Particle Dynamics in the Earth's Radiation Belts: Review of Current

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INTRODUCTION TO Particle Dynamics in the Earth's Radiation Belts: Review A SPECIAL SECTION of Current Research and Open Questions 10.1029/2019JA026735 J.‐F. Ripoll1, S. G. Claudepierre2,3, A. Y. Ukhorskiy4, C. Colpitts5,X.Li6, J. F. Fennell2, and 7 Special Section: C. Crabtree Particle Dynamics in the Earth's Radiation Belts 1CEA, DAM, DIF, Arpajon, France, 2The Aerospace Corporation, El Segundo, CA, USA, 3Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA, USA, 4The Johns Hopkins University Applied Physics Laboratory, Laurel, MD, USA, 5School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, USA, Key Points: 6 7 • We review and discuss current LASP, University of Colorado Boulder, Boulder, CO, USA, Naval Research Laboratory, Washington, DC, USA research and open questions relative to Earth's radiation belts • Aspects of modern radiation belt Abstract The past decade transformed our observational understanding of energetic particle processes in research concern particle near‐Earth space. An unprecedented suite of observational systems was in operation including the Van acceleration and transport, particle loss, and the role of nonlinear Allen Probes, Arase, Magnetospheric Multiscale, Time History of Events and Macroscale Interactions during processes Substorms, Cluster, GPS, GOES, and Los Alamos National Laboratory‐GEO magnetospheric missions. • We also discuss new radiation belt They were supported by conjugate low‐altitude measurements on spacecraft, balloons, and ground‐based modeling capabilities, the fi quantification of model arrays. Together, these signi cantly improved our ability to determine and quantify the mechanisms that uncertainties, and laboratory plasma control the buildup and subsequent variability of energetic particle intensities in the inner magnetosphere. experiments The high‐quality data from National Aeronautics and Space Administration's Van Allen Probes are the most comprehensive in situ measurements ever taken in the near‐Earth space radiation environment. These observations, coupled with recent advances in radiation belt theory and modeling, including dramatic Correspondence to: increases in computational power, have ushered in a new era, perhaps a “golden era,” in radiation belt ‐ J. F. Ripoll, research. We have edited a Journal of Geophysical Research: Space Science Special Collection dedicated to jean‐[email protected] Particle Dynamics in the Earth's Radiation Belts in which we gather the most recent scientific findings and understanding of this important region of geospace. This collection includes the results presented at the Citation: American Geophysical Union Chapman International Conference in Cascais, Portugal (March 2018) and Ripoll, J.‐F., Claudepierre, S. G., Ukhorskiy, A. Y., Colpitts, C., Li, X., many other recent and relevant contributions. The present article introduces and review the context, current Fennell, J., & Crabtree, C. (2020). research, and main questions that motivate modern radiation belt research divided into the following Particle Dynamics in the Earth's topics: (1) particle acceleration and transport, (2) particle loss, (3) the role of nonlinear processes, (4) Radiation Belts: Review of Current fi Research and Open Questions. Journal new radiation belt modeling capabilities and the quanti cation of model uncertainties, and (5) laboratory of Geophysical Research: Space Physics, plasma experiments. 125, e2019JA026735. https://doi.org/ 10.1029/2019JA026735 1. Introduction Received 27 MAR 2019 Accepted 20 NOV 2019 Earth's radiation belts consist of two toroidal belts of energetic charged particles (electrons and ions) sur- Accepted article online 26 DEC 2019 rounding Earth. The outer belt typically lies at geocentric radial distances between 3 and 7 Earth radii (1 Earth radius = 6,370 km) in the equatorial plane and consists primarily of highly energetic (0.1–10 MeV) electrons and high‐energy protons (1–100 keV), though other ion species and lower‐energy particles are also present. The inner belt sits between 1 and 3 Earth radii and contains primarily hundreds of kiloelectron volts electrons along with extremely energetic (e.g., hundreds of megaelectron volts) protons. This description is, however, an idealized representation of a simplified structure. This representation can be valid during quiet geomagnetic times but dynamic/disturbed conditions bring complex dynamic monobelt or multibelt structures (e.g., Baker, Kanekal, Hoxie, Henderson, et al., 2013) forming within the inner magnetosphere below ~7–8 Earth radii. Earth's radiation belt location is also energy dependent. Many competing processes contribute to the dynamic formation and depletion of the belts, including radial transport, local wave acceleration, particle loss to the magnetopause, particle precipitation into the atmosphere, and others. These competing energization, loss, and transport mechanisms greatly contribute to generating complex structures far beyond the ideal two‐belt structure. These competing mechanisms typically occur simultaneously (e.g., Baker et al., 2019 in this collection) and are energy dependent; an accurate description of the radiation belts must account for their combined effects. The relative importance of each process is the most fundamental, unan-

©2019. American Geophysical Union. swered question in radiation belt physics. This question cannot be answered fully without the combined All Rights Reserved. effort of, and collaboration between, experimentalists, theorists, and modelers.

