ultra-relativistic electron loss in the heart of the outer radiation belt measured by Van Allen Probes Journal of Geophysical Research SpacePhysics 122 10102ndash10111 httpsdoiorg1010022017JA024485

Baker D N Erickson P J Fennell J F Foster J C Jaynes A N amp Verronen P T (2018) Space weather effects in the Earths radiationbelts Space Science Reviews 214 17 httpsdoiorg101007s11214‐017‐0452‐7

Baker D N Hoxie V Zhao H Jaynes A N Kanekal S Li X amp Elkington S (2019) Multi‐year measurements of radiation beltelectrons Acceleration transport and loss Journal of Geophysical Research Space Physics 124 2588ndash2602 httpsdoiorg1010292018JA026257

Baker D N Jaynes A N Hoxie V C Thorne R M Foster J C Li X et al (2014) An impenetrable barrier to ultrarelativistic elec-trons in the Van Allen radiation belts Nature 515(7528) 531ndash534 httpsdoiorg101038nature13956

Baker D N Kanekal S G Hoxie V C Batiste S Bolton M Li X et al (2013) The Relativistic Electron‐Proton Telescope (REPT)instrument on board the Radiation Belt Storm Probes (RBSP) spacecraft Characterization of Earths radiation belt high‐energy particlepopulations Space Science Reviews 179(1ndash4) 337ndash381 httpsdoiorg101007s11214‐012‐9950‐9

Baker D N Kanekal S G Hoxie V C Henderson M G Li X Spence H E et al (2013) A long‐lived relativistic electron storage ringembedded in Earths outer Van Allen Belt Science 340(6129) 186ndash190 httpsdoiorg101126science1233518

Baker D N Kanekal S G Li X Monk S P Goldstein J amp Burch J L (2004) An extreme distortion of the Van Allen belt arising fromthe lsquoHalloweenrsquo solar storm in 2003 Nature 432 878ndash881 httpsdoiorg101038nature03116

Baker D N Mason G M Figueroa O Colon G Watzin J G amp Aleman R M (1993) An overview of the Solar Anomalous andMagnetospheric Particle Explorer (SAMPEX) mission IEEE Transactions on Geoscience and Remote Sensing 31(3) 531ndash541 httpsdoiorg10110936225519

Baker D N Summers D amp Mann I R (2011) Chapman Conference on the Earths radiation belts and inner magnetosphere SpaceWeather 9 S10008 httpsdoiorg1010292011SW000725

Balescu R (1960) Irreversible processes in ionized gases Physics of Fluids 3(1) 52 httpsdoiorg10106311706002Beutier T amp Boscher D (1995) A three‐dimensional analysis of the electron radiation belt by the Salammbo code Journal of Geophysical

Research 100 14853ndash14861 httpsdoiorg10102994JA03066Beutier T Boscher D amp France D M (1995) SALAMMBO A three‐dimensional simulation of the proton radiation belt Journal of

Geophysical Research 100(A9) 17181ndash17188 September 1 1995



Bingham S T Mouikis C G Kistler L M Boyd A J Paulson K Farrugia C J et al (2018) The outer radiation belt response to thestorm time development of seed electrons and chorus wave activity during CME and CIR driven storms Journal of Geophysical ResearchSpace Physics 123 10139ndash10157 httpsdoiorg1010292018JA025963

Bingham S T Mouikis C G Kistler L M Paulson K W Farrugia C J Huang C L et al (2019) The storm‐time development ofsource electrons and chorus wave activity during CME‐ and CIR‐driven storms Journal of Geophysical Research Space Physics in press124 6438ndash6452 httpsdoiorg1010292019JA026689

Blackwell D D Walker D N amp Amatucci W E (2010) Whistler wave propagation in the antenna near and far fields in the NavalResearch Laboratory Space Physics Simulation Chamber Physics of Plasmas 17(1) American Institute of Physics) 012901 httpsdoiorg10106313274453

Blake J B Carranza P A Claudepierre S G Clemmons J H Crain W R Dotan Y et al (2013) The Magnetic Electron IonSpectrometer (MagEIS) instruments aboard the Radiation Belt Storm Probes (RBSP) spacecraft Space Science Reviews 179(1ndash4)383ndash421 httpsdoiorg101007s11214‐013‐9991‐8

Blake J B Kolasinski W A Fillius R W ampMullen E G (1992) Injection of electrons and protons with energies of tens of MeV into L lt3 on March 24 1991 Geophysical Research Letters 19 821ndash824 httpsdoiorg10102992GL00624

Blake J B Looper M D Keppler E Heber B Kunow H amp Quen J J (1997) Ulysses observations of short‐period (~lt30 days)modulation of the galactic cosmic rays Geophysical Research Letters 24(6) 671ndash674

Blum L W Artemyev A Agapitov O Mourenas D Boardsen S amp Schiller Q (2019) EMIC wave‐driven bounce resonance scatteringof energetic electrons in the inner magnetosphere Journal of Geophysical Research Space Physics 124 2484ndash2496 httpsdoiorg1010292018JA026427

Blum L W Halford A Millan R Bonnell J W Goldstein J Usanova M et al (2015) Observations of coincident EMIC wave activityand duskside energetic electron precipitation on 18ndash19 January 2013 Geophysical Research Letters 42 5727ndash5735 httpsdoiorg1010022015GL065245

Blum L W Li X amp Denton M (2015) Rapid MeV electron precipitation as observed by SAMPEXHILT during high‐speed stream‐

driven storms Journal of Geophysical Research Space Physics 120 3783ndash3794 httpsdoiorg1010022014JA020633Borisov S amp Cyamukungu M (2015) The PROBA‐VEPT data analysis Upgrade of the data production (Technical Note 1 109 p)Borovsky J E Cayton T E Denton M H Belian R D Christensen R A amp Ingraham J C (2016) The proton and electron radiation

belts at geosynchronous orbit Statistics and behavior during high‐speed stream‐driven storms Journal of Geophysical Research SpacePhysics 121 5449ndash5488 httpsdoiorg1010022016JA022520

Bortnik J Inan U S amp Bell T F (2006) Temporal signatures of radiation belt electron precipitation induced by lightning‐generated MRwhistler waves 1 Methodology Journal of Geophysical Research 111 A02204 httpsdoiorg1010292005JA011182

Bortnik J Thorne R M amp Inan U S (2008) Nonlinear interaction of energetic electrons with large amplitude chorus GeophysicalResearch Letters 35 L21102 httpsdoiorg1010292008GL035500

Bortnik J Thorne R M amp Meredith N P (2008) The unexpected origin of plasmaspheric hiss from discrete chorus emissions Nature452 62ndash66 httpsdoiorg101038nature06741

Bourdarie S Boscher D Beutier T Sauvaud J amp Blanc M (1996) Magnetic storm modeling in the Earths electron belt by theSalammbo code Journal of Geophysical Research 101(A12) 27171ndash27176 httpsdoiorg10102996JA02284

Bourdarie S Boscher D Blanc M amp Sauvaud J‐A (2000) A physical 4D radiation belt model including a time‐dependent magneticfield Advances in Space Research 25(12) 2303ndash2306

Bourdarie S Friedel R H W Fennell J Kanekal S amp Cayton T E (2005) Radiation belt representation of the energetic electronenviron‐ ment Model and data synthesis using the Salammbo radiation belt transport code and Los Alamos geosynchronous and GPSenergetic particle data Space Weather 3 S04S01 httpsdoiorg1010292004SW000065

Boyd A J Turner D L Reeves G D Spence H E Baker D N amp Blake J B (2018) What causes radiation belt enhancements Asurvey of the Van Allen Probes Era Geophysical Research Letters 45 5253ndash5259 httpsdoiorg1010292018GL077699

Brautigam D H amp Albert J M (2000) Radial diffusion analysis of outer radiation belt electrons during the 9 October 1990 magneticstorm Journal of Geophysical Research 105(A1) 291ndash309 httpsdoiorg1010291999JA900344

Breneman A Cattell C Wygant J Kersten K Wilson L B III Schreiner S et al (2011) Large‐amplitude transmitter‐associated andlightning‐associated whistler waves in the Earths inner plasmasphere at L lt 2 Journal of Geophysical Research 116 A06310 httpsdoiorg1010292010JA016288

Breneman A W Crew A Sample J Klumpar D Johnson A Agapitov O et al (2017) Observations directly linking relativistic elec‐tron microbursts to whistler mode chorus Van Allen Probes and FIREBIRD II Geophysical Research Letters 44 11265ndash11272 httpsdoiorg1010022017GL075001

Breneman A W Halford A Millan R McCarthy M Fennell J Sample J et al (2015) Global‐scale coherence modulation ofradiation‐belt electron loss from plasmaspheric hiss Nature 523(7559) 193ndash195 httpsdoiorg101038nature14515

Bunch N L Spasojevic M Shprits Y Y Gu X amp Foust F (2013) The spectral extent of chorus in the off‐equatorial magnetosphereJournal of Geophysical Research Space Physics 118 1700ndash1705 httpsdoiorg1010292012JA018182

Burch J L Torbert R B Phan T D Chen L J Moore T E Ergun R E et al (2016) Electron‐scale measurements of magneticreconnection in space Science 352(6290) aaf2939 httpsdoiorg101126scienceaaf2939

Camporeale E (2015) Resonant and nonresonant whistlers‐particle interaction in the radiation belts Geophysical Research Letters 423114ndash3121 httpsdoiorg1010022015GL063874

Camporeale E Delzanno G L Zaharia S amp Koller J (2013a) On the numerical simulation of particle dynamics in the radiation beltPart I Implicit and semi‐implicit schemes Journal of Geophysical Research Space Physics 118 3463ndash3475 httpsdoiorg101002jgra50293

Camporeale E Delzanno G L Zaharia S amp Koller J (2013b) On the numerical simulation of particle dynamics in the radiation beltPart II Procedure based on the diagonalization of the diffusion tensor Journal of Geophysical Research Space Physics 118 3476ndash3484httpsdoiorg101002jgra50278

Cao X Ni B Summers D Bortnik J Tao X Shprits Y Y et al (2017) Bounce resonance scattering of radiation belt electrons by H+band EMIC waves Journal of Geophysical Research Space Physics 122 1702ndash1713 httpsdoiorg1010022016JA023607

Cao X Ni B Summers D Zou Z Fu S amp Zhang W (2017) Bounce resonance scattering of radiation belt electrons by low‐frequencyhiss Comparison with cyclotron and Landau resonances Geophysical Research Letters 44 9547ndash9554 httpsdoiorg1010022017GL075104



Capannolo L Li W Ma Q Shen X C Zhang X J Redmon R J et al (2019) Energetic electron precipitation Multievent analysis ofits spatial extent during EMIC wave activity Journal of Geophysical Research Space Physics 124 2466ndash2483 httpsdoiorg1010292018JA026291

Capannolo L Li W Ma Q Zhang X J Redmon R J Rodriguez J V et al (2018) Understanding the driver of energetic electronprecipitation using coordinated multisatellite measurements Geophysical Research Letters 45 6755ndash6765 httpsdoiorg1010292018GL078604

Carpenter D L (1968) Ducted whistler‐mode propagation in the magnetosphere a half‐gyrofrequency upper intensity cutoff and someassociated wave growth phenomena Journal of Geophysical Research 73(9) 2919ndash2928 httpsdoiorg101029JA073i009p02919

Carpenter D L amp Anderson R (1992) An ISEEwhistler model of equatorial electron density in the magnetosphere Journal ofGeophysical Research 97(A2) 1097ndash1108 httpsdoiorg10102991JA01548

Cary J R amp Brizard A J (2009) Hamiltonian theory of guiding‐center motion Rev of modern physics 81(2) 693ndash738 httpsdoiorg101103RevModPhys81693

Cattell C Wygant J R Goetz K Kersten K Kellogg P J von Rosenvinge T et al (2008) Discovery of very large amplitude whistler‐mode waves in Earths radiation belts Geophysical Research Letters 35 L01105 httpsdoiorg1010292007GL032009

Cecil D J (2001) LISOTD 05 degree high resolution full climatology (HRMC) (HRMC_COM_FR) Dataset available online from theNASA Global Hydrology Center DAAC Huntsville Alabama USA httpsdoiorg105067LISLIS‐OTDDATA302

Cecil D J Buechler D E amp Blakeslee R J (2014) Gridded lightning climatology from TRMM‐LIS and OTD Dataset descriptionAtmospheric Research 135ndash136 404ndash414 httpsdoiorg101016jatmosres201206028

Chan K‐W amp Holzer R E (1976) ELF hiss associated with plasma density enhancements in the outer magnetosphere Journal ofGeophysical Research 81(13) 2267ndash2274 httpsdoiorg101029JA081i013p02267

Chang S Ni B Cao X Zhang X Zhu Z amp Luo W (2018) Energetic electron diffusion by modulated heating of the ionosphereJournal of Geophysical Research Space Physics 123 5516ndash5527 httpsdoiorg1010292018JA025737

Chaston C C Bonnell J W Halford A J Reeves G D Baker D N Kletzing C A amp Wygant J R (2018) Pitch angle scattering andloss of radiation belt electrons in broadband electromagnetic waves Geophysical Research Letters 45 9344ndash9352 httpsdoiorg1010292018GL079527

Chaston C C Bonnell J W Kletzing C A Hospodarsky G B Wygant J R amp Smith C W (2015) Broadband low‐frequency elec-tromagnetic waves in the inner magnetosphere Journal of Geophysical Research Space Physics 120 8603ndash8615 httpsdoiorg1010022015JA021690

Chen L Bortnik J Li W Thorne R M ampHorne R B (2012b) Modeling the properties of plasmaspheric hiss 1 Dependence on choruswave emission Journal of Geophysical Research 117 A05201 httpsdoiorg1010292011JA017201

Chen L Bortnik J Li W Thorne R M amp Horne R B (2012c) Modeling the properties of plasmaspheric hiss 2 Dependence on theplasma density distribution Journal of Geophysical Research 117 A05202 httpsdoiorg1010292011JA017202

Chen L Li W Bortnik J amp Thorne R M (2012) Amplification of whistler‐mode hiss inside the plasmasphere Geophysical ResearchLetters 39 L08111 httpsdoiorg1010292012GL051488

Chen L Sun J Lu Q Wang X Gao X Wang D amp Wang S (2018) Two‐dimensional particle‐in‐cell simulation of magnetosonicwave excitation in a dipole magnetic field Geophysical Research Letters 45 8712ndash8720 httpsdoiorg1010292018GL079067

Chen L Thorne R M Bortnik J amp Zhang X‐J (2016) Nonresonant interactions of electromagnetic ion cyclotron waves with relati-vistic electrons Journal of Geophysical Research Space Physics 121 9913ndash9925 Retrieved from httpsdoiorg1010022016JA022813

Chen Y Friedel R H W Henderson M G Claudepierre S G Morley S K amp Spence H E (2014) REPAD An empirical model ofpitch angle distributions for energetic electrons in the Earths outer radiation belt Journal of Geophysical Research Space Physics 1191693ndash1708 httpsdoiorg1010022013JA019431

Chen Y Reeves G Friedel R H W Thomsen M F Looper M Evans D amp Sauvaud J‐A (2012) LEEM A new empirical model ofradiation‐belt electrons in the low‐Earth‐orbit region Journal of Geophysical Research 117 A11205 httpsdoiorg1010292012JA017941

Christian H J Blakeslee R J Boccippio D J Boeck W L Buechler D E Driscoll K T et al (2003) Global frequency and distri-bution of lightning as observed from space by the optical transient detector Journal of Geophysical Research 108(D1) 4005 httpsdoiorg1010292002JD002347

Christon S P Hamilton D C Plane J M C Mitchell D G Grebowsky J M Spjeldvik W N amp Nylund S R (2017) Discovery ofsuprathermal ionospheric origin Fe and near Earths magnetosphere Journal of Geophysical Research Space Physics 122 11175ndash11200httpsdoiorg1010022017JA024414

Chu X N Bortnik J Li W Ma Q Angelopoulos V amp Thorne R M (2017) Erosion and refilling of the plasmasphere during a geo-magnetic storm modeled by a neural network Journal of Geophysical Research Space Physics 122 7118ndash7129 httpsdoiorg1010022017JA023948

Claudepierre S G OBrien T P Fennell J F Blake J B Clemmons J H Looper M D et al (2017) The hidden dynamics of rela-tivistic electrons (07ndash15 MeV) in the inner zone and slot region Journal of Geophysical Research Space Physics 122 3127ndash3144 httpsdoiorg1010022016JA023719

Claudepierre S G OBrien T P Looper M D Blake J B Fennell J F Roeder J L et al (2019) A revised look at relativistic electronsin the Earths inner radiation zone and slot region Journal of Geophysical Research Space Physics 124 934ndash951 httpsdoiorg1010292018JA026349

Claudepierre S G Toffoletto F R ampWiltberger M (2016) Global MHDmodeling of resonant ULFwaves Simulations with and withouta plasmasphere Journal of Geophysical Research Space Physics 121 227ndash244 httpsdoiorg1010022015JA022048

Clilverd M A Duthie R Hardman R Hendry A T Rodger C J Raita T et al (2015) Electron precipitation from EMIC waves Acase study from 31 May 2013 Journal of Geophysical Research Space Physics 120 3618ndash3631 Retrieved from httpsdoiorg1010022015JA021090

Clilverd M A Rodger C J McCarthy M Millan R Blum L W Cobbett N et al (2017) Investigating energetic electron precipitationthrough combining ground‐based and balloon observations Journal of Geophysical Research Space Physics 122 534ndash546 httpsdoiorg1010022016JA022812

Clilverd M A Rodger C J amp Nunn D (2004) Radiation belt electron precipitation fluxes associated with lightning Journal ofGeophysical Research 109 A12208 httpsdoiorg1010292004JA010644

Clilverd M A Rodger C J Thomson N R Brundell J B Ulich T Lichtenberger J et al (2009) Remote sensing space weatherevents The AARDDVARK network Space Weather 7 S04001 httpsdoiorg1010292008SW000412



Clilverd M A Rodger C J Gamble R Meredith N P Parrot M Berthelier J‐J amp Thomson N R (2008) Ground‐based transmittersignals observed from space Ducted or nonducted Journal of Geophysical Research 113 A04211 httpsdoiorg1010292007JA012602

Colman J J amp Starks M J (2013) VLFwave intensity in the plasmasphere due to tropospheric lightning Journal of Geophysical ResearchSpace Physics 118 4471ndash4482 httpsdoiorg101002jgra50217

Colpitts C A Cattell C A Engebretson M Broughton M Tian S Wygant J et al (2016) Van Allen Probes observations of cross‐scale coupling between electromagnetic ion cyclotron waves and higher‐frequency wave modes Geophysical Research Letters 4311510ndash11518 httpsdoiorg1010022016GL071566

Crabtree C Rudakov L Ganguli G Mithaiwala M Galinsky V amp Shevchenko V (2012) Weak turbulence in the magnetosphereFormation of whistler wave cavity by nonlinear scattering Physics of Plasmas 19(3) 032903 httpsdoiorg10106313692092

Crabtree C Ganguli G amp Tejero E M (2017a) Analytical and numerical analysis of self‐consistent whistler wave Hamiltonian PlasmaPhysics and Controlled Fusion 59(11) IOP Publishing) 114002 httpsdoiorg1010881361‐6587aa837a

Crabtree C Ganguli G amp Tejero E (2017b) Analysis of self‐consistent nonlinear wave‐particle interactions of whistler waves inlaboratory and space plasmas Physics of Plasmas 24(5) American Institute of Physics) 056501 httpsdoiorg10106314977539

Crabtree C Tejero E Ganguli G Hospodarsky G B amp Kletzing C A (2017) Bayesian spectral analysis of chorus subelements fromthe Van Allen Probes Journal of Geophysical Research Space Physics 122 John Wiley amp Sons Ltd 6088ndash6106 httpsdoiorg1010022016JA023547

Crombie D D (1964) Periodic fading of VLF signals received over long paths during sunrise and sunset Journal of Research NationalBureau of Standards Radio Science 68D(34) 27ndash548

Cully C M Angelopoulos V Auster U Bonnell J amp Le Contel O (2011) Observational evidence of the generation mechanism forrising‐tone chorus Geophysical Research Letters 38 L01106 httpsdoiorg1010292010GL045793

Cummins K L Murphy M J Bardo E A Hiscox W L Pyle R B amp Pifer A E (1998) A combined TOAMDF technology upgrade ofthe US National Lightning Detection Network Journal of Geophysical Research 103(D8) 9035ndash9044 httpsdoiorg10102998JD00153