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The motion of a charged particle in the Earth's magnetic field was first formulated by Störmer (2018) and was subsequently studied by him and several others in connection with auroral phenomena and cosmic rays (Störmer, 2017). The motion and the stability of charged and trapped particles in Earth's magnetic field was then well established by 1960 (e.g., Northrop & Teller, 1960; Dragt, 1965; Fälthammar, 1965) and has provided the theoretical basis for the presence of Earth's radiation belts discovered by pioneering space missions (Van Allen, 1959; Vernov et al., 1959). It was shown that in the approximately dipolar magnetic field of the inner magnetosphere including the Earth's Van Allen radiation belts, charged particles undergo quasiperiodic motion composed of gyro, bounce, and gradient‐curvature drift motions, each 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 significantly with time, which requires violation of one or more of the adiabatic invariants. The theoretical interpretation of the variability of radiation belt intensities was largely inspired by the experiments in particle acceleration by random‐phased electrostatic waves in synchrocyclotron devices and by the subsequent development of the theory of weak plasma turbulence. It was thus suggested that the adiabatic invariants of trapped particles can be violated by small‐amplitude waves, which resonantly interact with the quasiperiodic particle motion (Balescu, 1960; Lenard, 1960; Vedenov et al., 1961). Since both the density and energy density of radiation belt particles are negligible compared to other plasma populations, their motion does not affect the fields that govern them (with some exceptions, e.g., chorus waves). Thus, it was suggested that the evolution of radiation belt intensities can be described kinetically and statistically as a quasilinear diffusion in the three adiabatic invariants (Northrop & Teller, 1960) under the action of prescribed wave fields, with the diffusion coefficients determined by resonant wave‐particle interactions (e.g., Hess, 1968; Walt, 1970; Schulz & Lanzerotti, 1974). The theoretical framework of quasilinear diffusion of radiation belt particles, developed within the first decade following the discovery of the belts, has been the backbone of most of the modeling of global variability of radiation belt intensities (see recent reviews, e.g., Hudson et al., 2008, Shprits et al., 2008a, 2008b, Thorne, 2010, and see discussion in section 5). We will see many aspects of this approach treated in this JGR Special Collection. In addition, it is now clear that nonlinear effects must also be considered in radiation belt dynamics and this will also be addressed specifically (e.g. section 4).

Understanding the variability of the Van Allen radiation belts, to the point of predictability, is one of the great outstanding questions in heliophysics research. In the coupled Sun‐Earth system, solar wind energy is transferred into the radiation belts, leading to charged particle dynamics over a broad range of timescales (e.g., seconds to years). Radiation belt enhancements have wide‐ranging implications for the man‐made technologies that operate in this region of geospace, such as radiation hazards that can affect astronauts, or charged particle spacecraft interactions that can damage satellites (e.g., Lanzerotti, 2017). Therefore, a more complete understanding of the highly variable dynamics of radiation belt particles is an international priority, which has led to many recent missions devoted to exploring the belts. The main current mission is National Aeronautics and Space Administration's (NASA) Van Allen Probes launched in 2012, a two‐spacecraft mission devoted to unraveling the mysteries of the dynamics of the particle radiation trapped by the Earth's magnetic ﬁeld (Mauk et al., 2013) that has ended in October 2019. In addition, low‐altitude Cubesat measurements, the Japanese Arase mission (Miyoshi et al., 2018), and the suite of other spacecraft such as the European Space Agency (ESA) Cluster (e.g., Pokhotelov et al., 2008), the Time History of Events and Macroscale Interactions during Substorms (THEMIS) (Angelopoulos, 2008), the Magnetospheric Multiscale (MMS) (Burch et al., 2016), the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) missions (Baker et al., 1993), National Oceanic and Atmospheric Administration's (NOAA) GOES, the Polar Orbiting Environmental Satellites (POES), composed of multiple National Oceanic and Atmospheric Administration spacecraft and of the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) MetOp satellites, High Earth Orbiting (HEO) satellites, Los Alamos National Laboratory (LANL) GEO and GPS satellites constellations, and the ESA Project for On‐ Board Autonomy and Vegetation (Proba‐V) (Borisov & Cyamukungu, 2015; Pierrard et al., 2019 in this collection), all probing the inner magnetosphere, have led to unprecedented coverage of this dynamic and important 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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magnetometer arrays, such as the Canadian Array for Real‐time Investigations of Magnetic Activity (CARISMA) magnetometer array database (e.g., Mann et al., 2008), or the Magnetometers‐Ionospheric Radars‐All‐sky Cameras Large Experiment (MIRACLE) instrument network in Finland (Sangalli et al., 2011). Incoherent scatter radars, such as the European Incoherent Scatter (EISCAT) very high frequency (VHF) radar in Tromsø in Norway, the Arecibo radar in Puerto Rico, and the Super Dual Auroral Radar Network (superDARN) (e.g., Fenrich et al., 1995), also provide contextual information. Broadband high‐ frequency ground radio and optical receivers exist in Canada (e.g., relative ionospheric opacity meters (riometers), All‐Sky Imagers (ASIs), and Meridian Scanning Photometers at the NORSTAR facility (e.g., 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 subionospheric very low frequency (VLF) radio wave receivers, called the Antarctic‐Arctic Radiation‐belt Dynamic Deposition VLF Atmospheric Research Konsortia (AARDDVARK) (Clilverd et al., 2009), which monitors energetic precipitation (e.g., Neal et al., 2015) and other energy inputs reaching the ionospheric D region.