Cunningham G S (2016) Radial diffusion of radiation belt particles in nondipolar magnetic fields Journal of Geophysical Research SpacePhysics 121 5149ndash5171 httpsdoiorg1010022015JA021981

Cunningham G S Loridan V Ripoll J‐F amp Schulz M (2018) Neoclassical diffusion of radiation‐belt electrons across very low L‐shellsJournal of Geophysical Research Space Physics 123 2884ndash2901 httpsdoiorg1010022017JA024931

da Silva C L Wu S Denton R E Hudson M K amp Millan R M (2017) Hybrid fluid‐particle simulation of whistler‐mode waves in acompressed dipole magnetic field Implications for dayside high‐latitude chorus Journal of Geophysical Research Space Physics 122432ndash448 httpsdoiorg1010022016JA023446

Daglis I Thorne R M Baumjohan W amp Oorsin S (1999) The terrestrial ring current Origin formation and decay Reviews ofGeophysics 37(4) 407ndash438 httpsdoiorg1010291999RG900009

Darrouzet F amp De Keyser J (2013) The dynamics of the plasmasphere Recent results Journal of Atmospheric and Solar‐TerrestrialPhysics 99(2013) 53ndash60 httpsdoiorg101016jjastp201207004

Darrouzet F Keyser J D amp Pierrard V (Eds) (2009) The Earths plasmasphere A Cluster and IMAGE perspective New York Springerhttpsdoiorg101007978‐1‐4419‐1323‐4

Davidson G amp Walt M (1977) Loss cone distribution of radiation belt electrons Journal of Geophysical Research 82(1) 48ndash54 httpsdoiorg101029JA082i001p00048

Dawson J M (1983) Particle simulation of plasmas Reviews of Modern Physics 55(2) 403ndash447 httpsdoiorg101103RevModPhys55403

De Pascuale S Jordanova V K Goldstein J Kletzing C A Kurth W S Thaller S A amp Wygant J (2018) Simulations of Van AllenProbes plasmaspheric electron density observations Journal of Geophysical Research Space Physics 123 9453ndash9475 httpsdoiorg1010292018JA025776

Degeling A W Ozeke L G Rankin R Mann I R amp Kabin K (2008) Drift resonant generation of peaked relativistic electron dis-tributions by Pc 5 ULF waves Journal of Geophysical Research 113 A02208 httpsdoiorg1010292007JA012411

Degeling A W Rankin R Wang Y Shi Q Q amp Zong Q‐G (2019) Alteration of particle drift resonance dynamics near poloidal modefield line resonance structures Journal of Geophysical Research Space Physics 124 7385ndash7401 httpsdoiorg1010292019JA026946

Delzanno G L Borovsky J E Thomsen M F Gilchrist B E amp Sanchez E (2016) Can an electron gun solve the outstanding problemof magnetosphere‐ionosphere connectivity Journal of Geophysical Research Space Physics 121 6769ndash6773 httpsdoiorg1010022016JA022728

Delzanno G L Borovsky J E Thomsen M F amp Moulton J D (2015) Future beam experiments in the magnetosphere with plasmacontactors The electron collection and ion emission routes Journal of Geophysical Research Space Physics 120 3588ndash3602 httpsdoiorg1010022014JA020683

Delzanno G L Camporeale E Moulton J D amp Borovsky J E (2013) E A MacDonald and M F Thomsen CPIC A curvilinearparticle‐in‐cell code for plasma‐material interaction studies IEEE Transactions on Plasma Science 41(12) 3577ndash3587

Delzanno G L amp Roytershteyn V (2019) High‐frequency plasma waves and pitch angle scattering induced by pulsed electron beamsJournal of Geophysical Research Space Physics 124 7543ndash7552 httpsdoiorg1010292019JA027046

Denton M H Borovsky J E Stepanova M amp Valdivia J A (2016) Preface Unsolved problems of magnetospheric physics Journal ofGeophysical Research Space Physics 121 783ndash10785 httpsdoiorg1010022016JA023362

Denton M H Kosch M J Borovsky J E Clilverd M A Friedel R H W amp Ulich T (2014) First optical observations of energeticelectron precipitation at 4278 Aring caused by a powerful VLF transmitter Geophysical Research Letters 41 2237ndash2242 httpsdoiorg1010022014GL059553

Denton R E Menietti J D Goldstein J Young S L amp Anderson R R (2004) Electron density in the magnetosphere Journal ofGeophysical Research 109 A09215 httpsdoiorg1010292003JA010245

Denton R E Ofman L Shprits Y Y Bortnik J Millan R M Rodger C J et al (2019) Pitch angle scattering of sub‐MeV relativisticelectrons by electromagnetic ion cyclotron waves Journal of Geophysical Research Space Physics 124 5610ndash5626 httpsdoiorg1010292018JA026384

Denton R E Takahashi K Galkin I A Nsumei P A Huang X Reinisch B W et al (2006) Distribution of density along magne-tospheric field lines Journal of Geophysical Research 111 A04213 httpsdoiorg1010292005JA011414

Denton M H Thomsen M F Jordanova V K Henderson M G Borovsky J E Denton J S et al (2015) An empirical model ofelectron and ion fluxes derived from observations at geosynchronous orbit Space Weather 13(4) 233ndash249 httpsdoiorg1010022015SW001168



De Zeeuw D L Gombosi T I Groth C P T Powell K G amp Stout Q F (2000) An adaptive MHD method for global space weathersimulations IEEE Transactions on Plasma Science 28 1956ndash1965

Dorfman S amp Carter T A (2013) Nonlinear excitation of acoustic modes by large‐amplitude Alfveacuten waves in a laboratory plasmaPhysical Review Letters 110(19) 195001

Douma E Rodger C J Blum L W amp Clilverd M A (2017) Occurrence characteristics of relativistic electron microbursts fromSAMPEX observations Journal of Geophysical Research Space Physics 122 8096ndash8107 httpsdoiorg1010022017JA024067

Douma E Rodger C J Clilverd M A Hendry A T Engebretson M J amp Lessard M R (2018) Comparison of relativistic microburstactivity seen by SAMPEX with ground‐based wave measurements at Halley Antarctica Journal of Geophysical Research Space Physics123 1279ndash1294 httpsdoiorg1010022017JA024754

Doveil F amp Macor A (2006) Wave‐particle interaction and Hamiltonian dynamics investigated in a traveling wave tube Physics ofPlasmas 13(5) 055704

Dragt A J (1965) Trapped orbits in a magnetic dipole field Reviews of Geophysics 3(2) 255 httpsdoiorg101029RG003i002p00255Drozdov A Y Shprits Y Y Aseev N A Kellerman A C amp Reeves G D (2017) Dependence of radiation belt simulations to assumed

radial diffusion rates tested for two empirical models of radial transport Space Weather 15 150ndash162 httpsdoiorg1010022016SW001426

Drozdov A Y Shprits Y Y Orlova K G Kellerman A C Subbotin D A Baker D N et al (2015) Energetic relativistic andultrarelativistic electrons Comparison of long‐term VERB code simulations with Van Allen Probes measurements Journal ofGeophysical Research Space Physics 120 3574ndash3587 httpsdoiorg1010022014JA020637

Drozdov A Y Shprits Y Y Usanova M E Aseev N A Kellerman A C amp Zhu H (2017) EMIC wave parameterization in the long‐term VERB code simulation Journal of Geophysical Research Space Physics 122 8488ndash8501 httpsdoiorg1010022017JA024389

DuBois A M Thomas E Amatucci W E amp Ganguli G (2013) Plasma response to a varying degree of stress Physical Review Letters111(14) 145002 httpsdoiorg101103PhysRevLett111145002

DuBois A M Thomas E Amatucci W E amp Ganguli G (2014) Experimental characterization of broadband electrostatic noise due toplasma compression Journal of Geophysical Research Space Physics 119 5624ndash5637 httpsdoiorg1010022014JA020198

Dunkel N amp Helliwell R A (1969) Whistler‐mode emissions on the OGO 1 satellite Journal of Geophysical Research 74 6371ndash6385Eastwood J P Nakamura R Turc L Mejnertsen L amp Hesse M (2017) The scientific foundations of forecasting magnetospheric space

weather Space Science Reviews 212 1221ndash1252 httpsdoiorg101007s11214‐017‐0399‐8Elkington S R Hudson M K Wiltberger M J amp Lyon J G (2002) MHDparticle simulations of radiation belt dynamics Journal of

Atmospheric and Solar‐Terrestrial Physics 64 607ndash615Elkington S R Wiltberger M Chan A A amp Baker D N (2004) Physical models of the geospace radiation environment Journal of

Atmospheric and Solar‐Terrestrial Physics 66(15‐16) 1371ndash1387 httpsdoiorg101016jjastp200403023Ellington S M Moldwin M B amp Liemohn M W (2016) Local time asymmetries and toroidal field line resonances Global magneto-

spheric modeling in SWMF Journal of Geophysical Research Space Physics 121 2033ndash2045 httpsdoiorg1010022015JA021920Engebretson M J Posch J L Braun D J Li W Ma Q Kellerman A C et al (2018) EMIC wave events during the four GEM

QARBM challenge intervals Journal of Geophysical Research Space Physics 123 6394ndash6423 httpsdoiorg1010292018JA025505Engebretson M J Posch J L Capman N S S Campuzano N G Bělik P Allen R C et al (2018) MMS Van Allen Probes GOES 13

and ground‐based magnetometer observations of EMIC wave events before during and after a modest interplanetary shock Journal ofGeophysical Research Space Physics 123 8331ndash8357 httpsdoiorg1010292018JA025984

Engebretson M J Posch J L Wygant J R Kletzing C A Lessard M R Huang C L et al (2015) Van Allen probes NOAA GOESand ground observations of an intense EMIC wave event extending over 12 h in magnetic local time Journal of Geophysical ResearchSpace Physics 120 5465ndash5488 httpsdoiorg1010022015JA021227

Falkowski B J Tsurutani B T Lakhina G S amp Pickett J S (2017) Two sources of dayside intense quasi‐coherent plasmaspheric hissA new mechanism for the slot region Journal of Geophysical Research Space Physics 122 1643ndash1657 httpsdoiorg1010022016JA023289

Faumllthammar C‐G (1965) Effects of time‐dependent electric fields on geomagnetically trapped radiation Journal of Geophysical Research70(11) 2503ndash2516 httpsdoiorg101029JZ070i011p02503

Faumllthammar C‐G (1968) Radial diffusion by violation of the third adiabatic invariant In B M McCormac (Ed) Earths particles andfields (pp 157ndash169) New York Reinhold

Fan K Gao X Lu Q Guo J amp Wang S (2019) The effects of thermal electrons on whistler mode waves excited by anisotropic hotelectrons Linear theory and 2‐D PIC simulations Journal of Geophysical Research Space Physics 124 5234ndash5245 httpsdoiorg1010292019JA026463

Fasoli A Skiff F amp Tran M Q (1994) Study of wavendashparticle interaction from the linear regime to dynamical chaos in a magnetizedplasma Physics of Plasmas 1(5) 1452ndash1460 httpsdoiorg1010631870695

Fei Y Chan A Elkington S amp Wiltberger M (2006) Radial diffusion and MHD particle simulations of relativistic electron transport byULF waves in the September 1998 storm Journal of Geophysical Research 111 A12209 httpsdoiorg1010292005JA011211

Fennell J F Claudepierre S G OBrien T P Blake J B Clemmons J H Spence H E amp Reeves G D (2015) Van Allen Probes showthe inner radiation zone contains no MeV electrons ECTMagEIS data Geophysical Research Letters 42 1283ndash1289 httpsdoiorg1010022014GL062874

Fennell J F Roeder J L Kurth W S Henderson M G Larsen B A Hospodarsky G et al (2014) Van Allen Probes observations ofdirect wave‐particle interactions Geophysical Research Letters 41 1869ndash1875 httpsdoiorg1010022013GL059165

Fennelly J A (2009) Demonstrations and Science Experiment (DSX) Space Weather Experiment (SWx) In S Fineschi amp A Judy (Eds)Proceedings of SPIE Solar Physics and Space Weather Instrumentation III (Vol 7438) Fennelly San Diego CA USA SPIE August 42009 httpwwwdticmildtictrfulltextu2a542684pdf

Fenrich F R Samson J C Sofko G amp Greenwald R A (1995) ULF high‐ and low‐m field line resonances observed with the Super DualAuroral Radar Network Journal of Geophysical Research 100 21535ndash21547

Fletcher A C Crabtree C Ganguli G Malaspina D Tejero E amp Chu X (2019) Kinetic equilibrium and stability analysis of dipo-larization fronts Journal of Geophysical Research Space Physics 124 2010ndash2028 httpsdoiorg1010292018JA026433

Fok M‐C Buzulukova N Y Chen S‐H Glocer A Nagai T Valek P amp Perez J D (2014) The comprehensive inner magnetosphere‐ionosphere model Journal of Geophysical Research Space Physics 119 7522ndash7540 httpsdoiorg1010022014JA020239

Fok M‐C Glocer A Zheng Q Horne R B Meredith N P Albert J M amp Nagai T (2011) Recent developments in the radiation beltenvironment model Journal of Atmospheric and Solar ‐ Terrestrial Physics 73 1435ndash1443 httpsdoiorg101016jjastp201009033



Fok M‐C Horne R B Meredith N P amp Glauert S A (2008) Radiation belt environment model Application to space weather now-casting Journal of Geophysical Research 113 A03S08 httpsdoiorg1010292007JA012558

Fok M C amp Moore T E (1997) Ring current modeling in a realistic magnetic field configuration Geophysical Research Letters 241775ndash1778 httpsdoiorg10102997GL01255

Fok M C Wolf R A Spiro R W amp Moore T E (2001) Comprehensive computational model of Earths ring current Journal ofGeophysical Research 106(A5) 8417ndash8424 httpsdoiorg1010292000JA000235

Forsyth C Rae I J Murphy K R Freeman M P Huang C L Spence H E et al (2016) What effect do substorms have on thecontent of the radiation belts Journal of Geophysical Research Space Physics 121 6292ndash6306 httpsdoiorg1010022016JA022620

Foster J C Erickson P J Omura Y Baker D N Kletzing C A amp Claudepierre S G (2017) Van Allen Probes observations of promptMeV radiation belt electron acceleration in nonlinear interactions with VLF chorus Journal of Geophysical Research Space Physics 122324ndash339 httpsdoiorg1010022016JA023429

Fraser B J Lotoainu T M amp Singer H J (2006) Electromagnetic ion cyclotron waves in the magnetosphere In K Takahashi et al(Eds) Magnetospheric ULF Waves Synthesis and New Directions Geophys Monogr Ser (Vol 169 p 195) Washington D C AGU

Friedel R H W Reeves G D amp Obara T (2002) Relativistic electron dynamics in the inner magnetospheremdashA review Journal ofAtmospheric and Solar‐Terrestrial Physics 64(2) 265ndash282 httpsdoiorg101016S1364‐6826(01)00088‐8

Fu X Cowee M M Friedel R H Funsten H O Gary S P Hospodarsky G B et al (2014) Whistler anisotropy instabilities as thesource of banded chorus Van Allen Probes observations and particle‐in‐cell simulations Journal of Geophysical Research Space Physics119 8288ndash8298 httpsdoiorg1010022014JA020364

Fu X Gary S P Reeves G D Winske D ampWoodroffe J R (2017) Generation of highly oblique lower band chorus via nonlinear three‐wave resonance Geophysical Research Letters 44 9532ndash9538 httpsdoiorg1010022017GL074411

Fung S F (1996) Recent developments in the NASA trapped radiation models In J F Lemaire D Heynderickx amp D N Baker (Eds)Radiation belts Models and standards ed by Geophys Monogr Ser (Vol 97 pp 79ndash91) Washington 1996 AGU

Funsten H O Skoug R M Guthrie A A MacDonald E A Baldonado J R Harper R W et al (2013) J Chen Helium OxygenProton and Electron (HOPE) mass spectrometer for the Radiation Belt Storm Probes mission Space Science Reviews 179(1‐4) 423ndash484httpsdoiorg101007s11214‐013‐9968‐7

Gamble R J Rodger C J Clilverd M A Sauvaud J‐A Thomson N R Stewart S L et al (2008) Radiation belt electron precipitationby man‐made VLF transmissions Journal of Geophysical Research 113 A10211 httpsdoiorg1010292008JA013369

Gamble R J Rodger C J Clilverd M A Sauvaud J‐A Thomson N R Stewart S L et al (2009) Correction to ldquoRadiation beltelectron precipitation by man‐made VLF transmissionsrdquo Journal of Geophysical Research 114 A05205 httpsdoiorg1010292009JA014304

Ganguli G Crabtree C Mithaiwala M Rudakov L amp ScalesW (2015) Evolution of lower hybrid turbulence in the ionosphere Physicsof Plasmas 22 112904 httpsdoiorg10106314936281

Gannon J L Li X amp Heynderickx D (2007) Pitch angle distribution analysis of radiation belt electrons based on Combined Release andRadiation Effects Satellite Medium Electrons A data Journal of Geophysical Research 112 A05212 httpsdoiorg1010292005JA011565

Ganushkina N Jaynes A amp Liemohn M (2017) Space weather effects produced by the ring current particles Space Science Reviews 2121315ndash1344 httpsdoiorg101007s11214‐017‐0412‐2

Gao Y Xiao F Yan Q Yang C Liu S He Y amp Zhou Q (2015) Influence of wave normal angles on hiss‐electron interaction inEarths slot region Journal of Geophysical Research Space Physics 120 9385ndash9400 httpsdoiorg1010022015JA021786

Garnier D T Hansen A K Kesner J Mauel M E Michael P C Minervini J V et al (2006) Design and initial operation of the LDXfacility Fusion Engineering and Design 81(20ndash22) 2371ndash2380 httpsdoiorg101016jfusengdes200607002

Gekelman W Pribyl P Lucky Z Drandell M Leneman D Maggs J et al (2016) The upgraded large plasma device a machine forstudying frontier basic plasma physics Review of Scientific Instruments 87(2) American Institute of Physics) 025105 httpsdoiorg10106314941079

Gemelos E S Inan U S Walt M Parrot M amp Sauvaud J A (2009) Seasonal dependence of energetic electron precipitation Evidencefor a global role of lightning Geophysical Research Letters 36 L21107 httpsdoiorg1010292009GL040396

Ginet G P Dichter B K Brautigam D H ampMadden D (2007) Proton flux anisotropy in low Earth orbit IEEE Transactions on NuclearScience 54(6) 1975ndash1980 httpsdoiorg101109TNS2007910041

Ginet G P OBrien T P Huston S L Johnston W R Guild T B Friedel R et al (2013) AE9 AP9 and SPM New models forspecifying the trapped energetic particle and space plasma environment In N Fox amp J L Burch (Eds) The Van Allen Probes MissionBoston MA Springer httpsdoiorg101007978‐1‐4899‐7433‐4_18

Gkioulidou M Ohtani S Mitchell D G Ukhorskiy A Y Reeves G D Turner D L et al (2015) Spatial structure and temporalevolution of energetic particle injections in the inner magnetosphere during the 14 July 2013 substorm event Journal of GeophysicalResearch Space Physics 120 1924ndash1938 httpsdoiorg1010022014JA020872

Gkioulidou M Ohtani S Ukhorskiy A Y Mitchell D G Takahashi K Spence H E et al (2019) Low‐energy (ltkeV) O+ ion outflowdirectly into the inner magnetosphere Van Allen Probes observations Journal of Geophysical Research Space Physics 124 405ndash419httpsdoiorg1010292018JA025862

Glauert S A amp Horne R B (2005) Calculation of pitch angle and energy diffusion coefficients with the PADIE code Journal ofGeophysical Research 110 A04206 httpsdoiorg1010292004JA010851

Glauert S A Horne R B amp Meredith N P (2014a) Three‐dimensional electron radiation belt simulations using the BAS radiation beltmodel with new diffusion models for chorus plasmaspheric hiss and lightning‐generated whistlers Journal of Geophysical ResearchSpace Physics 119 268ndash289 httpsdoiorg1010022013JA019281

Glauert S A Horne R B ampMeredith N P (2014b) Simulating the Earths radiation belts Internal acceleration and continuous losses tothe magnetopause Journal of Geophysical Research Space Physics 119 7444ndash7463 httpsdoiorg1010022014JA020092

Glauert S A Horne R B amp Meredith N P (2018) A 30‐year simulation of the outer electron radiation belt Space Weather 161498ndash1522 httpsdoiorg1010292018SW001981