This article is a preface, written as a comprehensive introduction, of the Special Collection of Journal of Geophysical Research (JGR): Space Science dedicated to Particle Dynamics in the Earth's Radiation Belts, in which we review the context, the main current research, and major open questions in radiation belt physics, without performing a systematic introduction of the main physical concepts or a fully exhaustive review. 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 necessary physical notions. Literature reviews can be found in Schulz (1982), Li and Temerin (2001), Friedel et 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 in Summers (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 complex interplay using unprecedented, comprehensive data coverage, along with recent advances in theory and state‐of‐the‐art modeling of radiation belt physics. These studies use valuable new assets to address many outstanding questions and also to open up new and unexpected avenues of research. This Special Collection is published 6 years after Summers et al.'s monograph (2013) on the dynamics of the Earth's radiation belts that reviewed the state of the art of this ﬁeld at the time of the Van Allen Probes launch. Both contributions demonstrate the scale of the scientiﬁc progress made in the intervening time. In addition, we include a focus on laboratory plasma experiments that can help shed light on important aspects of radiation belt dynamics.

However, we do not discuss the proton radiation belt since we do not have contributions on this subject in this Special Collection. More information on the proton belt can be found in, for example, Spjeldvik (1977), Beutier et al. (1995), Albert et al. (1998), Looper et al. (2005), Selesnick, Looper, and Mewaldt (2007), Ginet et al. (2007), Selesnick, Hudson, and Kress (2013), Selesnick et al. (2014, 2016, 2018), Mazur et al. (2013, 2014), Tu, Cowee, and 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 (e.g., Gusev, Kohno et al., 1996; Gusev, Martin et al., 1996; Pugacheva et al., 2013; Selesnick, Looper, Mewaldt, & Labrador, 2007), suprathermal ionospheric heavy ions (e.g., Spjeldvik, 1979) such as iron ions (Christon et al., 2017; Spjeldvik et al., 2006) or carbon ions (Spjeldvik, 2004), high‐energy solar protons (e.g., O'Brien et al., 2018), or cosmic rays (e.g., Amato & Blasi, 2018; Blake et al., 1997; Smart et al., 2000; Shea et al., 1992; Smart & Shea, 2002).

This Special Collection focuses on five major themes in radiation belt research that are each discussed in following: (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) laboratory plasma experiments related to radiation belts physics. In the following, we develop each of these themes, discussing the scientific context of all the articles that compose the Special Collection (with the exception of the articles that are currently under review and were not accepted for publication in the collection before the writing of this preface).

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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 ~ 8–10), undergoes signiﬁcant changes of phase space density (PSD) on a range of timescales from seconds to decades (i.e., from timescales ranging from the gyro or bounce or drift motion up to many years for the most stably trapped particles) and over a wide range of magnetic moments or energies. We will focus on the processes that cause these changes in particle PSD, from both observational and theoretical perspectives, and discuss the most fundamental, unresolved questions therein. This is a voluminous subject that is only brieﬂy discussed here. By nature of the complex interplay between the processes at work in the radiation belts, many of the questions raised here overlap with the sections that consider loss, modeling, and nonlinear processes (sections 3–5).

The current paradigms for particle acceleration and transport in the outer radiation belt (L ~ 3–7, where L refers to the equatorial crossing of a dipole magnetic field line, measured in Earth radii) include the effects of numerous processes, such as convective transport; particle injections, either by shocks associated with traveling interplanetary disturbances or by inductive electric and magnetic fields generated during magnetospheric substorms; in situ acceleration by wave‐particle interactions; radial transport by interactions with low‐frequency field fluctuations; and interactions with electrostatic structures. We need to determine quantitatively which of these processes are dominant in the radiation belts (e.g., Reeves et al., 2013; Turner et al., 2014), both statistically and for specific external conditions, such as storms driven by coronal mass ejections or corotating interaction regions, and at both local and global spatial scales.