Glocer A Fok M Meng X Toth G Buzulukova N Chen S amp Lin K (2013) CRCM + BATS‐R‐US two‐way coupling Journal ofGeophysical Research Space Physics 118 1635ndash1650 httpsdoiorg101002jgra50221

Glocer A Fok M‐C Nagai T Toacuteth G Guild T amp Blake J (2011) Rapid rebuilding of the outer radiation belt Journal of GeophysicalResearch 116 A09213 httpsdoiorg1010292011JA016516



Glocer A Toacuteth G Fok M Gombosi T amp Liemohn M (2009) Integration of the radiation belt environment model into the spaceweather modeling framework Journal of Atmospheric and Solar ‐ Terrestrial Physics 71 1653ndash1663 httpsdoiorg101016jjastp200901003

Goldstein J Baker D N Blake J B de Pascuale S Funsten H O Jaynes A N et al (2016) The relationship between the plasma-pause and outer belt electrons Journal of Geophysical Research Space Physics 121 8392ndash8416 httpsdoiorg1010022016JA023046

Goldstein J De Pascuale S Kletzing C Kurth W Genestreti K J Skoug R M et al (2014) Simulation of Van Allen Probes plas-mapause encounters Journal of Geophysical Research Space Physics 119 7464ndash7484 httpsdoiorg1010022014JA020252

Goldstein J Sandel B R Forrester W T Thomsen M F amp Hairston M R (2005) Global plasmasphere evolution 22ndash23 April 2001Journal of Geophysical Research 110 A12218 httpsdoiorg1010292005JA011282

Gombosi T I Baker D N Balogh A Erickson P J Huba J D amp Lanzerotti L J (2017) Anthropogenic space weather Space ScienceReviews 212 985ndash1039 httpsdoiorg101007s11214‐017‐0357‐5

Gombosi T I Powell K G De Zeeuw D L Clauer C R Hansen K C Manchester W B et al (2004) Solution‐adaptive magneto-hydrodynamics for space plasmas Sun‐to‐Earth simulations Computing in Science amp Engineering 06(2) 14ndash35

Gordeev E Sergeev V Honkonen I Kuznetsova M Rastaumltter L Palmroth M et al (2015) Assessing the performance of community‐available global MHD models using key system parameters and empirical relation‐ ships Space Weather 13 868ndash884 httpsdoiorg1010022015SW001307

Graf K L Inan U S Piddyachiy D Kulkarni P Parrot M amp Sauvaud J A (2009) DEMETER observations of transmitter‐inducedprecipitation of inner radiation belt electrons Journal of Geophysical Research 114 A07205 httpsdoiorg1010292008JA013949

Grandin M Aikio A T Kozlovsky A Ulich T amp Raita T (2015) Effects of solar wind high‐speed streams on the high‐latitude iono-sphere Superposed epoch study Journal of Geophysical Research Space Physics 120 669ndash10687 httpsdoiorg1010022015JA021785

Grandin M Aikio A T Kozlovsky A Ulich T amp Raita T (2017) Cosmic radio noise absorption in the high‐latitude ionosphere duringsolar wind high‐speed streams Journal of Geophysical Research Space Physics 122 5203ndash5223 httpsdoiorg1010022017JA023923

Greeley A D Kanekal S G Baker D N Klecker B amp Schiller Q (2019) Quantifying the contribution of microbursts to global electronloss in the radiation belts Journal of Geophysical Research Space Physics 124 1111ndash1124 httpsdoiorg1010292018JA026368

Green J C amp Kivelson M G (2004) Relativistic electrons in the outer radiation belt Differentiating between acceleration mechanismsJournal of Geophysical Research 109 A03213 httpsdoiorg1010292003JA010153

Gusev A A Kohno T Spjeldvik W N Martin I M Pugacheva G I amp Turtelli A Jr (1996) Dynamics of the low‐altitude energeticproton fluxes beneath the main terrestrial radiation belts Journal of Geophysical Research 101(A9) 19659ndash19663

Gusev A A Martin I M Pugacheva G I Turtelli A Jr amp Spjeldvik W N (1996) Energetic‐positron population in the inner zone IlNuovo Cimento C 19(4) 461ndash467 httpsdoiorg101007BF02523763

Haerendel G (1968) Diffusion theory of trapped particles and the observed proton distribution In B M McCormac (Ed) Earths particlesand fields (pp 171ndash191) New York Reinhold Book Corp

Haiducek J D Welling D T Ganushkina N Y Morley S K amp Ozturk D S (2017) SWMF global magnetosphere simulations ofJanuary 2005 Geomagnetic indices and cross‐polar cap potential Space Weather 15 1567ndash1587 httpsdoiorg1010022017SW001695

Hands A D P Ryden K A Meredith N P Glauert S A amp Horne R B (2018) Radiation effects on satellites during extreme spaceweather events Space Weather 16 1216ndash1226 httpsdoiorg1010292018SW001913

Hao Y X Zong Q G Zhou X Z Rankin R Chen X R Liu Y et al (2019) Global‐scale ULF waves associated with SSC acceleratemagnetospheric ultrarelativistic electrons Journal of Geophysical Research Space Physics 124 1525ndash1538 httpsdoiorg1010292018JA026134

Hardman R Clilverd M A Rodger C J Brundell J B Duthie R Holzworth R H et al (2015) A case study of electron precipitationfluxes due to plasmaspheric hiss Journal of Geophysical Research Space Physics 120 6736ndash6748 httpsdoiorg1010022015JA021429

Hartley D P Kletzing C A Chen L Horne R B amp Santoliacutek O (2019) Van Allen Probes observations of chorus wave vector orien-tations Implications for the chorus‐to‐hiss mechanism Geophysical Research Letters 46 2337ndash2346 httpsdoiorg1010292019GL082111

Hartley D P Kletzing C A De Pascuale S Kurth W S amp Santoliacutek O (2018) Determining plasmaspheric densities from observationsof plasmaspheric hiss Journal of Geophysical Research Space Physics 123 6679ndash6691 httpsdoiorg1010292018JA025658

Hartley D P Kletzing C A Santoliacutek O Chen L amp Horne R B (2018) Statistical properties of plasmaspheric hiss from Van AllenProbes observations Journal of Geophysical Research Space Physics 123 2605ndash2619 httpsdoiorg1010022017JA024593

He Z Chen L Liu X Zhu H Liu S Gao Z amp Cao Y (2019) Local generation of high‐frequency plasmaspheric hiss observed by VanAllen Probes Geophysical Research Letters 46 1141ndash1148 httpsdoiorg1010292018GL081578

Helliwell R A (1969) Low‐frequency waves in the magnetosphere Reviews of Geophysics 7(1 2) 281 httpsdoiorg101029RG007i001p00281

Helliwell R A Katsufrakis J P amp Trimpi M L (1973) Whistler‐induced amplitude perturbation in VLF propagation Journal ofGeophysical Research 78(22) 4679ndash4688 httpsdoiorg101029JA078i022p04679

Hendry A T Rodger C J Clilverd M A Engebretson M J Mann I R Lessard M R et al (2016) Confirmation of EMIC wave‐driven relativistic electron precipitation Journal of Geophysical Research Space Physics 121 5366ndash5383 httpsdoiorg1010022015JA022224

Hendry A T Santoliacutek O Kletzing C A Rodger C J Shiokawa K amp Baishev D (2019) Multi‐instrument observation of nonlinearEMIC‐driven electron precipitation at sub‐MeV energies Geophysical Research Letters 46 7248ndash7257 httpsdoiorg1010292019GL082401

Hess W N (1968) The radiation belt and magnetosphere Waltham Mass Blaisdell Pub CoHerrera D Maget V F amp Sicard‐Piet A (2016) Characterizing magnetopause shadowing effects in the outer electron radiation belt

during geomagnetic storms Journal of Geophysical Research Space Physics 121 9517ndash9530 httpsdoiorg1010022016JA022825Hikishima M Yagitani S Omura Y amp Nagano I (2009) Full particle simulation of whistler‐mode rising chorus emissions in the

magnetosphere Journal of Geophysical Research 114 A01203 httpsdoiorg1010292008JA013625Hoilijoki S Ganse U Pfau‐Kempf Y Cassak P A Walsh B M Hietala H et al (2017) Reconnection rates and X line motion at the

magnetopause Global 2D‐3V hybrid‐Vlasov simulation results Journal of Geophysical Research Space Physics 122 2877ndash2888 httpsdoiorg1010022016JA023709

Holzworth R H McCarthy M P Pfaff R F Jacobson A R Willcockson W L amp Rowland D E (2011) Lightning‐generated whistlerwaves observed by probes on the CommunicationNavigation Outage Forecast System satellite at low latitudes Journal of GeophysicalResearch 116 A06306 httpsdoiorg1010292010JA016198



Hood L L (1983) Radial diffusion in Saturns radiation belts A modeling analysis assuming satellite and ring E absorption Journal ofGeophysical Research 88(A2) 808ndash818 httpsdoiorg101029JA088iA02p00808

Horne R B Glauert S A Meredith N P Boscher D Maget V Heynderickx D amp Pitchford D (2013) Space weather impacts onsatellites and forecasting the Earths electron radiation belts with SPACECAST Space Weather 11 169ndash186 httpsdoiorg101002swe20023

Horne R B Glauert S A amp Thorne R M (2003) Resonant diffusion of radiation belt electrons by whistler‐mode chorus GeophysicalResearch Letters 30(9) 1493 httpsdoiorg1010292003GL016963

Horne R B Meredith N P Thorne R M Heynderickx D Iles R H A amp An‐derson R R (2003) Evolution of energetic electron pitchangle distributions during storm time electron acceleration to megaelectronvolt energies Journal of Geophysical Research 108(A1)1016 httpsdoiorg1010292001JA009165

Horne R B Phillips M W Glauert S A Meredith N P Hands A D P Ryden K amp Li W (2018) Realistic worst case for a severespace weather event driven by a fast solar wind stream Space Weather 16 1202ndash1215 httpsdoiorg1010292018SW001948

Horne R B amp Thorne R M (1998) Potential waves for relativistic electron scattering and stochastic acceleration duringmagnetic stormsGeophysical Research Letters 25(15) 3011ndash3014

Horne R B amp Thorne R M (2003) Relativistic electron acceleration and precipitation during resonant interactions with whistler‐modechorus Geophysical Research Letters 30(10) 1527 httpsdoiorg1010292003GL016973

Horne R B Thorne R M Glauert S A Albert J M Meredith N P amp Anderson R R (2005) Timescale for radiation belt electronacceleration by whistler mode chorus waves Journal of Geophysical Research 110 A03225 httpsdoiorg1010292004JA010811

Horne R B Thorne R M Glauert S A Meredith N P Pokhotelov D amp Santolik O (2007) Electron acceleration in the Van Allenradiation belts by fast magnetosonic waves Geophysical Research Letters 34 L17107 httpsdoiorg1010292007GL030267

Horne R B Thorne R M Shprits Y Y Meredith N P Glauert S A Smith A J et al (2005) Wave acceleration of electrons in theVan Allen radiation belts Nature 437(7056) 227ndash230 httpsdoiorg101038nature03939

Hospodarsky G B Kurth W S Kletzing C A Bounds S R Santoliacutek O Thorne R M et al (2016) Plasma wave measurements fromthe Van Allen Probes In C R Chappell et al (Eds)Magnetosphere‐ionosphere coupling in the solar system (pp 127ndash143) Hoboken NJJohn Wiley httpsdoiorg1010029781119066880ch10

Hua M Ni B Li W Gu X Fu S Shi R et al (2019) Evolution of radiation belt electron pitch angle distribution due to combinedscattering by plasmaspheric hiss and magnetosonic waves Geophysical Research Letters 46(6) 3033ndash3042 httpsdoiorg1010292018GL081828

Hu Y amp Denton R E (2009) Two‐dimensional hybrid code simulation of electromagnetic ion cyclotron waves in a dipole magnetic fieldJournal of Geophysical Research 114 A12217 httpsdoiorg1010292009JA014570

Hu Y Denton R E amp Johnson J R (2010) Two‐dimensional hybrid code simulation of electromagnetic ion cyclotron waves of multi‐ion plasmas in a dipole magnetic field Journal of Geophysical Research 115 A09218 httpsdoiorg1010292009JA015158

Hudson M K Kress B T Mueller H‐R Zastrow J A amp Blake J B (2008) Relationship of the Van Allen radiation belts to solar winddrivers Journal of Atmospheric and Solar ‐ Terrestrial Physics 70(5) 708ndash729 httpsdoiorg101016jjastp200711003

Hudson M K Elkington S R Lyon J G Marchenko V A Roth I Temerin M Blake J B Gussenhoven M S amp Wygan J R(1997) Simulations of radiation belt formation during storm sudden commencements Journal of Geophysical Research 102(A7) 14087‐14102

Hutchins M L Holzworth R H Brundell J B amp Rodger C J (2012) Relative detection efficiency of the World Wide LightningLocation Network Radio Science 47 RS6005 httpsdoiorg1010292012RS005049

Hutchins M L Holzworth R H Rodger C J amp Brundell J B (2012) Far‐field power of lightning strokes as measured by the WorldWide Lightning Location Network Journal of Atmospheric and Oceanic Technology 29(8) 1102ndash1110 httpsdoiorg101175JTECH‐

D‐11‐001741Hwang J amp Yoon P H (2018) High‐frequency thermal fluctuations and instabilities in the radiation belt environment Journal of

Geophysical Research Space Physics 123 9239ndash9251 httpsdoiorg1010292018JA025643Imhof W L Reagan J B Voss H D Gaines E E Datlowe D W amp Mobilia J (1983) The modulated precipitation of radiation belt

electrons by controlled signals from VLF Transmitters Geophysical Research Letters 10(8) 615ndash618Imhof W L Voss H D Walt M Gaines E E Mobilia J Datlowe D W amp Reagan J B (1986) Slot region electron precipitation by

lightning VLF chorus and plasmaspheric hiss Journal of Geophysical Research 91(A8) 8883ndash8894Inan U S amp Bell T F (1977) The plasmaspause as a VLF wave guide Journal of Geophysical Research 82(19) 2819ndash2827 httpsdoiorg

101029JA082i019p02819Inan U S Chang C amp Helliwell R A (1984) Electron precipitation zones around major ground‐based VLF signal sources Journal of

Geophysical Research 89(A5) 2891ndash2906Inan U S Golkowski M Casey M K Moore R C Peter W Kulkarni P et al (2007) Subionospheric VLF observations of trans-

mitter‐induced precipitation of inner radiation belt electrons Geophysical Research Letters 34 L02106 httpsdoiorg1010292006GL028494

Inan U S Wolf T G amp Carpenter D L (1988) Geographic distribution of lightning‐induced electron precipitation observed as VLFLFperturbation events Journal of Geophysical Research 93(A9) 9841ndash9853

Jaynes A N Ali A F Elkington S R Malaspina DM Baker D N Li X et al (2018) Fast diffusion of ultrarelativistic electrons in theouter radiation belt 17 March 2015 storm event Geophysical Research Letters 45 10874ndash10882 httpsdoiorg1010292018GL079786

Jaynes A N Baker D N Singer H J Rodriguez J V Lotoaniu T M Ali A F et al (2015) Source and seed populations for rela-tivistic electrons Their roles in radiation belt changes Journal of Geophysical Research Space Physics 120 7240ndash7254 httpsdoiorg1010022015JA021234

Jentsch V (1984) The radial distribution of radiation belt protons Approximate solution of the steady state transport equation at arbitrarypitch angle Journal of Geophysical Research 89(A3) 1527ndash1539 httpsdoiorg101029JA089iA03p01527

Johnstone A D Walton D M Liu R amp Hardy D A (1993) Pitch angle diffusion of low‐energy electrons by whistler mode wavesJournal of Geophysical Research 98(A4) 5959ndash5967 httpsdoiorg10102992JA02376

Jolliffe I T amp Stephenson D B (2012) Forecast verification A practitioners guide in atmospheric science Hoboken NJ Wiley‐BlackwellJones A D Kanekal S G Baker D N Klecker B Looper M D Mazur J E amp Schiller Q (2017) SAMPEX observations of the South

Atlantic anomaly secular drift during solar cycles 22ndash24 Space Weather 15 44ndash52 httpsdoiorg1010022016SW001525Jordanova V K Albert J ampMiyoshi Y (2008) Relativistic electron precipitation by EMIC waves from self‐consistent global simulations

Journal of Geophysical Research 113 A00A10 httpsdoiorg1010292008JA013239



Jordanova V K Kistler L M Kozyra J U Khazanov G V amp Nagy A F (1996) Collisional losses of ring current ions Journal ofGeophysical Research 101(A1) 111ndash126 httpsdoiorg10102995JA02000

Jordanova V K Kozyra J Nagy A amp Khazanov G (1997) Kinetic model of the ring current‐atmosphere interactions Journal ofGeophysical Research 102(A7) 14279ndash14291 httpsdoiorg10102996JA03699

Jordanova V K ampMiyoshi Y S (2005) Relativistic model of ring current and radiation belt ions and electrons Initial resultsGeophysicalResearch Letters 32 L14104 httpsdoiorg1010292005GL023020

Jordanova V K Miyoshi Y S Zaharia S Thomsen M F Reeves G D Evans D S et al (2006) Kinetic simulations of ring currentevolution during the Geospace Environment Modeling challenge events Journal of Geophysical Research 111 A11S10 httpsdoiorg1010292006JA011644

Jordanova V K Tu W Chen Y Morley S K Panaitescu A‐D Reeves G D amp Kletzing C A (2016) RAM‐SCB simulations ofelectron transport and plasma wave scattering during the October 2012 ldquodouble‐diprdquo storm Journal of Geophysical Research SpacePhysics 121 8712ndash8727 httpsdoiorg1010022016JA022470

Jordanova V K Yu Y Niehof J T Skoug R M Reeves G D Kletzing C A et al (2014) Simulations of inner magnetospheredynamics with an expanded RAM‐SCB model and compar‐ isons with Van Allen Probes observations Geophysical Research Letters 412687ndash2694 httpsdoiorg1010022014GL059533

Jordanova V K Zaharia S amp Welling D T (2010) Comparative study of ring current development using empirical dipolar and self‐consistent magnetic field simulations Journal of Geophysical Research 115 A00J11 httpsdoiorg1010292010JA015671

Kamiya K Seki K Saito S Amano T amp Miyoshi Y (2018) Formation of butterfly pitch angle distributions of relativistic electrons inthe outer radiation belt with amonochromatic Pc5 wave Journal of Geophysical Research Space Physics 123 4679ndash4691 httpsdoiorg1010022017JA024764

Kang S‐B Fok M‐C Glocer A Min K‐W Choi C‐R Choi E amp Hwang J (2016) Simulation of a rapid dropout event for highlyrelativistic electrons with the RBE model Journal of Geophysical Research Space Physics 121 4092ndash4102 httpsdoiorg1010022015JA021966

Kang S‐B Fok M‐C Komar C Glocer A Li W amp Buzulukova N (2018) An energetic electron flux dropout due to magnetopauseshadowing on 1 June 2013 Journal of Geophysical Research Space Physics 123 1178ndash1190 httpsdoiorg1010022017JA024879

Kang S‐B Min K‐W Fok M‐C Hwang J amp Choi C‐R (2015) Estimation of pitch angle diffusion rates and precipitation time scalesof electrons due to EMICwaves in a realistic field model Journal of Geophysical Research Space Physics 120 8529ndash8546 httpsdoiorg1010022014JA020644

Katoh Y amp Omura Y (2004) Acceleration of relativistic electrons due to resonant scattering by whistler mode waves generated bytemperature anisotropy in the inner magnetosphere Journal of Geophysical Research 109 A12214 httpsdoiorg1010292004JA010654

Katoh Y amp Omura Y (2006) A study of generation mechanism of VLF triggered emission by self‐consistent particle code Journal ofGeophysical Research 111(A12) A12207 httpsdoiorg1010292006JA011704

Katoh Y amp Omura Y (2007) Computer simulation of chorus wave generation in the Earths inner magnetosphere Geophysical ResearchLetters 34 L03102 httpsdoiorg1010292006GL028594

Katoh Y amp Omura Y (2013) Effect of the background magnetic field in homogeneity on generation processes of whistler‐mode chorusand broadband hiss‐like emissions Journal of Geophysical Research Space Physics 118(7) 4189ndash4198 httpsdoiorg101002jgra50395

Katoh Y Omura Y Miyake Y Usui H amp Nakashima H (2018) Dependence of generation of whistler mode chorus emissions on thetemperature anisotropy and density of energetic electrons in the Earths inner magnetosphere Journal of Geophysical Research SpacePhysics 123 1165ndash1177 httpsdoiorg1010022017JA024801