2.1. 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 energies outside of the plasmasphere (Thorne, 2010). However, these internal, “local acceleration” processes are themselves complicated and require a specific chain of events to occur on the proper timescales in order to be effective. The current proposed global scheme is that there exist two distinct electron populations resulting from magnetospheric substorm activity that are crucial elements for electron acceleration in the outer belt: the electron source population (tens of keV), which is directly injected by substorm processes in the magnetotail and gives rise to local VLF wave growth in the vicinity of the outer belt; and the seed population (hundreds of kiloelectron volts), which penetrates the outer belt and drifts inward, becoming in turn, accelerated to much higher energies (up to megaelectron volts) through VLF wave resonant interactions generated by the electron source population (e.g., Jaynes et al., 2015; Rodger et al., 2016). Relativistic energization in the outer radiation belt by such wave‐particle interactions (essentially energy diffusion) requires that the seed population of electrons of order hundreds of kiloelectron volts be present, while plasma waves, such as lower band chorus, are generated and subsequently act on this seed population. The waves in question must be generated by nonlinear instabilities in yet another part of the plasma regime, identified as the lower‐energy source population (generally tens of kiloelectron volts). Generally, it has been assumed that the seed population is injected simultaneously with the source population. This crucial assumption has to be tested and examined. Bingham et al. (2018) in this collection show the importance of the timing and the level of the seed electron enhancements in radiation belt dynamics through a superposed epoch analysis of the chorus wave activity, the seed electron development, and the outer radiation belt electron response between L* = 2.5 and L* = 5.5, for 25 coronal mass ejection and 35 corotating interaction region storms using Van Allen Probes observations (see also Bingham et al., 2019). Khoo et al. (2018) in this collection show that the initial enhancement of tens of kiloelectron volt electrons was observed before the initial enhancement of hundreds of kiloelectron volt electrons for five intense storm periods observed with the the Magnetic Electron Ion Spectrometer (MagEIS) instrument on board the Van Allen Probes (Blake et al., 2013). This and a further study (Khoo et al., 2019) indicate that the initial enhancement from 30 keV to 2 MeV always occurs outside of the innermost plasmapause itself computed with two plasmapause models (the Liu et al., 2015, model and the Plasmapause Test Particle simulation of Goldstein et al., 2014). Tang et al. (2018) in this collection investigate the role of the transient and intense substorm electric fields, the convection electric field, and drift resonance with ultralow frequency (ULF) waves for understanding the dynamics of the seed populations in the heart of the outer radiation belt.

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2.2. Reaching Relativistic Energies If any of the components in this process chain are missing, this wave‐particle explanation for generating relativistic electrons may fail. Recent work (Jaynes et al., 2015) has shown that such failure resulted when the seed population was present but neither the source population nor the associated waves were present. This raises the crucial question: how/when is the seed population generated if not through a substorm injection? Is there a high‐latitude zone of the Earth's atmosphere that plays the role of a source, or are there external injections? Generally, there is a loss of nearly all particles at the onset of a geomagnetic storm (see sections 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 being directly injected (cf. sections 4 and 5)? This highlights the question of how often such enhancement failures occur because of missing elements and can/does the process ever still succeed in producing enhanced PSD in spite of a break in the sequence of processes? How do these loss and source processes end up affecting the total electron content of the radiation belts (e.g., Forsyth et al., 2016; Murphy et al., 2018)? These questions form some of the core elements of the theme on acceleration and transport and cross over into other themes as noted above.

2.3. Radial Transport In addition to local acceleration, the radial transport of electrons by interaction with field fluctuations and waves at ULFs (in the Pc3 to Pc5 frequency range, approximately millihertz, e.g., Mann et al., 2012) can increase the electron PSD over a wide range of energies, while preserving the first and second adiabatic invariants (Hudson et al., 2008; Mann et al., 2013). Recently, Jaynes et al. (2018) found that ultrarelativistic electrons up to ∼8 MeV are accelerated primarily or entirely by ULF wave‐driven diffusion, in the absence of local acceleration. Zhao et al. (2019) in this collection analyze the solar wind conditions during moderate and intense storms that produce ultrarelativistic electron (2–8 MeV) flux enhancements. We note, however, that if this radial transport is diffusive, then acceleration requires that the PSD is sufficiently large at the higher L values in order to be effective and operates on longer timescales than local acceleration. During sudden injections, coherent ULF waves can produce a local peak in PSD into the heart of the outer belt (e.g., Degeling et al., 2008). In that case, acceleration timescales can be comparable to local acceleration (whistler‐driven) timescales (e.g., Ukhorskiy et al., 2006). Many analyses and models have used the radial transport paradigm to explain the observed PSD profiles in much of the radiation. Often, the models combine the radial transport with magnetopause shadowing and wave‐particle losses to obtain a realistic spatiotemporal PSD distribution (e.g., Mann et al., 2016; Ozeke et al., 2018). This is even more complicated when considering the complex PSD structures that arise during storms (e.g., Turner et al., 2012, 2013). Recent electron PSD compilations measured from both the Relativistic Electron‐Proton Telescope (REPT; Baker, Kanekal, Hoxie, Batiste, et al., 2013) and the MagEIS instruments on board the Van Allen Probes can be found, for instance, in Zhao et al. (2019) and Boyd et al. (2018). Analytic solutions are possible only in simple configuration; 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 subject of debate. A large choice of model is available and the main statistical radial diffusion coefficients include 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 data respectively measured by EMFISIS and by the EFW instrument on board the Van Allen Probes. These four models are compared together at all energies for all L‐shells (L < 6) for a quiet event in Ripoll et al. (2017), with some noticeable differences found among them. Additional radial diffusion coefficient models can be found in Selesnick et al. (1997), Ukhorskiy and Sitnov (2008), Ozeke et al. (2012), and Ali et al. (2016). All of these models depend on the theoretical expressions derived by either Fälthammar, 1965, Fälthammar, 1968) or Fei et al. (2006), as discussed in Lejosne (2019). Fälthammar assumes a background magnetic dipole field and equatorial (Fälthammar, 1965) or not (Fälthammar, 1968) trapped particles that are radially driven by both magnetic field fluctuations, including the effect of the induced electric fields, and electric potential fluctuations. Fei et al. (2006) assume a slightly asymmetric background magnetic field for equatorial trapped