Kempf Y Pokhotelov D Gutynska O Wilson L B III Walsh B M von Alfthan S et al (2015) Ion distributions in the Earthsforeshock Hybrid‐Vlasov simulation and THEMIS observations Journal of Geophysical Research Space Physics 120 3684ndash3701 httpsdoiorg1010022014JA020519

Kennel C F amp Petschek H E (1966) Limit on stably trapped particle fluxes Journal of Geophysical Research 71(1) 1ndash28Kersten T Horne R B Glauert S A Meredith N P Fraser B J amp Grew R S (2014) Electron losses from the radiation belts caused by

EMIC waves Journal of Geophysical Research Space Physics 119 8820ndash8837 httpsdoiorg1010022014JA02036Khoo L‐Y Li X Zhao H Chu X Xiang Z amp Zhang K (2019) How sudden intense energetic electron enhancements correlate with

the innermost plasmapause locations under various solar wind drivers and geomagnetic conditions Journal of Geophysical ResearchSpace Physics 124 8992ndash9002 httpsdoiorg1010292019JA027412

Khoo L‐Y Li X Zhao H Sarris T E Xiang Z Zhang K et al (2018) On the initial enhancement of energetic electrons and theinnermost plasmapause locations Coronal mass ejection‐driven storm periods Journal of Geophysical Research Space Physics 1239252ndash9264 httpsdoiorg1010292018JA026074

Kim K‐C Lee D‐Y amp Shprits Y (2015) Dependence of plasmaspheric hiss on solar wind parameters and geomagnetic activity andmodeling of its global distribution Journal of Geophysical Research Space Physics 120 1153ndash1167 httpsdoiorg1010022014JA020687

Kim K‐C Shprits Y Y amp Blake J B (2016) Fast injection of the relativistic electrons into the inner zone and the formation of the split‐zone structure during the Bastille Day storm in July 2000 Journal of Geophysical Research Space Physics 121 8329ndash8342 httpsdoiorg1010022015JA022072

Kim K‐C Shprits Y Subbotin D amp Ni B (2012) Relativistic radiation belt electron responses to GEMmagnetic storms Comparison ofCRRES observations with 3‐D VERB simulations Journal of Geophysical Research 117 A08221 httpsdoiorg1010292011JA017460

Kim K‐C Shprits Y Subbotin D amp Ni B (2011) Understanding the dynamic evolution of the relativistic electron slot region includingradial and pitch angle diffusion Journal of Geophysical Research 116(A10) A10214 httpsdoiorg1010292011JA016684

Kletzing C A Kurth W S Acuna M MacDowall R J Torbert R B Averkamp T et al (2013) The Electric and Magnetic FieldInstrument Suite and Integrated Science (EMFISIS) on RBSP Space Science Reviews 179(1ndash4) 127ndash181 httpsdoiorg101007s11214‐013‐9993‐6

Komar C M Glocer A Hartinger M D Murphy K R Fok M‐C H amp Kang S‐B (2017) Electron drift resonance in the MHD‐coupled Comprehensive Inner Magnetosphere‐Ionosphere model Journal of Geophysical Research Space Physics 122 12006ndash12018httpsdoiorg1010022017JA024163

Kress B T Hudson M K Looper M D Albert J Lyon J G amp Goodrich C C (2007) Global MHD test particle simulations of gt10MeV radiation belt electrons during storm sudden commencement Journal of Geophysical Research 112 A09215 httpsdoiorg1010292006JA012218



Kress B T Hudson M K Looper M D Lyon J G amp Goodrich C C (2008) Global MHD test particle simulations of solar energeticelectron trapping in the Earths radiation belts Journal of Atmospheric and Solar‐Terrestrial Physics 70(14) 1727ndash1737

Kress B T Hudson M K Ukhorskiy A Y amp Mueller H‐R (2012) Nonlinear radial transport in the Earths radiation belts In DSummers et al (Eds) Dynamics of the Earths radiation belts and inner magnetosphere Geophys Monogr Ser (Vol 199 p 151)Washington DC AGU httpsdoiorg1010292012GM001333

Kubota Y amp Omura Y (2018) Nonlinear dynamics of radiation belt electrons interacting with chorus emissions localized in longitudeJournal of Geophysical Research Space Physics 123 4835ndash4857 httpsdoiorg1010292017JA025050

Kubota Y Omura Y amp Summers D (2015) Relativistic electron precipitation induced by EMIC‐triggered emissionsin a dipole mag-netosphere Journal of Geophysical Research Space Physics 120 4384ndash4399 httpsdoiorg1010022015JA021017

Kurth W S De Pascuale S Faden J B Kletzing C A Hospodarsky G B Thaller S ampWygant J R (2015) Electron densities inferredfrom plasma wave spectra obtained by the Waves instrument on Van Allen Probes Journal of Geophysical Research Space Physics 120904ndash914 httpsdoiorg1010022014JA020857

Lanzerotti L J (2017) Space weather Historical and contemporary perspectives Space Science Reviews 212 1253ndash1270 httpsdoiorg101007s11214‐017‐0408‐y

Lanzerotti L J amp Baker D N (2017) Space weather research Earths radiation belts Space Weather 15 742ndash745 httpsdoiorg1010022017SW001654

Lauben D S Inan U S amp Bell T F (2001) Precipitation of radiation belt electrons induced by obliquely propagating lightning‐gener-ated whistlers Journal of Geophysical Research 106(A12) 29745ndash29770

LeDocq M J Gurnett D A amp Hospodarsky G B (1998) Chorus source locations from VLF Poynting flux measurements with the Polarspacecraft Geophysical Research Letters 25(21) 4063ndash4066 httpsdoiorg1010291998GL900

Lejosne S (2019) Analytic expressions for radial diffusion Journal of Geophysical Research Space Physics 124 4278ndash4294 httpsdoiorg1010292019JA026786

Lejosne S Boscher D Maget V amp Rolland G (2012) Bounce‐averaged approach to radial diffusion modeling From a new derivation ofthe instantaneous rate of change of the third adiabatic invariant to the characterization of the radial diffusion process Journal ofGeophysical Research 117 A08231 httpsdoiorg1010292012JA018011

Lejosne S Kunduri B S R Mozer F S amp Turner D L (2018) Energetic electron injections deep into the inner magnetosphere A resultof the subauroral polarization stream (SAPS) potential drop Geophysical Research Letters 45 3811ndash3819 httpsdoiorg1010292018GL077969

Lejosne S ampMozer F S (2017) Subauroral Polarization Streams (SAPS) duration as determined from Van Allen probe successive electricdrift measurements Geophysical Research Letters 44 9134ndash9141 httpsdoiorg1010022017GL074985

Lejosne S amp Roederer J G (2016) The ldquozebra stripesrdquo An effect of F region zonal plasma drifts on the longitudinal distribution ofradiation belt particles Journal of Geophysical Research Space Physics 121 507ndash518 httpsdoiorg1010022015JA021925

Lenard A (1960) On Bogoliubovs kinetic equation for a spatially homogeneous plasma Ann Phys 10(3) 390ndash400 httpsdoiorg1010160003‐4916(60)90003‐8

Lerche I (1968) Quasilinear Theory of Resonant Diffusion in a Magneto‐Active Relativistic Plasma The Physics of Fluids 11(8)1720ndash1727 httpsdoiorg10106311692186

Lessard M R Paulson K Spence H E Weaver C Engebretson M J Millan R et al (2019) Generation of EMICwaves and effects onparticle precipitation during a solar wind pressure inten‐ sification with Bz gt 0 Journal of Geophysical Research Space Physics 1244492ndash4508 httpsdoiorg1010292019JA026477

Li J Ni B Ma Q Xie L Pu Z Fu S et al (2016) Formation of energetic electron butterfly distributions by magnetosonic waves viaLandau resonance Geophysical Research Letters 43 3009ndash3016 httpsdoiorg1010022016GL067853

Li W Ma Q Thorne R M Bortnik J Kletzing C A Kurth W S et al (2015) Statistical properties of plasmaspheric hiss derived fromVan Allen Probes data and their effects on radiation belt electron dynamics Journal of Geophysical Research Space Physics 1203393ndash3405 httpsdoiorg1010022015JA021048

Li W Ma Q Thorne R M Bortnik J Zhang X J Li J et al (2016) Radiation belt electron acceleration during the 17 March 2015geomagnetic storm Observations and simulations Journal of Geophysical Research Space Physics 121 5520ndash5536 httpsdoiorg1010022016JA022400

Li W Ni B Thorne R M Bortnik J Nishimura Y Green J C et al (2014) Quantifying hiss‐driven energetic electron precipitation Adetailed conjunction event analysis Geophysical Research Letters 41 1085ndash1092 httpsdoiorg1010022013GL059132

Li W Shen X‐C Ma Q Capannolo L Shi R Redmon R J et al (2019) Quantification of energetic Electron precipitation driven byplume whistler mode waves Plasmaspheric hiss and exohiss Geophysical Research Letters 46 3615ndash3624 httpsdoiorg1010292019GL082095

Li W Shprits Y amp Thorne R (2007) Dynamic evolution of energetic outer zone electrons due to wave‐particle interactions duringstorms Journal of Geophysical Research 112 A10220 httpsdoiorg1010292007JA012368

Li W Thorne R M Ma Q Ni B Bortnik J Baker D N et al (2014) Radiation belt electron acceleration by chorus waves during the17 March 2013 storm Journal of Geophysical Research Space Physics 119 4681ndash4693 httpsdoiorg1010022014JA019945

Li X Baker D N Zhao H Zhang K Jaynes A N Schiller Q et al (2017) Radiation belt electron dynamics at low L (lt4) Van AllenProbes era versus previous two solar cycles Journal of Geophysical Research Space Physics 122 5224ndash5234 httpsdoiorg1010022017JA023924

Li X Roth I Temerin M Wygant J Hudson M K amp Blake J B (1993) Simulation of the prompt energization and transport ofradiation particles during the March 24 1991 SSC Geophysical Research Letters 20 2423ndash2426 httpsdoiorg10102993GL02701

Li X Selesnick R Schiller Q Zhang K Zhao H Baker D N amp Temerin M A (2017) Measurement of electrons from albedo neutrondecay and neutron density in near‐Earth space Nature 552(7685) 382ndash385 httpsdoiorg101038nature24642

Li X amp Temerin M (2001) The electron radiation belt Space Science Reviews 96(1ndash2) httpsdoiorg101023A1005221108016Li Z Millan R M amp Hudson M K (2013) Simulation of the energy distribution of relativistic electron precipitation caused by quasi‐

linear interactions with EMIC waves Journal of Geophysical Research Space Physics 118 7576ndash7583 httpsdoiorg1010022013JA019163

Li Z Millan R M HudsonM K Woodger L A Smith DM Chen Y et al (2014) Investigation of EMICwave scattering as the causefor the BARREL 17 January 2013 relativistic electron precipitation event A quantitative comparison of simulation with observationsGeophysical Research Letters 41 8722ndash8729 httpsdoiorg1010022014GL062273

Liang J Liu W W Spanswick E amp Donovan E F (2007) Azimuthal structures of substorm electron injection and their signatures inriometer observations Journal of Geophysical Research 112 A09209 httpsdoiorg1010292007JA012354



Liemohn M W (2006) Introduction to the special section on ldquoResults of the national science foundation geospace environment modelinginner magnetospherestorms assessment challengerdquo Journal of Geophysical Research 111 A11S01 httpsdoiorg1010292006JA011970

Liemohn M W amp Chan A A (2007) Unraveling the causes of radiation belt enhancements Eos 88(42) 425ndash426 httpsdoiorg1010292007EO420001

Liemohn M W Ganushkina N Y de Zeeuw D L Rastaetter L Kuznetsova M Welling D T et al (2018) Real‐time SWMF atCCMC Assessing the Dst output from continuous operational simulations Space Weather 16 1583ndash1603 httpsdoiorg1010292018SW001953

Liemohn M W Ganushkina N Y Ilie R amp Welling D T (2016) Challenges associated with near‐Earth nightside current Journal ofGeophysical Research Space Physics 121 6763ndash6768 httpsdoiorg1010022016JA022948

Liemohn M W McCollough J P Jordanova V K Ngwira C M Morley S K Cid C et al (2018) Model evaluation guidelines forgeomagnetic index predictions Space Weather 16 2079ndash2102 httpsdoiorg1010292018SW002067

Liu N Su Z Gao Z Zheng H Wang Y Wang S et al (2017) Simultaneous disappearances of plasmaspheric hiss exohiss andchorus waves triggered by a sudden decrease in solar wind dynamic pressure Geophysical Research Letters 44 52ndash61 httpsdoiorg1010022016GL071987

Liu W Tu W Li X Sarris T Khotyaintsev Y Fu H et al (2016) On the calculation of electric diffusion coefficient of radiation beltelectrons with in situ electric field measurements by THEMIS Geophysical Research Letters 43 1023ndash1030 httpsdoiorg1010022015GL067398

Liu W W Liang J Spanswick E amp Donovan E F (2007) Remote‐sensing magnetospheric dynamics with riometers Observation andtheory Journal of Geophysical Research 112 A05214 httpsdoiorg1010292006JA012115

Liu X Chen L Gu W amp Zhang X‐J (2018) Electron cyclotron harmonic wave instability by loss cone distribution Journal ofGeophysical Research Space Physics 123 9035ndash9044 httpsdoiorg1010292018JA025925

Liu X Liu W Cao J B Fu H S Yu J amp Li X (2015) Dynamic plasmapause model based on THEMIS measurements Journal ofGeophysical Research Space Physics 120 10543ndash10556 httpsdoiorg1010022015JA021801

Looper M D Blake J B amp Mewaldt R A (2005) Response of the inner radiation belt to the violent Sun‐Earth connection events ofOctoberndashNovember 2003 Geophysical Research Letters 32 L03S06 httpsdoiorg1010292004GL021502

Lopez A E Baker D N amp Allen J (2004) Sun Unleashes Halloween Storm Eos 85(11) 105 httpsdoiorg1010292004EO110002Lorentzen K R Blake J B Inan U S amp Bortnik J (2001) Observations of relativistic electron microbursts in association with VLF

chorus Journal of Geophysical Research 106 6017ndash6027 httpsdoiorg1010292000JA003018Loridan V Ripoll J‐F amp de Vuyst F (2017) The analytical solution of the transient radial diffusion equation with a nonuniform loss

term Journal of Geophysical Research Space Physics 122 5979ndash6006 httpsdoiorg1010022017JA023868Loridan V Ripoll J‐F Tu W amp Cunningham G (2019) On the use of different magnetic field models for the major storm of October

1990 Journal of Geophysical Research Space Physics in press 124 6453ndash6486 httpsdoiorg1010292018JA026392Lotoaniu T M Singer H J Waters C L Angelopoulos V Mann I R Elkington S R amp Bonnell J W (2010) Relativistic electron

loss due to ultralow frequency waves and enhanced outward radial diffusion Journal of Geophysical Research 115 A12245 httpsdoiorg1010292010JA015755

Lu Q Ke Y Wang X Liu K Gao X Chen L amp Wang S (2019) Two‐dimensional general curvilinear particle‐in‐cell (gcPIC)simulation of rising‐tone chorus waves in a dipole magnetic field Journal of Geophysical Research Space Physics 124 4157ndash4167httpsdoiorg1010292019JA026586

Lucco Castello F Delzanno G L Borovsky J E Miars G Leon O amp Gilchrist B E (2018) Spacecraft‐charging mitigation of a high‐power electron beam emitted by a magnetospheric spacecraft Simple theoretical model for the transient of the spacecraft potentialJournal of Geophysical Research Space Physics 123 6424ndash6442 httpsdoiorg1010292017JA024926

Lyon J Fedder J amp Mobarry C (2004) The LyonndashFedderndashMobarry (LFM) global MHD magnetospheric simulation code Journal ofAtmospheric and Solar ‐ Terrestrial Physics 66(15‐16) 1333ndash1350 httpsdoiorg101016jjastp200403020

Lyons L R (1974a) Pitch angle and energy diffusion coefficients fromresonant interactionswith ion‐cyclotron and whistlerwaves Journalof Plasma Physics 12 417ndash432

Lyons L R (1974b) General relations for resonant particle diffusion in pitch angle and energy Journal of Plasma Physics 12 part 1 45ndash49Lyons L R amp Thorne R M (1973) Equilibrium structure of radiation belt electrons Journal of Geophysical Research 78(13) 2142ndash2149

httpsdoiorg101029JA078i013p02142Lyons L R Thorne R M amp Kennel C F (1971) Electron pitch‐angle diffusion driven by oblique whistler‐mode turbulence Plasma

Physics 6 part 3 589ndash606Lyons L R Thorne R M amp Kennel C F (1972) Pitch‐angle diffusion of radiation belt electrons within the plasmasphere Journal of

Geophysical Research 77(19) 3455ndash3474 httpsdoiorg101029JA077i019p03455Ma Q Li W Bortnik J Thorne R M Chu X Ozeke L G et al (2018) Quantitative evaluation of radial diffusion and local accel-

eration processes during GEM challenge events Journal of Geophysical Research Space Physics 123 1938ndash1952 httpsdoiorg1010022017JA025114

Ma Q Li W Thorne R M Bortnik J Reeves G D Kletzing C A et al (2016) Characteristic energy range of electron scattering dueto plasmaspheric hiss Journal of Geophysical Research Space Physics 121 11737ndash11749 httpsdoiorg1010022016JA023311

Ma Q Li W Thorne R M Bortnik J Reeves G D Spence H E et al (2017) Diffusive transport of several hundred keV electrons inthe Earths slot region Journal of Geophysical Research Space Physics 122 10235ndash10246 httpsdoiorg1010022017JA024452

Ma Q Li W Thorne R M Ni B Kletzing C A Kurth W S et al (2015) Modeling inward diffusion and slow decay of energeticelectrons in the Earths outer radiation belt Geophysical Research Letters 42 987ndash995 httpsdoiorg1010022014GL062977

Ma Q Li W Thorne R M Nishimura Y Zhang X J Reeves G D et al (2016) Simulation of energy‐dependent electron diffusionprocesses in the Earths outer radiation belt Journal of Geophysical Research Space Physics 121 4217ndash4231 httpsdoiorg1010022016JA022507

Maget V Sicard‐Piet A Bourdarie S Lazaro D Turner D L Daglis I A amp Sandberg I (2015) Improved outer boundary conditionsfor outer radiation belt data assimilation using THEMIS‐SST data and the Salammbo‐EnKF code Journal of Geophysical Research SpacePhysics 120 5608ndash5622 httpsdoiorg1010022015JA021001

Malaspina D M Jaynes A N Bouleacute C Bortnik J Thaller S A Ergun R E et al (2016) The distribution of plasmaspheric hiss wavepower with respect to plasmapause location Geophysical Review Letters 43 7878ndash7886 httpsdoiorg1010022016GL069982

Malaspina D M Jaynes A N Hospodarsky G Bortnik J Ergun R E amp Wygant J (2017) Statistical properties of low‐frequencyplasmaspheric hiss Journal of Geophysical Research Space Physics 122 8340ndash8352 httpsdoiorg1010022017JA024328



Malaspina D M Ripoll J‐F Chu X Hospodarsky G amp Wygant J (2018) Variation in plasmaspheric hiss wave power with plasmadensity Geophysical Research Letters 45 9417ndash9426 httpsdoiorg1010292018GL078564

Mann I R Lee E A Claudepierre S G Fennell J F Degeling A Rae I J et al (2013) Discovery of the action of a geophysicalsynchrotron in the Earths Van Allen radiation belts Nature Communications 4(1) 2795 httpsdoiorg101038ncomms3795

Mann I R Milling D K Rae I J Ozeke L G Kale A Kale Z C et al (2008) The upgraded CARISMA magnetometer array in theTHEMIS Era Space Science Reviews 141(1‐4) 413ndash451 httpsdoiorg101007s11214‐008‐9457‐6

Mann I R Murphy K R Ozeke L G Rae I J Milling D K Kale A A amp Honary F F (2012) The role of ultralow frequency wavesin radiation belt dynamics Geophysical Monograph Series 199 69ndash91

Mann I R Ozeke L G Murphy K R Claudepierre S G Turner D L Baker D N et al (2016) Explaining the dynamics of the ultra‐relativistic third Van Allen radiation belt Nature Physics 12(10) 978ndash983 httpsdoiorg101038nphys3799

Mann I R Di Pippo S Opgenoorth H J Kuznetsova M amp Kendall D J (2018) International collaboration within the United NationsCommittee on the Peaceful Uses of Outer Space Framework for international space weather services (2018ndash2030) Space Weather 16428ndash433 httpsdoiorg1010292018SW001815

Marshall R A Newsome R T Lehtinen N G Lavassar N amp Inan U S (2010a) Optical signatures of radiation belt electron preci-pitation induced by ground‐based VLF transmitters Journal of Geophysical Research 115 A08206 httpsdoiorg1010292010JA015394

Marshall R A Newsome R T Lehtinen N G Lavassar N amp Inan U S (2010b) Correction to ldquoOptical signatures of radiation beltelectron precipitation induced by ground‐based VLF transmittersrdquo Journal of Geophysical Research 115 A09213 httpsdoiorg1010292010JA016025

Matsumoto Y amp Seki K (2010) Formation of a broad plasma turbulent layer by forward and inverse energy cascades of the KelvinndashHelmholtz instability Journal of Geophysical Research 115 A10231 httpsdoiorg1010292009JA014637

Matthes K Funke B Andersson M E Barnard L Beer J Charbonneau P et al (2017) Solar forcing for CMIP6 (v32) GeoscientificModel Development 10(6) 2247ndash2302 httpsdoiorg105194gmd‐10‐2247‐2017

Mauk B H Fox N J Kanekal S G Kessel R L Sibeck D G amp Ukhorskiy A (2013) Science objectives and rationale for the RadiationBelt Storm Probes mission Space Science Reviews 179(1ndash4) 3ndash27 httpsdoiorg101007s11214‐012‐9908‐y

Mazur J Friesen L Lin A Mabry D Katz N Dotan Y et al (2013) The Relativistic Proton Spectrometer (RPS) for the Radiation BeltStorm Probes Mission Space Science Reviews 179 221ndash261 httpsdoiorg101007s11214‐012‐9926‐9

Mazur J E OBrien T P Looper M D amp Blake J B (2014) Large anisotropies of gt60 MeV protons throughout the inner belt observedwith the Van Allen Probes mission Geophysical Research Letters 41 3738ndash3743 httpsdoiorg1010022014GL060029

McIlwain C E (1961) Coordinates for mapping the distribution of magnetically trapped particles Journal of Geophysical Research 66(11)3681ndash3691 httpsdoiorg101029JZ066i011p03681

McKay‐Bukowski D Vierinen J Virtanen I I Fallows R Postila M Ulich T et al (2015) KAIRA The Kilpisjaumlrvi AtmosphericImaging Receiver Array System Overview and First Results IEEE Transactions on Geoscience and Remote Sensing 53(3) 1440ndash1451httpsdoiorg101109TGRS20142342252

Means J D (1972) Use of the three‐dimensional covariance matrix in analyzing the polarization properties of plane waves Journal ofGeophysical Research 77(28) 5551ndash5559

Meierbachtol C S Svyatskiy D Delzanno G L Vernon L J amp Moulton J D (2017) An electrostatic particle‐in‐cell code on multi‐block structured meshes Journal of Computational Physics 350 796ndash823 httpsdoiorg101016jjcp201709016

Meredith N P Horne R B Bortnik J Thorne R M Chen L Li W amp Sicard‐Piet A (2013) Global statistical evidence for chorus asthe embryonic source of plasmaspheric hiss Geophysical Research Letters 40 2891ndash2896 httpsdoiorg101002grl50593

Meredith N P Horne R B Clilverd M A Horsfall D Thorne R M amp Anderson R R (2006) Origins of plasmaspheric hiss Journalof Geophysical Research 111 A09217 httpsdoiorg1010292006JA011707

Meredith N P Horne R B Clilverd M A amp Ross J P J (2019) An investigation of VLF transmitter wave power in the inner radiationbelt and slot region Journal of Geophysical Research Space Physics 124 5246ndash5259 httpsdoiorg1010292019JA026715

Meredith N P Horne R B Glauert S A amp Anderson R R (2007) Slot region electron loss timescales due to plasmaspheric hiss andlightning‐generated whistlers Journal of Geophysical Research 112 A08214 httpsdoiorg1010292007JA012413

Meredith N P Horne R B Glauert S A Baker D N Kanekal S G amp Albert J M (2009) Relativistic electron loss timescales in theslot region Journal of Geophysical Research 114 A03222 httpsdoiorg1010292008JA013889

Meredith N P Horne R B Glauert S A Thorne R M Summers D Albert J M amp Anderson R R (2006) Energetic outer zoneelectron loss timescales during low geomagnetic activity Journal of Geophysical Research 111 A05212 httpsdoiorg1010292005JA011516

Meredith N P Horne R B Isles J D amp Green J C (2016) Extreme energetic electron fluxes in low Earth orbit Analysis of POES E gt30 E gt 100 and E gt 300 keV electrons Space Weather 14 136ndash150 httpsdoiorg1010022015SW001348

Meredith N P Horne R B Isles J D amp Rodriguez J V (2015) Extreme relativistic electron fluxes at geosynchronous orbit Analysis ofGOES E gt 2 MeV electrons Space Weather 13 170ndash184 httpsdoiorg1010022014SW001143

Meredith N P Horne R B Kersten T Li W Bortnik J Sicard A amp Yearby K H (2018) Global model of plasmaspheric hiss frommultiple satellite observations Journal of Geophysical Research Space Physics 123 4526ndash4541 httpsdoiorg1010292018JA025226

Meredith N P Horne R B Li W Thorne R M amp Sicard‐Piet A (2014) Global model of low‐frequency chorus (fLHR lt f lt 01 fce)from multiple satellite observations Geophysical Research Letters 41 280ndash286 httpsdoiorg1010022013GL059050

Meredith N P Horne R B Sandberg I Papadimitriou C amp Evans H D R (2017) Extreme relativistic electron fluxes in the Earthsouter radiation belt Analysis of INTEGRAL IREM data Space Weather 15 917ndash933 httpsdoiorg1010022017SW001651

Meredith N P Horne R B Sicard‐Piet A Boscher D Yearby K H Li W amp Thorne R M (2012) Global models of lower band andupper band chorus from multiple satellite observations Journal of Geophysical Research 117 A10225 httpsdoiorg1010292012JA017978

Meredith N P Horne R B Thorne R M amp Anderson R R (2009) Survey of upper band chorus and ECH waves Implications for thediffuse aurora Journal of Geophysical Research 114 A07218 httpsdoiorg1010292009JA014230

Meredith N P Horne R B Thorne R M Summers D amp Anderson R R (2004) Substorm dependence of plasmaspheric hiss Journalof Geophysical Research 109 A06209 httpsdoiorg1010292004JA010387

Meredith N P Johnstone A D Szita S Horne R B amp Anderson R R (2000) An investiguation into the roles of ECH and whistlermode waves in the formation of ldquopancakerdquo electron distribution using data from the CRRES satellite Advances in Space Research25(12) 2339ndash2342



Millan R M amp Baker D N (2012) Acceleration of particles to high energies in Earths radiation belts Space Science Reviews 173103ndash131 httpsdoiorg101007s11214‐012‐9941‐x

Millan R M McCarthy M P Sample J G Smith D M Thompson L D McGaw D G et al (2013) The Balloon Array for RBSPRelativistic Electron Losses (BARREL) Space Science Reviews 179(1‐4) 503ndash530 httpsdoiorg101007s11214‐013‐9971‐z

Millan R M amp Thorne R M (2007) Review of radiation belt relativistic electron losses Journal of Atmospheric and Solar‐TerrestrialPhysics 69(3) 362ndash377 ISSN 1364ndash6826 httpsdoiorg101016jjastp200606019

Millan R M von Steiger R Ariel M Bartalev S Borgeaud M Campagnola S et al (2019) Small satellites for space science ACOSPAR scientific roadmap Advances in Space Research 64(8) 1466ndash1517 httpsdoiorg101016jasr201907035

Min K Neměc F Liu K Denton R E amp Boardsen S A (2019) Equatorial propagation of the magnetosonic mode across the plas-mapause 2‐D PIC simulations Journal of Geophysical Research Space Physics 124 4424ndash4444 httpsdoiorg1010292019JA026567

Miyoshi Y Jordanova V K Morioka A Thomsen M F Reeves G D Evans D S amp Green J C (2006) Observa‐ tions and modelingof energetic electron dynamics during the October 2001 storm Journal of Geophysical Research 111 A11S02 httpsdoiorg1010292005JA011351

Miyoshi Y Katoh Y Nishiyama T Sakanoi T Asamura K amp Hirahara M (2010) Time of flight analysis of pulsating aurora electronsconsidering wave‐particle interactions with propagating whistler mode waves Journal of Geophysical Research 115 A10312 httpsdoiorg1010292009JA015127

Miyoshi Y Oyama S Saito S Kurita S Fujiwara H Kataoka R et al (2015) Energetic electron precipitation associated with pul-sating aurora EISCAT and Van Allen Probe observations Journal of Geophysical Research Space Physics 120 2754ndash2766 httpsdoiorg1010022014JA020690

Miyoshi Y Sakaguchi K Shiokawa K Evans D Albert J Connors M amp Jordanova V (2008) Precipitation of radiation belt electronsby EMIC waves observed from ground and space Geophysical Research Letters 35 L23101 httpsdoiorg1010292008GL035727

Miyoshi Y Shinohara I Takashima T Asamura K Higashio N Mitani T et al (2018) Geospace exploration project ERG EarthPlanets and Space 70(1) 101 httpsdoiorg101186s40623‐018‐0862‐0

Moldwin M B (2010) Vector Fluxgate Magnetometer (VMAG) Development for DSX UCLA Final report httpwwwdticmilcgi‐inGetTRDocLocation=U2ampdoc=GetTRDocpdfampAD=ADA529004

Moldwin M B Downward L Rassoul H K Amin R amp Anderson R R (2002) A new model of the location of the plasmapauseCRRES results Journal of Geophysical Research 107(A11) 1339 httpsdoiorg1010292001JA009211

Morley S K Brito T V amp Welling D T (2018) Measures of model performance based on the log accuracy ratio Space Weather 1669ndash88 httpsdoiorg1010022017SW001669

Morley S K Welling D T amp Woodroffe J R (2018) Perturbed input ensemble modeling with the space weather modeling frameworkSpace Weather 16 1330ndash1347 httpsdoiorg1010292018SW002000

Mourenas D amp Ripoll J‐F (2012) Analytical estimates of quasi‐linear diffusion coefficients and electron lifetimes in the inner radiationbelt Journal of Geophysical Research Space Physics 117 A01204 httpsdoiorg1010292011JA016985

Mozer F S Agapitov O V Artemyev A Drake J F Krasnoselskikh V Lejosne S amp Vasko I (2015) Time domain structures Whatand where they are what they do and how they are made Geophysical Research Letters 42 3627ndash3638 httpsdoiorg1010022015GL063946

Mozer F S Agapitov O V Blake J B amp Vasko I Y (2018) Simultaneous observations of lower band chorus emissions at the equatorand microburst precipitating electrons in the ionosphere Geophysical Research Letters 45 511ndash516 httpsdoiorg1010022017GL076120

Mozer F S Agapitov O V Hull A Lejosne S amp Vasko I Y (2017) Pulsating auroras produced by interactions of electrons and timedomain structures Journal of Geophysical Research Space Physics 122 8604ndash8616 httpsdoiorg1010022017JA024223

Murphy K R Watt C E J Mann I R Jonathan Rae I Sibeck D G Boyd A J et al (2018) The global statistical response of the outerradiation belt during geomagnetic storms Geophysical Research Letters 45 3783ndash3792 httpsdoiorg1010022017GL076674

Nakamura S Omura Y Kletzing C amp Baker D N (2019) Rapid precipitation of relativistic electron by EMIC rising‐tone emissionsobserved by the Van Allen Probes Journal of Geophysical Research Space Physics 124 6701ndash6714 httpsdoiorg1010292019JA026772

Nakamura S Omura Y Shoji M Noseacute M Summers D amp Angelopoulos V (2015) Subpacket structures in EMIC rising tone emis-sions observed by the THEMIS probes Journal of Geophysical Research Space Physics 120 7318ndash7330 httpsdoiorg1010022014JA020764

Nakamura S Omura Y Summers D amp Kletzing C A (2016) Observational evidence of the nonlinear wave growth theory of plas-maspheric hiss Geophysical Research Letters 43 10040ndash10049 httpsdoiorg1010022016GL070333

National Space Weather Action Plan National Science and Technology Council White House Office United States October 2015National Space Weather Strategy National Science and Technology Council White House Office United States October 2015National Space Weather Strategy and Action Plan National Science and Technology Council White House Office United States March

2019Neal J J Rodger C J Clilverd M A Thomson N R Raita T amp Ulich T (2015) Long‐term determination of energetic electron

precipitation into the atmosphere from AARDDVARK subionospheric VLF observations Journal of Geophysical Research SpacePhysics 120 2194ndash2211 httpsdoiorg1010022014JA020689

Newnham D A Espy P J Clilverd M A Rodger C J Seppaumllauml A Maxfield D J et al (2013) Observations of nitric oxide in theAntarctic middle atmosphere during recurrent geomagnetic storms Journal of Geophysical Research Space Physics 118 7874ndash7885httpsdoiorg1010022013JA019056

Ni B Thorne R M Shprits Y Y amp Bortnik J (2008) Resonant scattering of plasma sheet electrons by whistler‐mode chorusContribution to diffuse auroral precipitation Geophysical Research Letters 35 L11106 httpsdoiorg1010292008GL034032

Ni B Bortnik J Thorne R M Ma Q amp Chen L (2013) Resonant scattering and resultant pitch angle evolution of relativistic electronsby plasmaspheric hiss Journal of Geophysical Research Space Physics 118 7740ndash7751 httpsdoiorg1010022013JA019260

Ni B Hua M Zhou R Yi J amp Fu S (2017) Competition between outer zone electron scattering by plasmaspheric hiss and magne-tosonic waves Geophysical Research Letters 44 3465ndash3474 httpsdoiorg1010022017GL072989

Ni B Li W Thorne R M Bortnik J Ma Q Chen L et al (2014) Resonant scattering of energetic electrons by unusual low frequencyhiss Geophysical Research Letters 41 1854ndash1861 httpsdoiorg1010022014GL059389

Ni B Thorne R M Meredith N P Shprits Y Y amp Horne R B (2011) Diffuse auroral scattering by whistler mode chorus wavesDependence on wave normal angle distribution Journal of Geophysical Research 116 A10207 httpsdoiorg1010292011JA016517



Ni B Zou Z Gu X Zhou C Thorne R M Bortnik J et al (2015) Variability of the pitch angle distribution of radiation belt ultra-relativistic electrons during and following intense geomagnetic storms Van Allen Probes observations Journal of Geophysical ResearchSpace Physics 120 4863ndash4876 httpsdoiorg1010022015JA021065

Ni B Zou Z Li X Bortnik J Xie L amp Gu X (2016) Occurrence characteristics of outer zone relativistic electron butterfly distributionA survey of Van Allen Probes REPT measurements Geophysical Research Letters 43 5644ndash5652 httpsdoiorg1010022016GL069350

Nishimura Y Bortnik J Li W Thorne R M Lyons L R Angelopoulos V et al (2010) Identifying the driver of pulsating aurorasScience 330(6000) 81ndash84 httpsdoiorg101126science1193186

Northrop T G (1963) The adiabatic motion of charged particles New York InterscienceNorthrop T G amp Teller E (1960) Stability of the adiabatic motion of charaged particles in the Earths field Physics Review 117(1)

215ndash225 httpsdoiorg101103PhysRev117215Nunn D amp Omura Y (2015) A computational and theoretical investigation of nonlinear wave‐particle interactions in oblique whistlers

Journal of Geophysical Research Space Physics 120 2890ndash2911 httpsdoiorg1010022014JA020898OBrien T P (2014) Breaking all the invariants Anomalous electron radiation belt diffusion by pitch angle scattering in the presence of

split magnetic drift shells Geophysical Research Letters 41 216ndash222 httpsdoiorg1010022013GL058712OBrien T P Mazur J E amp Looper M D (2018) Solar energetic proton access to the magnetosphere during the 10ndash14 September 2017

particle event Space Weather 16 2022ndash2037 httpsdoiorg1010292018SW001960OBrien T P amp Moldwin M B (2003) Empirical plasmapause models from magnetic indices Geophysical Research Letters 30(4) 1152

httpsdoiorg1010292002GL016007Olifer L Mann I R Ozeke L G Rae I J amp Morley S K (2019) On the relative strength of electric and magnetic ULF wave radial

diffusion during the March 2015 geomagnetic storm Journal of Geophysical Research Space Physics 124 2569ndash2587 httpsdoiorg1010292018JA026348

Olson W P amp Pfitzer K A (1974) A quantitative model of the magnetospheric magnetic field Journal of Geophysical Research 79 3739httpsdoiorg101029JA079i025p03739

Omura Y HikishimaM Katoh Y Summers D amp Yagitani S (2009) Nonlinear mechanisms of lower band and upper‐band VLF chorusemissions in the magnetosphere Journal of Geophysical Research Space Physics 114 A07217 httpsdoiorg1010292009JA014206

Omura Y Hsieh Y‐K Foster J C Erickson P J Kletzing C A amp Baker D N (2019) Cyclotron acceleration of relativistic electronsthrough Landau resonance with obliquely propagating whistler‐mode chorus emissions Journal of Geophysical Research Space Physics124 2795ndash2810 httpsdoiorg1010292018JA026374

Omura Y Katoh Y amp Summers D (2008) Theory and simulation of the generation of whistler‐mode chorus Journal of GeophysicalResearch 113 A04223 httpsdoiorg1010292007JA012622

Omura Y Miyashita Y Yoshikawa M Summers D Hikishima M Ebihara Y amp Kubota Y (2015) Formation process of relativisticelectron flux through interaction with chorus emissions in the Earths inner magnetosphere Journal of Geophysical Research SpacePhysics 120 9545ndash9562 httpsdoiorg1010022015JA021563

Omura Y Nakamura S Kletzing C A Summers D amp Hikishima M (2015) Nonlinear wave growth theory of coherent hiss emissionsin the plasmasphere Journal of Geophysical Research Space Physics 120 7642ndash7657 httpsdoiorg1010022015JA021520

Omura Y amp Zhao Q (2012) Nonlinear pitch angle scattering of relativistic electrons by EMIC waves in the inner magnetosphere Journalof Geophysical Research 117 A08227 httpsdoiorg1010292012JA017943

Omura Y amp Zhao Q (2013) Relativistic electron microbursts due to nonlinear pitch angle scattering by EMIC triggered emissionsJournal of Geophysical Research Space Physics 118 5008ndash5020 httpsdoiorg101002jgra50477

Orlova K amp Shprits Y (2014) Model of lifetimes of the outer radiation belt electrons in a realistic magnetic field using realistic choruswave parameters Journal of Geophysical Research Space Physics 119 770ndash780 httpsdoiorg1010022013JA019596

Orlova K G amp Shprits Y Y (2010) Dependence of pitchangle scattering rates andloss timescales on the magnetic field modelGeophysical Research Letters 37(5) httpsdoiorg1010292009GL041639

Orlova K Spasojevic M amp Shprits Y (2014) Activity‐dependent global model of electron loss inside the plasmasphere GeophysicalResearch Letters 41 3744ndash3751 httpsdoiorg1010022014GL060100

Oyama S Kero A Rodger C J Clilverd M A Miyoshi Y Partamies N et al (2017) Energetic electron precipitation and auroralmorphology at the substorm recovery phase Journal of Geophysical Research Space Physics 122 6508ndash6527 httpsdoiorg1010022016JA023484

Ozhogin P Tu J Song P amp Reinisch B W (2006) Fieldaligned distribution of the plasmaspheric electron density An empiricalmodelderived from the IMAGE RPI measurements Journal Geophysics Research 117 A06225 httpsdoiorg1010292011JA017330

Ozeke L G Mann I R Claudepierre S G Henderson M Morley S K Murphy K R et al (2019) The March 2015 superstormrevisited Phase space density profiles and fast ULF wave diffusive transport Journal of Geophysical Research Space Physics 1241143ndash1156 httpsdoiorg1010292018JA026326

Ozeke L G Mann I R Murphy K R Degeling AW Claudepierre S G amp Spence H E (2018) Explaining the apparent impenetrablebarrier to ultra‐relativistic electrons in the outer Van Allen beltNature Communications 9(1) 1844 httpsdoiorg101038s41467‐018‐04162‐3

Ozeke L G Mann I R Murphy K R Jonathan Rae I amp Milling D K (2014) Analytic expressions for ULF wave radiation belt radialdiffusion coefficients Journal of Geophysical Research Space Physics 119 1587ndash1605 httpsdoiorg1010022013JA019204