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particles radially driven by both magnetic field fluctuations, in the absence of electric field fluctuation, and uncorrelated electric field fluctuations. For instance, the models of Ali et al. (2016), Liu et al. (2016), and Ozeke et al. (2012, 2014) rely on the decomposition proposed by Fei et al. (2006). Lejosne (2019) demonstrates that Fei et al.'s formulas for computing radial diffusion coefficients are erroneous in the presence of magnetic field fluctuations, underestimating radial diffusion by a factor of 2. Lejosne (2019) proposes a new general method based on the rate of change of the third adiabatic invariant (see also Lejosne et al., 2012), without any assumption regarding the topology of the background magnetic field and without any artificial uncorrelation between the magnetic and electric fluctuations driving cross drift shell motion (the latter assumption causing the error in Fei et al., 2006). Olifer et al. (2019) in this collection compute radial diffusion coefficients derived from Pc4 and Pc5 ULF wave power during the intense geomagnetic storm on 17–18 March 2015. They show the radial diffusion coefficients do not correspond to statistical estimates during storm main phase (while they confirm it does during storm recovery) and do not behave as expected since the electric component is reduced and the magnetic component increases, becoming nonnegligible.

2.4. Magnetic Field Accounting for the complexity of the magnetic field during storm times is also a key component that directly influences the PSD profile (Green & Kivelson, 2004; Selesnick & Blake, 2000). The representation of the PSD profile in the physical space with respect to either the McIlwain's L value McIlwain (1961) or L*, pitch angle, and energy relie on both a thoroughly tested magnetic field model and an accurate field line tracer and is essential in order to differentiate adiabatic from nonadiabatic effects (Roederer & Lejosne, 2018). Loridan et al. (2019) and Ozeke et al. (2019), both in this collection, show how dramatic the effect of the magnetic field is when one generates PSD profile from observations. Both of these articles question the systematic attribution of PSD local peaks to wave‐particle interactions associated with chorus waves and show it can be erroneous. Furthermore, in situ measurements have shown that there can be drift resonant interactions with 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 Relativistic Electron‐Proton Telescope (REPT) measurements) associated with the storm sudden commencement of the 16 July 2017 geomagnetic storm. These authors explain and reproduce the prompt electron acceleration response (from 2 to 3.4 MeV in less than 1 hr) to the shock‐induced ULF wave in the Pc5 frequency range using a generalized drift resonance theory. One of the primary questions is whether these radial transport processes ever become dominant in the core of the radiation belts (defined here as the high flux regions surrounding the Earth below L ~ 8). There are hints that this may be the case in the outer edge of the slot region, where the outer radiation belt electrons have been observed to diffuse inward slowly to lower L. There is also evidence that the PSD radial profiles from the slot region into the inner zone are consistent with such radial transport. When the magnetic field is disrupted or deviates from a dipole field (e.g., in the South Atlantic Anomaly (SAA), cf. Jones et al., 2017), transport can also occur in an anomalous diffusive (Roederer et al., 1973) form that has been found to play an important role in both the outer belt (O'Brien, 2014) and the inner belt (Cunningham et al., 2018). In addition, it was recently recognized that Cosmic Ray Albedo Neutron Decay is a dominant source of quasi‐trapped energetic electrons at the inner edge of the inner belt, up to 782 keV (Li, Selesnick, et al., 2017; Xiang et al., 2019; Zhang, Li, et al., 2019). (Quasi‐trapped electrons are defined as having a lifetime greater than a bounce time period but less than a drift time period because they are precipitated due to the change of pitch angle associated to the change of the magnetic field in the South Atlantic Anomaly (SAA). Finally, there are also injection like signatures that directly transport and energize electrons in these same regions. Determining which of these are the dominant processes for maintaining the inner and outer zone electron fluxes is thus another important element of the research studies.

2.5. Deep Low‐Energy Injections The electron PSD in hundreds of kiloelectron volt energy regime waxes and wanes in the outer zone, throughout the slot region (L < 3.5), and even in the outer region of the inner zone. A number of open questions remain surrounding the dynamics of these numerous seed electrons: what are the processes that control these PSD changes? How deeply can electrons be directly injected? Observationally, the tens to hundreds of kiloelectron volt electrons appear rapidly (within hours) in the slot region and even in the inner zone during storms (e.g., Reeves et al., 2016; Turner et al., 2015; Zhao et al., 2016). (These electrons have quite low magnetic moments compared to the electrons in the peak of the outer radiation belt.) For instance,

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Lejosne et al. (2018) showed some of the injections occurring deep into the inner magnetosphere could be due to a potential drop associated with subauroral polarization stream (SAPS) (e.g., Lejosne & Mozer, 2017). Are these electrons locally accelerated? Is this a result of inductive electric ﬁelds acting on the electrons? What fraction is convected inward? What is the electric ﬁeld at these low L values during such events? Do the processes require that the plasmasphere boundary be eroded to the lowest L value where the electrons quickly appear? What is the real timing of their appearance relative to storm onset? These major, unresolved questions regarding the radiation belt seed/source population dynamics will be addressed in this Special 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, including particle acceleration and transport (addressed in both the ﬁrst and third sections) and particle loss. Particle transport can act as both a source and loss of particles. Particle acceleration can also be perceived as both a source and loss of particles of different energies, considering the number of particles being locally constant. This section is fully dedicated to particle loss processes, addressing the loss of trapped particles from observational, theoretical, and computational view points for radiation belt particles (electrons and ions) from close to the Earth (L ~ 1.1) to geostationary orbit and beyond (L > 6).