Ozeke L G Mann I R Murphy K R Rae I J Milling D K Elkington S R et al (2012) ULF wave derived radiation belt radialdiffusion coefficients Journal of Geophysical Research 117 A04222 httpsdoiorg1010292011JA017463

Ozeke L G Mann I R Murphy K R Sibeck D G amp Baker D N (2017) Ultra‐relativistic radiation belt extinction and ULF waveradial diffusion Modeling the September 2014 extended dropout event Geophysical Research Letters 44 2624ndash2633 httpsdoiorg1010022017GL072811

Palmroth M Archer M Vainio R Hietala H Pfau‐Kempf Y Hoilijoki S et al (2015) ULF foreshock under radial IMF THEMISobservations and global kinetic simulation Vlasiator results compared Journal of Geophysical Research Space Physics 120 8782ndash8798httpsdoiorg1010022015JA021526

Palmroth M amp the Vlasiator team (2019) Vlasiator Hybrid‐Vlasov simulation code Github repository (Version 30 last access09052019) Retrieved from httpsgithubcomfmihpcvlasiator

Perraut S Roux A Robert P Gendrin R Savaud J A Bosqued J M et al (1982) A system‐ atic study of ULF waves above fH+ fromGEOS 1 and 2 measurements and their relationship with proton ring distributions Journal of Geophysical Research 87 6219ndash6236httpsdoiorg101029JA087iA08p06219



Peter W B amp Inan U S (2005) Electron precipitation events driven by lightning in hurricanes Journal of Geophysical Research 110A05305 httpsdoiorg1010292004JA010899

Pierrard V Lopez Rosson G amp Botek E (2019) Dynamics of MeV electrons observed in the inner belt by PROBA‐VEPT Journal ofGeophysical Research Space Physics 124 1651ndash1659 httpsdoiorg1010292018JA026289

Pokhotelov D Lefeuvre F Horne R B amp Cornilleau‐Wehrlin N (2008) Survey of ELF‐VLF plasma waves in outer radiation beltobserved by Cluster STAFF‐SA experiment Annales de Geophysique 26 3269ndash3277

Powell K Roe P Linde T Gombosi T amp De Zeeuw D L (1999) A solution‐adaptive upwind scheme for ideal magnetohydrodynamicsJournal of Computational Physics 154(2) 284ndash309 httpsdoiorg101006jcph19996299

Presidential Executive Order Executive Order on Coordinating National Resilience to Electromagnetic Pulses White House Office UnitedStates 26 March 2019 httpswwwwhitehousegovpresidential‐actionsexecutive‐order‐coordinating‐nation

Pugacheva G I Boscher D M Gusev A A Martin I M amp Spjeldvik W N (2000) Transport modeling of energetic electrons in theinner magnetosphere with synchrotron energy losses Advances in Space Research 25(12) 2303ndash2306

Pugacheva G I Martin I amp Spjeldvik W (2013) Spectrum of antiprotons confined in the Earths magnetosphere Journal of PhysicsConference Series 409 012041 23rd European Cosmic Ray Symposium (and 32nd Russian Cosmic Ray Conference) httpsdoiorg1010881742‐65964091012041

Pulkkinen A Kuznetsova M Ridley A Raeder J Vapirev A Weimer D et al (2011) Geospace Environment Modeling 2008ndash2009Challenge Ground magnetic field perturbations Space Weather 9 S02004 httpsdoiorg1010292010SW000600

Purvis C K Garrett H B Whittlesey A C amp Stevens N J (1984) Design Guidelines for Assessing and Controlling Space craft ChargingEffects NASA Technical Paper 2361

Qin M Hudson M Li Z Millan R Shen X Shprits Y et al (2019) Investigating loss of relativistic electrons associated with EMICwaves at low L values on 22 June 2015 Journal of Geophysical Research Space Physics 124 4022ndash4036 httpsdoiorg1010292018JA025726

Raeder J Wang Y L amp Fuller‐Rowell T (2001) Geomagnetic storm simulation with a coupled magnetosphere‐ionosphere‐thermo-sphere model In P Song G Siscoe amp H J Singer (Eds) Space Weather Geophys Monogr Ser (Vol 125 pp 377ndash384) Washington DC AGU

Reeves G D Chan A amp Rodger C (2009) New directions for radiation belt research Space Weather 7 S07004 httpsdoiorg1010292008SW000436

Reeves G D Chen Y Cunningham G S Friedel R W H Henderson M G Jordanova V K et al (2012) Dynamic RadiationEnvironment Assimilation Model DREAM Space Weather 10 S03006 httpsdoiorg1010292011SW000729

Reeves G D Friedel R HW Larsen B A Skoug R M Funsten H O Claudepierre S G et al (2016) Energy‐dependent dynamics ofkeV to MeV electrons in the inner zone outer zone and slot regions Journal of Geophysical Research Space Physics 121 397ndash412httpsdoiorg1010022015JA021569

Reeves G D Spence H E Henderson M G Morley S K Friedel R H W Funsten H O et al (2013) Electron acceleration in theheart of the Van Allen radiation belts Science 341(6149) 991ndash994 httpsdoiorg101126science1237743

Reacuteveilleacute T (1997) Etude de meacutecanismes de pertes de particules dans les ceintures artificielles de Van Allen (thegravese de doctorat PhDThesis) France Univ Henri Poincareacute Nancy‐I

Ripoll J‐F Albert J M amp Cunningham G S (2014) Electron lifetimes from narrowband wave‐particle interactions within the plas-masphere Journal of Geophysical Research Space Physics 119 8858ndash8880 httpsdoiorg1010022014JA020217

Ripoll J‐F Chen Y Fennell J F amp Friedel R H W (2014) On long decays of electrons in the vicinity of the slot region observed byHEO3 Journal of Geophysical Research Space Physics 120 460ndash478 httpsdoiorg1010022014JA020449

Ripoll J‐F Farges T Lay E H amp Cunningham G S (2019) Local and statistical maps of lightning‐generated wave power densityestimated at the Van Allen Probes footprints from the World‐Wide Lightning Location Network database Geophysical Research Letters46 4122ndash4133 httpsdoiorg1010292018GL081146

Ripoll J‐F Loridan V Cunningham G S Reeves G D amp Shprits Y Y (2016) On the time needed to reach an equilibrium structure ofthe radiation belts Journal of Geophysical Research Space Physics 121 7684ndash7698 httpsdoiorg1010022015JA022207

Ripoll J‐F Loridan V Denton M H Cunningham G Reeves G Santoliacutek O et al (2019) Observations and Fokker-Planck simu‐lations of the L‐shell energy and pitch angle structure of Earths electron radiation belts during quiet times Journal of GeophysicalResearch Space Physics 124 1125ndash1142 httpsdoiorg1010292018JA026111

Ripoll J‐F Reeves G D Cunningham G S Loridan V Denton M Santoliacutek O et al (2016) Reproducing the observed energy‐dependent structure of Earths electron radiation belts during storm recovery with an event‐specific diffusion model GeophysicalResearch Letters 43 5616ndash5625 httpsdoiorg1010022016GL068869

Ripoll J‐F Santoliacutek O Reeves G D Kurth W S Denton M H Loridan V et al (2017) Effects of whistler mode hiss waves in March2013 Journal of Geophysical Research Space Physics 122 7433ndash7462 httpsdoiorg1010022017JA024139

Roberts C S (1969) Pitch‐angle diffusion of electrons in the magnetosphere Reviews of Geophysics 7(1ndash2) 305ndash337 httpsdoiorg101029RG007i001p00305

Rodger C J Brundell J B Holzworth R H amp Lay E H (2009) Growing detection efficiency of the World Wide Lightning LocationNetwork In N B Crosby T‐Y Huang amp M J Rycroft (Eds) Coupling of thunderstorms and lightning discharges to near‐earth(CP1118) American Institute of Physics 978ndash0ndash7354‐0657‐509

Rodger C J Clilverd M A amp McCormick R J (2003) Significance of lightning‐generated whistlers to inner radiation belt electronlifetimes Journal of Geophysical Research 108(A12) 1462 httpsdoiorg1010292003JA009906

Rodger C J Cresswell‐Moorcock K amp Clilverd M A (2016) Natures Grand Experiment Linkage between magnetospheric convectionand the radiation belts Journal of Geophysical Research Space Physics 121 171ndash189 httpsdoiorg1010022015JA021537

Rodger C J Hendry A T Clilverd M A Kletzing C A Brundell J B amp Reeves G D (2015) High‐resolution in‐situ observations ofelectron precipitation‐causing emic waves Geophysical Research Letters 42 9633ndash9641 Retrieved from httpsdoiorg1010022015GL066581

Rodger C J Raita T Clilverd M A Seppaumllauml A Dietrich S Thomson N R amp Ulich T (2008) Observations of relativistic electronprecipitation from the radiation belts driven by EMIC waves Geophysical Research Letters 35 L16106 httpsdoiorg1010292008GL034804

Roederer J G (1970) In J G Roederer amp J Zahringer (Eds) Dynamics of geomagnetically trapped radiation in Physics and chemistry inspace ed By (Vol 2) Berlin Springer

Roederer J G Hilton H H amp Schulz M (1973) Drift shell splitting by internal geomagnetic multipoles Journal of Geophysical Research78(1) 133ndash144 httpsdoiorg101029JA078i001p00133



Roederer J G amp Lejosne S (2018) Coordinates for representing radiation belt particle flux Journal of Geophysical Research SpacePhysics 123 1381ndash1387 httpsdoiorg1010022017JA025053

Roederer J G amp Zhang H (2014) Dynamics of magnetically trapped particles Foundations of the physics of radiation belts and spaceplasmas Berlin Heidelberg Astrophysics and Space Science Library Springer

Romero H amp Ganguli G (1994) Relaxation of the stressed plasma sheet boundary layer Geophysical Research Letters 21(8) 645ndash648httpsdoiorg10102993GL03385

Romero H Ganguli G Palmadesso P amp Dusenbery P B (1990) Equilibrium structure of the plasma sheet boundary layer‐lobeinterface Geophysical Research Letters 17(13) 2313ndash2316 httpsdoiorg101029GL017i013p02313

Ross J P J Meredith N P Glauert S A Horne R B amp Clilverd M A (2019) Effects of VLF transmitter waves on the inner belt andslot region Journal of Geophysical Research Space Physics 124 5260ndash5277 httpsdoiorg1010292019JA026716

Russell C T Holzer R E amp Smith E J (1970) OGO 3 observations of ELF noise in the magnetosphere The nature of equatorial noiseJournal of Geophysical Research 75(4) 755ndash768 httpsdoiorg101029JA075i004p00755

Saikin A A Zhang J‐C Allen R C Smith C W Kistler L M Spence H E et al (2015) The occurrence and wave properties of H+‐

He+‐ and O+‐band EMIC waves observed by the Van Allen Probes Journal of Geophysical Research Space Physics 120 7477ndash7492

httpsdoiorg1010022015JA021358Saikin A A Zhang J‐C Smith C W Spence H E Torbert R B amp Kletzing C A (2016) The dependence on geomagnetic conditions

and solar wind dynamic pressure of the spatial distributions of EMIC waves observed by the Van Allen Probes Journal of GeophysicalResearch Space Physics 121 4362ndash4377 httpsdoiorg1010022016JA022523

Saito S Miyoshi Y amp Seki K (2012) Relativistic electron microbursts associated with whistler chorus rising tone elements GEMSIS‐RBW simulations Journal of Geophysical Research 117 A10206 httpsdoiorg1010292012JA018020

Saito S Miyoshi Y amp Seki K (2010) A split in the outer radiation belt bymagnetopause shadowing Test particle simulations Journal ofGeophysical Research 115 A08210 httpsdoiorg1010292009JA014738

Sangalli L Partamies N Syrj suo M Enell C‐F Kauristie K amp M kinen S (2011) Performance study of the new EMCCD‐based all‐sky cameras for auroral imaging International Journal of Remote Sensing 32 2987ndash3003 httpsdoiorg101080014311612010541505

Santoliacutek O Gurnett D A Pickett J S Parrot M amp Cornilleau‐Wehrlin N (2004) A microscopic and nanoscopic view of storm‐timechorus on 31 March 2001 Geophysical Research Letters 31 L02801 httpsdoiorg1010292003GL018757

Santoliacutek O Gurnett D A Pickett J S Parrot M amp Cornilleau‐Wehrlin N (2003) Spatio‐temporal structure of storm‐time chorusJournal of Geophysical Research 108(A7) 1278 httpsdoiorg1010292002JA009791

Santoliacutek O Kletzing C A Kurth W S Hospodarsky G B amp Bounds S R (2014) Fine structure of large‐amplitude chorus wavepackets Geophysical Research Letters 41 293ndash299 httpsdoiorg1010022013GL058889

Santoliacutek O Nemec F Gereova K Macusova E de Conchy Y amp Cornilleau‐Wehrlin N (2004) Systematic analysis of equatorial noisebelow the lower hybrid frequency Annales de Geophysique 22(7) 2587ndash2595 httpsdoiorg105194angeo‐22‐2587‐2004

Santoliacutek O amp Parrot M (2000) Application of wave distribution function methods to an ELF hiss event at high latitudes Journal ofGeophysical Research 105(A8) 18885ndash18894

Santoliacutek O Parrot M amp Lefeuvre F (2003) Singular value decomposition methods for wave propagation analysis Radio Science 38(1)1010 httpsdoiorg1010292000RS002523

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Schiller Q Tu W Ali A F Li X Godinez H C Turner D L et al (2017) Simultaneous event‐specific estimates of transport loss andsource rates for relativistic outer radiation belt electrons Journal of Geophysical Research Space Physics 122 3354ndash3373 httpsdoiorg1010022016JA023093

Schulz M (1982) Earths radiation belts Reviews of Geophysics and Space Physics 20(3) 613ndash621Schulz M (1986) Eigenfunction methods in magnetospheric radial‐diffusion theory In T Chang et al (Eds) Ion acceleration in the

magnetosphere and ionosphere (pp 158ndash163) Washington D C AGU httpsdoiorg101029GM038p0158Schulz M amp Lanzerotti L (1974) Particle diffusion in the radiation belts Physics and chemistry in space Berlin SpringerSchulz M amp Newman A L (1988) Eigenfunctions of the magnetospheric radial‐diffusion operator Physica Scripta 37(4) 632ndash639Selesnick R Blake J Kolasinski W amp Fritz T (1997) A quiescent state of 3 to 8 MeV radiation belt electrons Geophysical Research

Letters 24(12) 1343ndash1346Selesnick R S (2012) Atmospheric scattering and decay of inner radiation belt electrons Journal of Geophysical Research 117 A08218

httpsdoiorg1010292012JA017793Selesnick R S (2015) Measurement of inner radiation belt electrons with kinetic energy above 1 MeV Journal of Geophysical Research

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belt CRAND and trapped solar protons Journal of Geophysical Research Space Physics 119 6541ndash6552 httpsdoiorg1010022014JA020188

Selesnick R S Baker D N Jaynes A N Li X Kanekal S G Hudson M K amp Kress B T (2016) Inward diffusion and loss ofradiation belt protons Journal of Geophysical Research Space Physics 121 1969ndash1978 httpsdoiorg1010022015JA022154

Selesnick R S Baker D N Kanekal S G Hoxie V C amp Li X (2018) Modeling the proton radiation belt with Van Allen ProbesRelativistic Electron‐Proton Telescope data Journal of Geophysical Research Space Physics 123 685ndash697 httpsdoiorg1010022017JA024661

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Selesnick R S Looper M D amp Mewaldt R A (2007) A theoretical model of the inner proton radiation belt Space Weather 5 S04003httpsdoiorg1010292006SW000275



Selesnick R S Looper M D Mewaldt R A amp Labrador A W (2007) Geomagnetically trapped antiprotons Geophysical ResearchLetters 34 L20104 httpsdoiorg1010292007GL031475

Shabansky V P (1971) Some processes in the magnetosphere Space Science Reviews 12(3) 299ndash418 httpsdoiorg101007BF00165511Shaw R R amp Gurnett D (1975) Electrostatic noise bands associated with the electron gyrofrequency and plasma frequency in the outer

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and related terrestrial phenomena during March 1991 IEEE Transactions on Nuclear Science 39 1754ndash1760 httpsdoiorg10110923211363

Sheeley B W M Moldwin B Rassoul H K amp Anderson R R (2001) An empirical plasmasphere and trough density model CRRESobservations Journal of Geophysical Research 106 25631ndash25641 httpsdoiorg1010292000JA000286

Shi R Li W Ma Q Green A Kletzing C A Kurth W S et al (2019) Properties of whistler mode waves in Earths plasmasphere andplumes Journal of Geophysical Research Space Physics 124 1035ndash1051 httpsdoiorg1010292018JA026041

Shi R Li W Ma Q Reeves G D Kletzing C A Kurth W S et al (2017) Systematic evaluation of low‐frequency hiss and energeticelectron injections Journal of Geophysical Research Space Physics 122 10263ndash10274 httpsdoiorg1010022017JA024571

Shi R Summers D Ni B Fennell J F Blake J B Spence H E amp Reeves G D (2016) Survey of radiation belt energetic electron pitchangle distributions based on the Van Allen Probes MagEIS measurements Journal of Geophysical Research Space Physics 1211078ndash1090 httpsdoiorg1010022015JA021724

Shklyar D amp Matsumoto H (2009) Oblique whistler‐mode waves in the inhomogeneous magnetospheric plasma Resonant interactionswith energetic charged particles Surveys in Geophysics 30 55 httpsdoiorg101007s10712‐009‐9061‐7

Shoji M amp Omura Y (2014) Spectrum characteristics of electro‐magnetic ion cyclotron triggered emissions and associated ener‐ geticproton dynamics Journal of Geophysical Research Space Physics 119 3480ndash3489 httpsdoiorg1010022013JA019695

Shprits Y Y (2016) Estimation of bounce resonant scattering by fast magnetosonic waves Geophysical Research Letters 43 998ndash1006httpsdoiorg1010022015GL066796

Shprits Y Y Daae M amp Ni B (2012) Statistical analysis of phase space density buildups and dropouts Journal of Geophysical Research117 A01219 httpsdoiorg1010292011JA016939

Shprits Y Y Drozdov A Y Spasojevic M Kellerman A C Usanova M E Engebretson M J et al (2016) Wave‐induced loss ofultra‐relativistic electrons in the Van Allen radiation belts Nature Communications 7(1) 883 httpsdoiorg101038ncomms12883

Shprits Y Y Elkington S R Meredith N P amp Subbotin D A (2008a) Review of modeling of losses and sources of relativistic electronsin the outer radiation belt I Radial transport Journal of Atmospheric and Solar ‐ Terrestrial Physics 70 1679 httpsdoiorg101016jjastp200806008

Shprits Y Y Elkington S R Meredith N P amp Subbotin D A (2008b) Review of modeling of losses and sources of relativistic electronsin the outer radiation belt II Local acceleration and loss Journal of Atmospheric and Solar ‐ Terrestrial Physics 70 1694 httpsdoiorg101016jjastp200806014

Shprits Y Y Kellerman A Aseev N Drozdov A Y amp Micortlis I (2017) Multi‐MeV electron loss in the heart of the radiation beltsGeophysical Research Letters 44 1204ndash1209 httpsdoiorg1010022016GL072258

Shprits Y Y Kellerman A C Drozdov A Y Spence H E Reeves G D amp Baker D N (2015) Combined convective and diffusivesimulations VERB‐4D comparison with 17 March 2013 Van Allen Probes observations Geophysical Research Letters 42 9600ndash9608httpsdoiorg1010022015GL065230

Shprits Y Y amp Ni B (2009) Dependence of the quasi‐linear scattering rates on the wave normal distribution of chorus waves Journal ofGeophysical Research 114 A11205 httpsdoiorg1010292009JA014223

Shprits Y Y Subbotin D Drozdov A Usanova M E Kellerman A Orlova K et al (2013) Unusual stable trapping of theultrare-lativistic electrons in the Van Allen radiation belts Nature Physics 9(11) 699ndash703 httpsdoiorg101038nphys2760

Shprits Y Y Subbotin D amp Ni B (2009) Evolution of electron fluxes in the outer radiation belt computed with the VERB code Journalof Geophysical Research 114 A11209 httpsdoiorg1010292008JA013784

Shprits Y Y Thorne R M Friedel R Reeves G D Fennell J Baker D N amp Kanekal S G (2006) Outward radial diffusion driven bylosses at magnetopause Journal of Geophysical Research 111 A11214 httpsdoiorg1010292006JA011657

Shprits Y Y Thorne R M Horne R B Glauert S A Cartwright M Russell C T et al (2006) Acceleration mechanism responsiblefor the formation of the new radiation belt during the 2003 Halloween solar storm Geophysical Research Letters 33 L05104 httpsdoiorg1010292005GL024256

Shprits Y Y Thorne R M Reeves G D amp Friedel R (2005) Radial diffusion modeling with empirical lifetimes Comparison withCRRES observations Annales de Geophysique 23(4) 1467ndash1471

Sicard‐Piet A Bourdarie S Boscher D Friedel R H W Thomsen M Goka T et al (2008) A new international geostationaryelectron model IGE‐2006 from 1 keV to 52 MeV Space Weather 6 S07003 httpsdoiorg1010292007SW000368

Singley GW JI Vette The AE‐4 model of the outer radiation zone electron environment NSSDC 72ndash06 (1972)Smart D F amp Shea M A (2002) A review of solar proton events during the 22nd solar cycle Advances in Space Research 30(4)

1033ndash1044 httpsdoiorg101016S0273-1177(02)00497-0Smart D F Shea M A amp Fluumlckiger E O (2000) Magnetospheric models and trajectory computations Space Science Reviews 93(12)

305ndash333 httpsdoiorg101023A1026556831199Sorathia K Merkin V G Ukhorskiy A Y Allen R C Nykyri K amp Wing S (2019) Solar wind ion entry into the magnetosphere

during northward IMF Journal of Geophysical Research Space Physics 124 5461ndash5481 httpsdoiorg1010292019JA026728Sorathia K A Merkin V G Ukhorskiy A Y Mauk B H amp Sibeck D G (2017) Energetic particle loss through the magnetopause A

combined global MHD and test‐particle study Journal of Geophysical Research Space Physics 122 9329ndash9343 httpsdoiorg1010022017JA024268

Sorathia K A Ukhorskiy A Y Merkin V G Fennell J F amp Claudepierre S G (2018) Modeling the depletion and recovery of theouter radiation belt during a geomagnetic storm Combined MHD and test particle simulations Journal of Geophysical Research SpacePhysics 123 5590ndash5609 httpsdoiorg1010292018JA025506

Spanswick E Donovan E Friedel R amp Korth A (2007) Ground based identification of dispersionless electron injections GeophysicalResearch Letters 34 L03101 httpsdoiorg1010292006GL02839

Spasojevic M Shprits Y Y amp Orlova K (2015) Global empirical models of plasmaspheric hiss using Van Allen Probes Journal ofGeophysical Research Space Physics 120 10 370ndash10383 httpsdoiorg1010022015JA021803



Spence H E Reeves G D Baker D N Blake J B Bolton M Bourdarie S et al (2013) Science goals and overview of the EnergeticParticle Composition and Thermal Plasma (ECT) suite on NASAs Radiation Belt Storm Probes (RBSP) mission Space Science Reviews179(1ndash4) 311ndash336 httpsdoiorg101007s11214‐013‐0007‐5

Spjeldvik W N (1977) Equilibrium structure of equatorially mirroring radiation belt proton Journal of Geophysical Research 82(19)2801ndash2808 httpsdoiorg101029JA082i019p02801

Spjeldvik W N (1979) Expected charge states of energetic ions in the magnetosphere Space Science Reviews 23(1979) 499ndash538Spjeldvik W N (1996) Numerical modeling of stably and transiently confined energetic heavy ion radiation in the Earths magnetosphere

Radiation Measurements 26(3) 309ndash320Spjeldvik W N Bourdarie S amp Boscher D (2002) Solar origin iron ions in the Earths radiation belts Multi‐dimensional equilibrium

configuration modeling with charge states 1 through 12 Advances in Space Research 30(12) 2835ndash2838Spjeldvik W N and L R Lyons (1980) On the predictability of radiation belt electron precipitation into the Earths atmosphere following

magnetic storms in conference proceedings Solar‐Terrestrial Predictions Proceedings Volume 4 prediction of terrestrial effects of solaractivity (R F Donnelly editor) p B59

Spjeldvik W N amp Thorne R M (1975) The cause of storm after effects in the middle latitude D‐region ionosphere Journal of Atmosphericand Terrestrial Physics 37(5) 777ndash795 httpsdoiorg1010160021‐9169(75)90021‐5

Spjeldvik W N amp Thorne R M (1976) Maintenance of the middle latitude nocturnal D‐layer by energetic electron precipitation Pureand applied geophysics 114(4) 497ndash508 httpsdoiorg101007BF00875646

Stix T H (1992) Waves in plasmas New York SpringerStorey L R O amp Lefeuvre F (1979) The analysis of 6‐component measurements of a random electromagnetic wave field in a magne-

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aurores boreales Archives des Sciences Physiques et Naturelles 24Stoumlrmer C (1955) The polar Aurora London Oxford University PressSu Z Gao Z Zheng H Wang Y Wang S Spence H E amp Wygant J R (2017) Rapid loss of radiation belt relativistic electrons by

EMIC waves Journal of Geophysical Research Space Physics 122 9880ndash9897 httpsdoiorg1010022017JA024169Su Z Gao Z Zhu H Li W Zheng H Wang Y et al (2016) Nonstorm time dropout of radiation belt electron fluxes on 24 September

2013 Journal of Geophysical Research Space Physics 121 6400ndash6416 httpsdoiorg1010022016JA022546Su Z Liu N Zheng H Wang Y amp Wang S (2018) Large‐amplitude extremely low frequency hiss waves in plasmaspheric plumes

Geophysical Research Letters 45 565ndash577 httpsdoiorg1010022017GL076754Su Z Xiao F Zheng H He Z Zhu H Zhang M et al (2014) Nonstorm time dynamics of electron radiation belts observed by the Van

Allen Probes Geophysical Research Letters 41 229ndash235 httpsdoiorg1010022013GL058912Su Z Xiao F Zheng H amp Wang S (2010) STEERB A three‐dimensional code for storm‐time evolution of electron radiation belt

Journal of Geophysical Research 115 A09208 httpsdoiorg1010292009JA015210Su Z Xiao F Zheng H amp Wang S (2011a) Radiation belt electron dynamics driven by adiabatic transport radial diffusion and wave‐

particle interactions Journal of Geophysical Research 116 A04205 httpsdoiorg1010292010JA016228Su Z Xiao F Zheng H amp Wang S (2011b) CRRES observation and STEERB simulation of the 9 October 1990 electron radiation belt

dropout event Geophysical Research Letters 38 L06106 httpsdoiorg1010292011GL046873Su Z Zheng H Chen L amp Wang S (2011) Numerical simulations of storm‐time outer radiation belt dynamics by wave‐particle

interactions including cross diffusion Journal of Atmospheric and Solar ‐ Terrestrial Physics 73 95ndash105 httpsdoiorg101016jjastp200908002

Su Z Zhu H Xiao F Zheng H Wang Y He Z et al (2014) Intense duskside lower band chorus waves observed by Van Allen ProbesGeneration and potential acceleration effect on radiation belt electrons Journal of Geophysical Research Space Physics 119 4266ndash4273httpsdoiorg1010022014JA019919

Subbotin D A amp Shprits Y Y (2009) Three‐dimensional modeling of the radiation belts using the Versatile Electron Radiation Belt(VERB) code Space Weather 7 S10001 httpsdoiorg1010292008SW000452

Subbotin D A amp Shprits Y Y (2012) Three‐dimensional radiation belt simulations in terms of adiabatic invariants using a singlenumerical grid Journal of Geophysical Research 117 A05205 httpsdoiorg1010292011JA017467

Subbotin D A Shprits Y Y amp Ni B (2010) Three‐dimensional VERB radiation belt simulations including mixed diffusion Journal ofGeophysical Research 115 A03205 httpsdoiorg1010292009JA015070

Subbotin D A Shprits Y Y amp Ni B (2011) Long‐term radiation belt simulation with the VERB 3‐D code Comparison with CRRESobservations Journal of Geophysical Research 116 A12210 httpsdoiorg1010292011JA017019

Summers D (2005) Quasi‐linear diffusion coefficients for field‐aligned electromagnetic waves with applications to the magnetosphereJournal of Geophysical Research 110 A08213 httpsdoiorg1010292005JA011159

Summers D (2011) State of the art in radiation belt research Eos 92(49) 6 December 2011Summers D Ni B amp Meredith N P (2007) Timescales for radiation belt electron acceleration and loss due to resonant wave‐particle

interactions 2 Evaluation for VLF chorus ELF hiss and electromagnetic ion cyclotron waves Journal of Geophysical Research 112A04207 httpsdoiorg1010292006JA011993

Summers D Ni B Meredith N P Horne R B Thorne R M Moldwin M B amp Anderson R R (2008) Electron scattering bywhistler‐mode ELF hiss in plasmaspheric plumes Journal of Geophysical Research 113 A04219 httpsdoiorg1010292007JA012678

Summers D Tang R amp Omura Y (2011) Effects of nonlinear wave growth on extreme radiation belt electron fluxes Journal ofGeophysical Research 116 A10226 httpsdoiorg1010292011JA016602

Summers D Thorne R M amp Xiao F (1998) Relativistic theory of wave‐particle resonant diffusion with application to electron accel-eration in the magnetosphere Journal of Geophysical Research 103 20487ndash20500 httpsdoiorg10102998JA01740

Summers D Mann R Baker D N amp Max‐Gotthard Schulz (2013) In D Summers et al (Eds) Dynamics of the Earths radiation beltsand inner magnetosphere Geophysical Monograph Series (Vol 199 pp 213ndash223) Washington D C AGU

Summers D Omura Y Nakamura S amp Kletzing C A (2014) Fine structure of plasmaspheric hiss Journal of Geophysical ResearchSpace Physics 119 9134ndash9149 httpsdoiorg1010022014JA020437

Tang C L Xie X J Ni B Su Z P Reeves G D Zhang J C et al (2018) Rapid enhancements of the seed populations in the heart ofthe Earths outer radiation belt A multicase study Journal of Geophysical Research Space Physics 123 4895ndash4907 httpsdoiorg1010292017JA025142

Tao X amp Bortnik J (2010) Nonlinear interactions between relativistic radiation belt electrons and oblique whistler mode wavesNonlinear Processes in Geophysics 17 599



Tao X Bortnik J Thorne R M Albert J M amp Li W (2012) Effects of amplitude modulation on nonlinear interactions betweenelectrons and chorus waves Geophysical Research Letters 39 L06102 httpsdoiorg1010292012GL051202

Tao X Chen L Liu X Lu Q amp Wang S (2017) Quasilinear analysis of saturation properties of broadband whistler mode wavesGeophysical Research Letters 44 8122ndash8129 httpsdoiorg1010022017GL074881

Tao X Thorne R M Li W Ni B Meredith N P amp Horne R B (2011) Evolution of electron pitch angle distributions followinginjection from the plasma sheet Journal of Geophysical Research 116 A04229 httpsdoiorg1010292010JA016245

Tejero E M Crabtree C Blackwell D D Amatucci W E Mithaiwala M Ganguli G amp Rudakov L (2015a) Laboratory studies ofnonlinear whistler wave processes in the Van Allen radiation belts Physics of Plasmas 22(9) 091503

Tejero E M Crabtree C Blackwell D D Amatucci W E Mithaiwala M Ganguli G amp Rudakov L (2015b) Nonlinear generation ofelectromagnetic waves through induced scattering by thermal plasma Scientific Reports 5 17852

Tejero E M Crabtree C Blackwell D D Amatuci W E Ganguli G amp Rudakov L (2016) Experimental characterization of nonlinearprocesses of whistler branch waves Physics of Plasmas 23 055707 (2016) httpsdoiorg10106314946020

Tetrick S S Engebretson M J Posch J L Olson C N Smith C W Denton R E et al (2017) Location of intense electromagnetic ioncyclotron (EMIC) wave events relative to the plasmapause Van Allen Probes observations Journal of Geophysical Research SpacePhysics 122 4064ndash4088 httpsdoiorg1010022016JA023392

Thaller S A et al (2015) Van Allen probes investigation of the large‐scale duskward electric field and its role in ring current formationand plasmasphere erosion in the 1 June 2013 storm J Geophys Res Space Physics 120 4531ndash4543 httpsdoi1010022014JA020875

Thaller S A Wygant J R Cattell C A Breneman A W Tyler E Tian S et al (2019) Solar rotation period driven modulations ofplasmaspheric density and convective electric field in the inner magnetosphere Journal of Geophysical Research Space Physics 1241726ndash1737 httpsdoiorg1010292018JA026365

Thomsen M F Denton M H Jordanova V K Chen L amp Thorne R M (2011) Free energy to drive equatorial magnetosonic waveinstability at geosynchronous orbit Journal of Geophysical Research 116 A08220 httpsdoiorg1010292011JA016644

Thomsen M F Goertz C K amp Van Allen J A (1977a) A determination of the L dependence of the radial diffusion coefficient forprotons in Jupiters inner magnetosphere Journal of Geophysical Research 82(25) 3655ndash3658 httpsdoiorg101029JA082i025p03655

Thomsen M F Goertz C K amp Van Allen J A (1977b) On determining magnetospheric diffusion coefficients from the observed effectsof Jupiters satellite Io Journal of Geophysical Research 82(35) 5541ndash5550 httpsdoiorg101029JA082i035p05541

Thorne R M (2010) Radiation belt dynamics The importance of wave‐particle interactions Geophysical Research Letters 37 L22107httpsdoiorg1010292010GL044990

Thorne R M Church S amp Gorney D (1979) On the origin of plasmaspheric hiss The importance of wave propagation and the plas-mapause Journal of Geophysical Research 84(A9) 5241ndash5247 httpsdoiorg101029JA084iA09p05241

Thorne R M amp Kennel C F (1971) Relativistic electron precipitation during magnetic storm main phase Journal of GeophysicalResearch 76(19) 4446ndash4453 httpsdoiorg101029JA076i019p04446

Thorne R M Li W Ni B Ma Q Bortnik J Chen L et al (2013) Rapid local acceleration of relativistic radiation belt electrons bymagnetospheric chorus Nature 504(7480) 411ndash414 httpsdoiorg101038nature12889

Thorne R M Ni B Tao X Horne R B amp Meredith N P (2010) Scattering by chorus waves as the dominant cause of diffuse auroraprecipitation Nature 467(7318) 943ndash946

Thorne R M Smith E J Burton R K amp Holzer R E (1973) Plasmaspheric hiss Journal of Geophysical Research 78(10) 1581ndash1596httpsdoiorg101029JA078i010p01581

Toacuteth G Sokolov I V Gombosi T I Chesney D R Clauer C Zeeuw D L D et al (2005) Space weather modeling framework A newtool for the space science community Journal of Geophysical Research 110 A12226 httpsdoiorg1010292005JA011126

Toacuteth G van der Holst B Sokolov I V de Zeeuw D L Gombosi T I Fang F et al (2012) Journal of Computational Physics 231(3)870ndash903 httpsdoiorg101016jjcp201102006

Trakhtengerts V Y (1999) A generation mechanism for chorus emission Annales Geophysicae 17(1) 95ndash100 httpsdoiorg101007s00585‐999‐0095‐4

Tsurutani B T Falkowski B J Pickett J S Santolik O amp Lakhina G S (2015) Plasmaspheric hiss properties Observations fromPolar Journal of Geophysical Research Space Physics 120 414ndash431 httpsdoiorg1010022014JA020518

Tsurutani B T amp Smith E J (1974) Postmidnight chorus A substorm phenomenon Journal of Geophysical Research 79(1) 118ndash127httpsdoiorg101029JA079i001p00118

Tsyganenko N A (1989) A magnetospheric magnetic field model with a warped tail current sheet Planetary and Space Science 37(1)5ndash20 httpsdoiorg1010160032‐0633(89)90066‐4

Tsyganenko N A amp Sitnov M I (2005) Modeling the dynamics of the inner magnetosphere during strong geomagnetic storms Journal ofGeophysical Research 110 A03208 httpsdoiorg1010292004JA010798

Tu W Li X Chen Y Reeves G D amp Temerin M (2009) Storm‐dependent radiation belt electron dynamics Journal of GeophysicalResearch 114(A2) A02217 httpsdoiorg1010292008JA013480

Tu W Cowee M M amp Liu K (2014) Modeling the loss of inner belt protons by magnetic field line curvature scattering Journal ofGeophysical Research Space Physics 119 5638ndash5650 httpsdoiorg1010022014JA019864

TuW Cunningham G S Chen Y Henderson M G Camporeale E amp Reeves G D (2013) Modeling radiation belt electron dynamicsduring GEM challenge intervals with the DREAM3D diffusion model Journal of Geophysical Research Space Physics 118 6197ndash6211httpsdoiorg101002jgra50560

Tu W Cunningham G S Chen Y Morley S K Reeves G D Blake J B et al (2014) Event‐specific chorus wave and electron seedpopulation models in DREAM3D using the Van Allen Probes Geophysical Research Letters 41 1359ndash1366 httpsdoiorg1010022013GL058819

Tu W Elkington S R Li X Liu W amp Bonnell J (2012) Quantifying radial diffusion coefficients of radiation belt electrons based onglobal MHD simulation and spacecraft measurements Journal of Geophysical Research 117 A10210 httpsdoiorg1010292012JA017901

Tu W Li W Albert J M amp Morley S K (2019) Quantitative assessment of radiation belt modeling Journal of Geophysical ResearchSpace Physics 124 898ndash904 httpsdoiorg1010292018JA026414

Turner D L Angelopoulos V Li W Bortnik J Ni B Ma Q et al (2014) Competing source and loss mechanisms due to wave‐particleinteractions in Earths outer radiation belt during the 30 September to 3 October 2012 geomag‐ netic storm Journal of GeophysicalResearch Space Physics 119 1960ndash1979 httpsdoiorg1010022014JA019770



Turner D L Angelopoulos V Li W Hartinger M D Usanova M Mann I R et al (2013) On the storm‐time evolution of relativisticelectron phase space density in Earths outer radiation belt Journal of Geophysical Research Space Physics 118 2196ndash2212 httpsdoiorg101002jgra50151

Turner D L Claudepierre S G Fennell J F OBrien T P Blake J B Lemon C et al (2015) Energetic electron injections deep intothe inner magnetosphere associated with substorm activity Geophysical Research Letters 42 2079ndash2087 httpsdoiorg1010022015GL063225

Turner D L Kilpua E K J Hietala H Claudepierre S G OBrien T P Fennell J F et al (2019) The response of Earths electronradiation belts to geomagnetic storms Statistics from the Van Allen Probes era including effects from different storm drivers Journal ofGeophysical Research Space Physics 124 1013ndash1034 httpsdoiorg1010292018JA026066

Turner D L Shprits Y Hartinger M amp Angelopoulos V (2012) Explaining sudden losses of outer radiation belt electrons duringgeomagnetic storms Nature Physics 8(3) 208ndash212 httpsdoiorg101038nphys2185

Turner D L amp Ukhorskiy A Y (2020) Outer radiation belt losses by magnetopause incursions and outward radial transport new insightand outstanding questions from the Van Allen Probes era httpsdoiorg101016B978‐0‐12‐813371‐200001‐9

Turunen E Kero A Verronen P T Miyoshi Y Oyama S‐I amp Saito S (2016) Mesospheric ozone destruction by high‐energy electronprecipitation associated with pulsating aurora Journal of Geophysical Research Atmospheres 121 11852ndash11861 httpsdoiorg1010022016JD025015

Ukhorskiy A Y Anderson B J Takahashi K amp Tsyganenko N A (2006) Impact of ULF oscillations in solar wind dynamic pressure onthe outer radiation belt electrons Geophysical Research Letters 33 L06111 httpsdoiorg1010292005GL024380

Ukhorskiy A Y amp Sitnov M I (2008) Radial transport in the outer radiation belt due to global magnetospheric com‐ pressions Journal ofAtmospheric and Solar ‐ Terrestrial Physics 70(14) 1714ndash1726 httpsdoiorg101016jjastp200807018

Ukhorskiy A Y amp Sitnov M I (2012) Dynamics of radiation belt particles Space Science Reviews 179 545ndash578 httpsdoiorg101007s11214-012-9938-5

Ukhorskiy A Y Sitnov M I Millan R M amp Kress B T (2011) The role of drift orbit bifurcations in energization and loss of electrons inthe outer radiation belt Journal of Geophysical Research 116 A09208 httpsdoiorg1010292011JA016623