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

3.1. On Coulomb Collision In the closest vicinity of the Earth (L ~ <1.5), pitch angle diffusion is induced by the process of elastic Coulomb collisions of radiation belt electrons with the molecules of the dense ambient air of the upper atmosphere (e.g., Walt & 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 the much heavier neutrals and ions of the atmosphere, ionosphere, and plasmasphere. However, energy loss occurs 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 ultimately diffuse into the loss cone and scatter in the atmosphere, and, sometimes, backscatter according to the energy and the zenith angle at which the electron strikes the atmosphere (Davidson & Walt, 1977; Selesnick et al., 2004). The Coulomb collision formalism has been recently revisited (Selesnick, 2012) and used in modern Monte Carlo and Fokker‐Planck codes (Selesnick, 2016). While these effects are known in general, Cunningham et al. (2018) recently showed evidence that Coulomb collisions can cause radial transport due to the asymmetry of the Earth's magnetic field (due to the South Atlantic Anomaly), which requires one to keep all cross terms in the Fokker‐Planck equation (usually they are neglected for simplicity and/ or computational resources). Such an effect was suggested over 40 years ago (Roederer et al., 1973). This work opens the path to revisit Coulomb interactions within the general complexity of the magnetic field and to confirm its effects, importance, timescales, etc.

3.2. On Magnetopause Losses and Radiation Belt Dropouts Flux dropouts due to magnetopause shadowing occur over a broad range in energy, equatorial pitch angle, and radial distance (e.g., Loto'aniu et al., 2010; Shprits et al., 2012; Sorathia et al., 2018; Turner et al., 2012; Ukhorskiy et al., 2015; Xiang et al., 2017, 2018). These spatial, energy, and pitch angle‐dependent characteristics can be exploited to differentiate and quantify the various loss processes. Both loss types can substantially decrease the trapped electron ﬂux over short timescales (e.g., a few hours). Extreme depletions of the belts during disturbed times such as interplanetary shocks (Xiang et al., 2017), substorms, or storms, will be considered, in addition to quiet time losses from the belts.

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Particle loss to the magnetopause occurs when the magnetopause is suddenly pushed Earthward, usually in response to increased solar wind dynamic pressure, allowing particles to drift from the magnetosphere into interplanetary space. This loss process generally acts in the outer regions of the radiation belts but can reach lower L shells (e.g., L < 4), where both an adiabatic inﬂation of the electron drift orbits caused by ring current growth, and/or outward radial transport can enhance the losses. A dedicated review to magnetopause losses is available in Turner and Ukhorskiy (2020). On the other hand, wave particle interactions occur throughout the radiation belts and are particularly prevalent inside the plasmasphere.

3.3. Waves Causing Loss in the Radiation Belts Radiation belt particle loss into the atmosphere by wave‐particle interactions is governed by cyclotron resonance and operates for a given wave over a speciﬁc energy and pitch angle range of particles located at a given L‐shell (e.g., Roberts, 1969; Lyons et al., 1972; Horne & Thorne, 1998; Summers et al., 1998; Albert, 2005; Glauert & Horne, 2005). A general review of the magnetospheric waves that contribute to wave particle interactions is given in Thorne et al. (2010). Hospodarsky et al. (2016) also review waves observed in the radiation belts by the Van Allen Probes. We review and discuss in the following the main waves that drive loss from wave‐particle acceleration, with a focus on main and recent ﬁndings (omitting ULF waves that were discussed in the previous section and are associated with electron transport and loss, but through transport to the magnetopause).

In the plasmasphere, VLF waves from ground‐based transmitters (e.g., Sauvaud et al., 2008), lightning‐generated whistler waves (e.g., Voss et al., 1998), and whistler mode hiss (Dunckel and Helliwell, 1969; Thorne et al., 1973) are the three main whistler mode waves that can interact with trapped electrons. 3.3.1. VLF Waves From Ground‐Based Transmitters Wave‐particle interactions that cause pitch angle diffusion and, ultimately, radiation belt electron precipitation have been reported as being induced by VLF waves from various ground‐based transmitters (e.g., Imhof et al., 1983). This includes, for instance, the 21.4‐kHz NPM transmitter in Hawaii with precipitation reported by subionospheric VLF remote sensing (Inan et al., 2007), the 16.4‐kHz JXN transmitter in Norway, with precipitation detected optically from cameras on the ground (Denton et al., 2014), two U.S. Navy transmitters on the U.S. East Coast operating at frequencies of 17.8 and 21.4 kHz (with nominal radiated powers of 1,000 and 265 kW, respectively) with precipitation reported from space (Imhof et al., 1986), and the powerful 19.8‐kHz NWC transmitter (1‐MW radiated power) in Australia at L = 1.45, with precipitation observed from the French microsatellites DEMETER (Gamble et al., 2008, 2009). Computer simulations support the precipitation observations (e.g., Inan et al., 1984; Marshall et al., 2010a, 2010b). Meredith et al. (2019) com- piled ∼5 years of plasma wave data from the Van Allen Probes to construct new models of the observed wave power from VLF transmitters. These authors show that the total average wave power from all VLF transmitters lies in the range 3–9pT2 in the region 1.3 < L* < 3.0, with approximately 50% of this power emanating from three VLF transmitters, NWC (W. Australia), NAA (Maine, USA), and DHO38 (Germany). Using Meredith et al.'s (2019) VLF wave power, Ross et al. (2019) show the VLF transmitters reduce electron lifetimes of 500‐keV electrons by a factor of ~10, down to the order of 200 days near the outer edge of the inner radiation belt (L ~ 1.8). However, VLF transmitter waves are ineffective at removing multi–megaelectron volt electrons (>~2 MeV) from either the inner radiation belt or slot region. 3.3.2. Lightning‐Generated Whistlers Cloud‐to‐ground lightning ﬂashes strongly emit electromagnetic radiation in the VLF band. This radiation propagates with low attenuation inside the Earth‐ionosphere waveguide (Crombie, 1964) for thousands of kilometers. These lightning‐generated whistlers can escape the waveguide to the magnetosphere in ducted modes along magnetic ﬁeld lines or in unducted modes (e.g., Carpenter, 1968; Clilverd et al., 2008; Helliwell, 1969; Inan & Bell, 1977). Lightning‐generated whistlers are impulsive electromagnetic radiation events with a frequency bandwidth (~2–12 kHz) (e.g., Meredith et al., 2007) that allows resonant interactions at the energy of trapped electrons, eventually leading to electron loss in the inner belt (e.g., Rodger et al., 2003). These plasmaspheric waves have been associated to electron precipitation using DEMETER observations (e.g., Gemelos et al., 2009; Graf et al., 2009) or seen from Trimpi effects (Helliwell et al., 1973) on VLF transmitter signals (e.g., Clilverd et al., 2004; Inan et al., 1988; Peter & Inan, 2005). Computer simulations based on ray tracing techniques (e.g., Bortnik et al., 2006; Lauben et al., 2001) have been carried out to reproduce observed precipitation, similar to the simulation of VLF‐transmitter waves induced precipitation.

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Analysis of lightning‐generated whistlers occurrence and/or effects is often also supported by lightning databases established from ground VLF stations. For instance, Peter and Inan (2005) use the U.S. National Lightning Detection Network (Cummins et al., 1998) and Zheng et al. (2016), Ripoll, Farges et al. (2019) and Záhlava et al. (2019) use the World‐Wide Lightning Location Network (e.g., Holzworth et al., 2011; Hutchins, Holzworth, Brundell, & Rodger, 2012; Hutchins, Holzworth, Rodger, & Brundell, 2012; Rodger et al., 2009). In turn, Colman and Starks (2013) use sensors from space such as the Optical Transient Detector (OTD) and its follow‐on the Lightning Imaging Sensor (LIS) (e.g., Cecil, 2001; Cecil et al., 2014; Christian et al., 2003). 3.3.3. Whistler Mode Hiss Waves Whistler mode hiss waves are the third main wave of the plasmasphere (e.g., Thorne et al., 1979), acting broadband from (~50 Hz to ~2 kHz) from L ~ 2 up to the plasmapause (Li et al., 2015; Meredith et al., 2004; Meredith, Horne, Clilverd, et al., 2006; Meredith et al., 2018; Tsurutani et al., 2015). These waves are right hand polarized with ellipticity above ~0.2 or more according to the authors (e.g., ellipticity >0.5 and polarization >0.5 in Hartley, Kletzing, Santolík, et al., 2018). Higher‐frequency hiss (2–10 kHz) have also been reported (He et al., 2019). Whistler mode hiss waves occur independently of the geomagnetic activity, being present in the plasmasphere during geomagnetic quiet times, during substorms, and during magnetic 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 outside the plasmasphere and are able to propagate into the plasmasphere where they become trapped. Ray tracing studies support this scenario (e.g., Chen, Li, et al., 2012; Chen, Reeves, et al., 2012; Chen et al., 2012b, 2012c). This thesis is also supported by global statistical evidence based on chorus waves measurements from 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 the origins, of plasmaspheric hiss remain an open question. Hartley et al. (2019) used Van Allen Probes observations coupled to ray tracing simulation and found a spatial limitation of the wave vector orientation that indicates that chorus waves may only contribute to a small fraction of the plasmaspheric hiss wave power. Internal generation is a plausible alternative. For instance, Falkowski et al. (2017) explained that a second source for plasmaspheric hiss could be the midnight injection of energetic electrons from substorm or small injection event (nonstorm events). Moreover, plasmaspheric hiss has been widely regarded as a broadband, structureless, and incoherent emission. Summers et al. (2014) showed evidence that plasmaspheric hiss could be a coherent emission with complex fine structure. Some coherence in the structure was in turn observed with polar in plumes during solar minimum conditions (Tsurutani et al., 2015) and in triggered plasmaspheric hiss above 1 kHz (Zhu, Liu, & Chen, 2019). A better understanding of the nonlinear mechanism of generation and growth of hiss waves may help to reveal their origin and to better understand their internal structure (e.g., Omura, Nakamura, et al., 2015; Nakamura et al., 2016). Whistler mode hiss waves are also observed in high‐density plumes outside the plasmasphere (Chan & Holzer, 1976; Summers et al., 2008) and the characterization of their properties and their effect outside the plasmasphere is ongoing (Woodroffe et al., 2017; Su et al., 2018; Shi et al., 2019; Li et al. 2019; Zhang et al., 2018; Zhang, Ni, et al., 2019). Whistler mode hiss waves are powerful waves and the main driver of the slot formation and the well‐known, energy dependent, two‐belt structure of the radiation belts (Lyons & Thorne, 1973), principally during quiet times (e.g., Meredith, Horne, Glauert, et al., 2006; Ripoll et al., 2017) (see discussions below). Their power can be locally high (>502 pT2), but their important effects come from their continuous existence (often with a power > ~102 pT2) in a broad domain (L > ~2 up to the plasmapause location). There is strong visible coherence between the hiss amplitude (1 to 4 days after a storm) and electron loss observed in the form of bremsstrahlung X‐rays measured from a BARREL balloons flying at altitudes of ~35 km over Antarctica, with modulations correlated with the variation of the plasma density and the magnetic field (Breneman et al., 2015) (see also discussion below about the results of Turner et al., 2019, and Ripoll et al., 2019, both in this collection). Due to their great contribution to particle scattering, the statistical distribution of hiss wave properties needs to be well characterized in magnetic local time (MLT), L‐shell, and geomagnetic activity. The most 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, Tsurutani et al. (2015) based on Polar, Kim et al. (2015) based on THEMIS, and Meredith et al. (2018) based on DE1,