Ukhorskiy A Y Sitnov M I Millan R M Kress B T Fennell J F Claudepierre S G amp Barnes R J (2015) Global storm timedepletion of the outer electron belt Journal of Geophysical Research Space Physics 120 2543ndash2556 httpsdoiorg1010022014JA020645

Ukhorskiy A Y SitnovM I Mitchell D G Takahashi K Lanzerotti L J ampMauk B H (2014) Rotationnally driven ldquozebra stripesrdquo inEarths inner radiation belt Nature 507(7492) 338ndash340 httpsdoiorg101038nature13046

Ukhorskiy A Y Sorathia K A Merkin V G Sitnov M I Mitchell D G amp Gkioulidou M (2018) Ion trapping and acceleration atdipolarization fronts High‐resolution MHDtest‐particle simulations Journal of Geophysical Research Space Physics 123 5580ndash5589httpsdoiorg1010292018JA025370

Usanova M E Drozdov A Orlova K Mann I R Shprits Y Robertson M T et al (2014) Effect of EMIC waves on relativistic andultrarelativistic electron populations Ground‐based and Van Allen Probes observations Geophysical Research Letters 41 1375ndash1381httpsdoiorg1010022013GL059024

Usanova M E Malaspina D M Jaynes A N Bruder R J Mann I R Wygant J R amp Ergun R E (2016) Van Allen Probes obser-vations of oxygen cyclotron harmonic waves in the inner magnetosphere Geophysical Research Letters 43 8827ndash8834 httpsdoiorg1010022016GL070233

Vampola A L (1997) Outer zone energetic electron environment update in Conference on the high energy radiation background inspace Workshop Record pp 128ndash136 doihttpsdoiorg101109CHERBS1997660263

Vampola A L Osborn J V amp Johnson B M (1992) CRRES magnetic electron spectrometer Journal of Spacecraft and Rockets 29(4)592ndash595 httpsdoiorg102514325504

Van Allen J A (1959) The geomagnetically trapped corpuscular radiation Journal of Geophysical Research 64(11) 1683ndash1689 httpsdoiorg101029JZ064i011p01683

Van Compernolle B An X Bortnik J Thorne R M Pribyl P amp Gekelman W (2015) Excitation of chirping whistler waves in alaboratory plasma Physical Review Letters 114(24) 245002

van de Kamp M Rodger C J Seppaumllauml A Clilverd M A amp Verronen P T (2018) An updated model providing long‐term data sets ofenergetic electron precipitation including zonal dependence Journal of Geophysical Research Atmospheres 123 9891ndash9915 httpsdoiorg1010292017JD028253

van de Kamp M Seppaumllauml A Clilverd M A Rodger C J Verronen P T amp Whittaker I C (2016) A model providing long‐term datasets of energetic electron precipitation during geomagnetic storms Journal of Geophysical Research Atmospheres 121 12520ndash12540httpsdoiorg1010022015JD024212

Varotsou A Boscher D Bourdarie S Horne R B Glauert S A amp Meredith N P (2005) Simulation of the outer radiation beltelectrons near geosynchronous orbit including both radial diffusion and resonant interaction with Whistler‐mode chorus wavesGeophysical Research Letters 32 L19106 httpsdoiorg1010292005GL023282

Varotsou A Boscher D Bourdarie S Horne R B Meredith N P Glauert S A amp Friedel R H (2008) Three‐dimensional testsimulations of the outer radiation belt electron dynamics including electron‐chorus resonant interactions Journal of GeophysicalResearch 113 A12212 httpsdoiorg1010292007JA012862

Vedenov A A Velikhov E P amp Sagdeev R Z (1961) Nonlinear oscillations of rare field plasma Nuclear Fusion 1(2) 82ndash100 httpsdoiorg1010880029‐551512003

Vernov S N A E Chudakov P V Vakulov and Y I Logachev (1959) Study of terrestrial corpuscular radiation and cosmic rays duringflight of the cosmic rocket Doklady Akad Nauk SSSR 125 304

Vette JI (1991) The AE‐8 trapped electron model environment (NSSDCWDC‐A‐RampS 91ndash24) Greenbelt MD NASAGoddard Space FlightCenter

Voss H D Walt M Imhof W L Mobilia J amp Inan U S (1998) Satellite observations of lightning‐induced electron precipitationJournal of Geophysical Research 103(A6) 11725ndash11744

Walt M (1966) Loss rates of trapped electrons by atmospheric collisions In B M McCormac (Ed) Radiation trapped in the Earthsmagnetic field (pp 337ndash351) Dordrecht Springer Netherlands

Walt M (1970) Radial diffusion of trapped particles In B M McCormac (Ed) Particles and fields in the magnetosphere (pp 410ndash415)Dordrecht Netherlands Springer

Walt M amp Farley T (1976) The Physical mechanisms of the inner Van Allen belt Fundamentals of Cosmic Physics 2 1ndash110



Walt M ampMacDonald WM (1964) The influence of the Earths atmosphere on geomagnetically trapped particles Reviews of Geophysics2(4) 543ndash577 httpsdoiorg101029RG002i004p00543

Wang D Shprits Y Y Zhelavskaya I S Agapitov O V Drozdov A Y amp Aseev N A (2019) Analytical chorus wave model derivedfrom Van Allen Probe observations Journal of Geophysical Research Space Physics 124 1063ndash1084 httpsdoiorg1010292018JA026183

Warren H P amp Mauel M E (1995) Observation of chaotic particle transport induced by drift‐resonant fluctuations in a magnetic dipolefield Physical Review Letters 74(8) 1351ndash1354

Welling D T Jordanova V K Zaharia S G Glocer A amp Toth G (2011) The effects of dynamic ionospheric outflow on the ringcurrent Journal of Geophysical Research 116 A00J19 httpsdoiorg1010292010JA015642

Welling D T Koller J amp Camporeale E (2013) Verification of SpacePys radial diffusion radiation belt model Geoscientific ModelDevelopment 5 277ndash287 wwwgeosci‐model‐devnet52772012doi105194gmd‐5‐277‐2012

Wiltberger M Merkin V Lyon J G amp Ohtani S (2015) High‐resolution global magnetohydrodynamic simulation of bursty bulk flowsJournal of Geophysical Research Space Physics 120 4555ndash4566 httpsdoiorg1010022015JA021080

Woodger L A Halford A J Millan R M McCarthy M P Smith D M Bowers G S et al (2015) A summary of the BARRELcampaigns Technique for studying electron precipitation Journal of Geophysical Research Space Physics 120 4922ndash4935 Retrievedfrom httpsdoiorg1010022014JA020874

Woodger L A Millan R M Li Z amp Sample J G (2018) Impact of background magnetic field for EMIC wave‐driven electron preci-pitation Journal of Geophysical Research Space Physics 123 8518ndash8532 httpsdoiorg1010292018JA025315

Woodroffe J R Jordanova V K Funsten H O Streltsov A V Bengtson M T Kletzing C A et al (2017) Van Allen Probesobservations of structured whistler mode activity and coincident electron Landau acceleration inside a remnant plasmaspheric plumeJournal of Geophysical Research Space Physics 122 3073ndash3086 httpsdoiorg1010022015JA022219

Wu S Denton R E Liu K amp Hudson M K (2015) One‐ and two‐dimensional hybrid simulations of whistler mode waves in a dipolefield Journal of Geophysical Research Space Physics 120 1908ndash1923 httpsdoiorg1010022014JA020736

Wu Y Tao X Lu Q amp Wang S (2019) Saturation properties of whistler wave instability in a plasma with two electron componentsJournal of Geophysical Research Space Physics 124 5121ndash5128 httpsdoiorg1010292019JA026752

Wygant J R Bonnell J W Goetz K Ergun R E Mozer F S Bale S D et al (2013) The Electric Field andWaves instruments on theRadiation Belt Storm Probes mission Space Science Reviews 179(1‐4) 183ndash220 httpsdoiorg101007s11214‐013‐0013‐7

Xiang Z Li X Selesnick R Temerin M A Ni B Zhao H et al (2019) Modeling the quasi‐trapped electron fluxes from Cosmic RayAlbedo Neutron Decay (CRAND) Geophysical Research Letters 46 1919ndash1928 httpsdoiorg1010292018GL081730

Xiang Z Tu W Li X Ni B Morley S K amp Baker D N (2017) Understanding the mechanisms of radiation belt dropouts observed byVan Allen Probes Journal of Geophysical Research Space Physics 122 9858ndash9879 httpsdoiorg1010022017JA024487

Xiang Z Tu W Ni B Henderson M G amp Cao X (2018) A statistical survey of radiation belt dropouts observed by Van Allen ProbesGeophysical Research Letters 45 8035ndash8043 httpsdoiorg1010292018GL078907

Xudong G Zhengyu Z Binbin N Yuri S amp Chen Z (2011) Statistical analysis of pitch angle distribution of radiation belt energeticelectrons near the geostationary orbit CRRES observations Journal of Geophysical Research 116 A01208 httpsdoiorg1010292010JA016052

Yoon P H Lee J Hwang J Seough J amp Choe G (2019) Whistler instability driven by electron thermal ring distribution with mag-netospheric application Journal of Geophysical Research Space Physics 124 5289ndash5301 httpsdoiorg1010292019JA026687

Yu J Li L Y Cao J B Chen L Wang J amp Yang J (2017) Propagation characteristics of plasmaspheric hiss Van Allen Probeobservations and global empirical models Journal of Geophysical Research Space Physics 122 4156ndash4167 httpsdoiorg1010022016JA023372

Yu J Li L Y Cui J amp Wang J (2018) Ultrawideband rising‐tone chorus waves observed inside the oscillating plasmapause Journal ofGeophysical Research Space Physics 123 6670ndash6678 httpsdoiorg1010292018JA025875

Yu Y Jordanova V Zaharia S Koller J Zhang J amp Kistler L M (2011) Validation study of the magnetically self‐consistent innermagnetosphere model RAM‐SCB Journal of Geophysical Research 117 A03222 httpsdoiorg1010292011JA017321

Yu Y Jordanova V K Ridley A J Toth G amp Heelis R (2017) Effects of electric field methods on modeling the midlatitude iono-spheric electrodynamics and inner magnetosphere dynamics Journal of Geophysical Research Space Physics 122 5321ndash5338 httpsdoiorg1010022016JA023850

Yu Y Liemohn M W Jordanova V K Lemon C amp Zhang J (2019) Recent advancements and remaining challenges associated withinner magnetosphere cross‐ energypopulation interactions (IMCEPI) Journal of Geophysical Research Space Physics 124 886ndash897httpsdoiorg1010292018JA026282

Zaharia S Jordanova V K Thomsen M F amp Reeves G D (2006) Self‐consistent modeling of magnetic fields and plasmas in the innermagnetosphere Application to a geomagnetic storm Journal of Geophysical Research 111 A11S14 httpsdoiorg1010292006JA011619

Zaharia S Jordanova V K Welling D amp Toacuteth G (2010) Self‐consistent inner magnetosphere simulation driven by a global MHDmodel Journal of Geophysical Research 115 A12228 httpsdoiorg1010292010JA015915

Zaacutehlava J Němec F Santoliacutek O Kolmašovaacute I Hospodarsky G B Parrot M et al (2019) Lightning contribution to overall whistlermode wave intensities in the plasmasphere Geophysical Research Letters 46 8607ndash8616 httpsdoiorg1010292019GL083918

Zhang B K Sorathia J Lyon V G Merkin and M Wiltberger (2018) A three‐dimensional finite‐volume MHD solver in non‐orthogonalcurvilinear geometry GAMERA a reinvention of LFM Ap J Suppl httpsarxivorgabs181010861

Zhang K Li X Zhao H Schiller Q Khoo L Y Xiang Z et al (2019) Cosmic Ray Albedo Neutron Decay (CRAND) as a source ofinner belt electrons Energy spectrum study Geophysical Research Letters 46 544ndash552 httpsdoiorg1010292018GL080887

Zhang W Fu S Gu X Ni B Xiang Z Summers D et al (2018) Electron scattering by plasmaspheric hiss in a nightside plumeGeophysical Research Letters 45 4618ndash4627 httpsdoiorg1010292018GL077212

Zhang W Ni B Huang H Summers D Fu S Xiang Z et al (2019) Statistical properties of hiss in plasmaspheric plumes andassociated scattering losses of radiation belt electrons Geophysical Research Letters 46 5670ndash5680 httpsdoiorg1010292018GL081863

Zhang X‐J Angelopoulos V Ni B amp Thorne R M (2015) Predominance of ECH wave contribution to diffuse aurora in Earths outermagnetosphere Journal of Geophysical Research Space Physics 120 295ndash309 httpsdoiorg1010022014JA020455

Zhang X‐J Li W Ma Q Thorne R M Angelopoulos V Bortnik J et al (2016) Direct evidence for EMIC wave scattering of rela-tivistic electrons in space Journal of Geophysical Research Space Physics 121 6620ndash6631 httpsdoiorg1010022016JA022521



Zhao H Baker D N Li X Jaynes A N amp Kanekal S G (2019) The effects of geomagnetic storms and solar wind conditions on theultrarelativistic electron flux enhancements Journal of Geophysical Research Space Physics 124 1948ndash1965 httpsdoiorg1010292018JA026257

Zhao H Johnston W R Baker D N Li X Ni B Jaynes A N et al (2019) Characterization and evolution of radiation belt electronenergy spectra based on the Van Allen Probes measurements Journal of Geophysical Research Space Physics 124 4217ndash4232 httpsdoiorg1010292019JA026697

Zhao H Li X Baker D N Claudepierre S G Fennell J F Blake J B et al (2016) Ring current electron dynamics during geo-magnetic storms based on the Van Allen Probes measurements Journal of Geophysical Research Space Physics 121 3333ndash3346 httpsdoiorg1010022016JA022358

Zhao H Li X Blake J B Fennell J F Claudepierre S G Baker D N et al (2014a) Peculiar pitch angle distribution of relativisticelectrons in the inner radiation belt and slot region Geophysical Research Letters 41 2250ndash2257 httpsdoiorg1010022014GL059725

Zhao H Li X Blake J B Fennell J F Claudepierre S G Baker D N et al (2014b) Characteristics of pitch angle distributions ofhundreds of keV electrons in the slot region and inner radiation belt Journal of Geophysical Research Space Physics 119 9543ndash9557httpsdoiorg1010022014JA020386

Zhelavskaya I S Spasojevic M Shprits Y Y amp Kurth W S (2016) Automated determination of electron density from electric fieldmeasurements on the Van Allen Probes spacecraft Journal of Geophysical Research Space Physics 121(5) 4611ndash4625 httpsdoiorg1010022015JA022132

Zhelavskaya I S Shprits Y Y amp Spasojević M (2017) Empirical modeling of the plasmasphere dynamics using neural networksJournal of Geophysical Research Space Physics 122 11227ndash11244 httpsdoiorg1010022017JA024406

Zheng H Holzworth R H Brundell J B Jacobson A R Wygant J R Hospodarsky G B et al (2016) A statistical study of whistlerwaves observed by Van Allen Probes (RBSP) and lightning detected by WWLLN Journal of Geophysical Research Space Physics 1212067ndash2079 httpsdoiorg1010022015JA022010

Zhu H Liu X amp Chen L (2019) Triggered plasmaspheric hiss Rising tone structures Geophysical Research Letters 46 5034ndash5044httpsdoiorg1010292019GL082688

Zhu H Shprits Y Y Spasojevic M amp Drozdov A Y (2019) New hiss and chorus waves diffusion coefficient parameterizations from theVan Allen Probes and their effect on long‐term relativistic electron radiation‐belt VERB simulations Journal of Atmospheric and Solar ‐Terrestrial Physics 193 105090 httpsdoiorg101016jjastp2019105090

Zou Y Nishimura Y Lyons L R amp Donovan E F (2012) A statistical study of the relative locations of electron and proton auroralboundaries inferred from meridian scanning photometer observations Journal of Geophysical Research 117 A06206 httpsdoiorg1010292011JA017357



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The motion of a charged particle in the Earths magnetic field was first formulated by Stoumlrmer (2018) andwas subsequently studied by him and several others in connection with auroral phenomena and cosmicrays (Stoumlrmer 2017) The motion and the stability of charged and trapped particles in Earths magneticfield was then well established by 1960 (eg Northrop amp Teller 1960 Dragt 1965 Faumllthammar 1965)and has provided the theoretical basis for the presence of Earths radiation belts discovered by pioneeringspace missions (Van Allen 1959 Vernov et al 1959) It was shown that in the approximately dipolarmagnetic field of the inner magnetosphere including the Earths Van Allen radiation belts charged par-ticles undergo quasiperiodic motion composed of gyro bounce and gradient‐curvature drift motionseach associated with an adiabatic invariant This set of three invariants defines a stable drift shell encir-cling Earth Subsequent experiments revealed that particle intensities across the belts can vary signifi-cantly with time which requires violation of one or more of the adiabatic invariants The theoreticalinterpretation of the variability of radiation belt intensities was largely inspired by the experiments inparticle acceleration by random‐phased electrostatic waves in synchrocyclotron devices and by the subse-quent development of the theory of weak plasma turbulence It was thus suggested that the adiabaticinvariants of trapped particles can be violated by small‐amplitude waves which resonantly interact withthe quasiperiodic particle motion (Balescu 1960 Lenard 1960 Vedenov et al 1961) Since both the den-sity and energy density of radiation belt particles are negligible compared to other plasma populationstheir motion does not affect the fields that govern them (with some exceptions eg chorus waves)Thus it was suggested that the evolution of radiation belt intensities can be described kinetically and sta-tistically as a quasilinear diffusion in the three adiabatic invariants (Northrop amp Teller 1960) under theaction of prescribed wave fields with the diffusion coefficients determined by resonant wave‐particleinteractions (eg Hess 1968 Walt 1970 Schulz amp Lanzerotti 1974) The theoretical framework of quasi-linear diffusion of radiation belt particles developed within the first decade following the discovery ofthe belts has been the backbone of most of the modeling of global variability of radiation belt intensities(see recent reviews eg Hudson et al 2008 Shprits et al 2008a 2008b Thorne 2010 and see discus-sion in section 5) We will see many aspects of this approach treated in this JGR Special Collection Inaddition it is now clear that nonlinear effects must also be considered in radiation belt dynamics andthis will also be addressed specifically (eg section 4)

Understanding the variability of the Van Allen radiation belts to the point of predictability is one of thegreat outstanding questions in heliophysics research In the coupled Sun‐Earth system solar wind energyis transferred into the radiation belts leading to charged particle dynamics over a broad range of timescales(eg seconds to years) Radiation belt enhancements have wide‐ranging implications for the man‐madetechnologies that operate in this region of geospace such as radiation hazards that can affect astronautsor charged particle spacecraft interactions that can damage satellites (eg Lanzerotti 2017) Therefore amore complete understanding of the highly variable dynamics of radiation belt particles is an internationalpriority which has led to many recent missions devoted to exploring the belts The main current mission isNational Aeronautics and Space Administrations (NASA) Van Allen Probes launched in 2012 a two‐space-craft mission devoted to unraveling the mysteries of the dynamics of the particle radiation trapped by theEarths magnetic field (Mauk et al 2013) that has ended in October 2019 In addition low‐altitudeCubesat measurements the Japanese Arase mission (Miyoshi et al 2018) and the suite of other spacecraftsuch as the European Space Agency (ESA) Cluster (eg Pokhotelov et al 2008) the Time History of Eventsand Macroscale Interactions during Substorms (THEMIS) (Angelopoulos 2008) the MagnetosphericMultiscale (MMS) (Burch et al 2016) the Solar Anomalous and Magnetospheric Particle Explorer(SAMPEX) missions (Baker et al 1993) National Oceanic and Atmospheric Administrations (NOAA)GOES the Polar Orbiting Environmental Satellites (POES) composed of multiple National Oceanic andAtmospheric Administration spacecraft and of the European Organisation for the Exploitation ofMeteorological Satellites (EUMETSAT) MetOp satellites High Earth Orbiting (HEO) satellites LosAlamos National Laboratory (LANL) GEO and GPS satellites constellations and the ESA Project for On‐Board Autonomy and Vegetation (Proba‐V) (Borisov amp Cyamukungu 2015 Pierrard et al 2019 in this col-lection) all probing the inner magnetosphere have led to unprecedented coverage of this dynamic andimportant region of geospace Observations of various phenomena in space can be complemented by subor-bital measurements particularly from balloons such as the BARREL balloon campaigns (Millan et al 2013)or ground‐based observations There is a large variety of ground‐based instruments starting with



















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337 Microbursts



































































513 MHD








































































































































































































































































































































































































































































































































































































































































































































































































Documents

Particle Dynamics in the Earth's Radiation Belts: Review