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Cluster, THEMIS, and the Van Allen Probes. An MLT‐dependent model of hiss amplitude is given in Spasojevic et al. (2015). Knowledge of the hiss wave normal angle is important for wave particle interactions (e.g., Yu, Li, et al., 2017), although Ripoll, Albert, and Cunningham (2014) showed pitch angle diffusion coefficients and electron lifetimes are not strongly dependent on the wave normal angle, unless the hiss wave normal angle becomes higher than ~60° which drastically reduces pitch angle diffusion and increases the electron lifetime. Numerous studies have been devoted to hiss‐driven loss (e.g., Li, Ni, et al., 2014; Ni et al., 2013, 2014, 2017; Orlova et al., 2014; Hardman et al., 2015; Gao et al., 2015; Hua et al., 2019; Li et al., 2019; Reeves et al., 2016; Ripoll et al., 2017). 3.3.4. Plasmaspheric Wave‐Induced Precipitation Plasmaspheric wave‐induced precipitation (e.g., Imhof et al., 1986; Meredith, Horne, Glauert, et al., 2006), which combines all three whistler waves, is theoretically supported by global Fokker‐Planck simulations of radiation belt electrons within the plasmasphere (e.g., Abel & Thorne, 1998a, 1998b, 1999; Meredith et al., 2007; Meredith, Horne, Glauert, Baker, et al., 2009; Kim et al., 2011; Selesnick, Albert, & Starks, 2013; Ripoll, Chen, et al., 2014; Glauert et al., 2014a) (see more discussions in section 5). In all cases, these predictions rely on a firm knowledge of the plasmasphere itself (see review in Darrouzet et al., 2009; Darrouzet & De Keyser, 2013). Outstanding questions concern the structure of the plasmasphere, its extent, its boundaries, and its filamentary and outlying regions. The characterization (both timewise and statistically) of the plasmasphere remains a problem of fundamental interest. Statistical models of the plasmasphere density have existed for years (e.g., Carpenter & Anderson, 1992; Albert 1999; Sheeley et al., 2001; Moldwin et al., 2002; O'Brien & Moldwin, 2003; Denton et al., 2004, 2006; Ozhogin et al., 2006) as well as dynamic simulations of the plasmasphere (De Pascuale et al., 2018; Goldstein et al., 2005, 2014, 2016). Plasmaspheric density is currently inferred from the upper 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 with the EMFISIS instrument (Kletzing et al., 2013) and the EFW instrument (Wygant et al., 2013) on board the Van Allen Probes. In the absence of data, a modeling alternative is to use neural network methods to provide plasma density estimates at any location and geomagnetic activity level (e.g., Zhelavskaya et al., 2016, 2017; Chu et al., 2017). 3.3.5. Electromagnetic Ion Cyclotron Waves Electromagnetic ion cyclotron (EMIC) waves (e.g., Fraser et al., 2006) can be found either inside or outside the plasmasphere. These waves drive considerable contemporary scientific interest, particularly during the recent Van Allen Probes mission. Many recent studies are dedicated to the loss they cause to ultrarelativistic electrons (e.g., Thorne & Kennel, 1971; Albert, 2003; Jordanova et al., 2008; Miyoshi et al., 2008; Rodger et al., 2008, Rodger et al., 2015; Li et al., 2013, 2014; Usanova et al., 2014, 2016; Kersten et al., 2014; Blum et al., 2015; Clilverd et al., 2015; Woodger et al., 2015, 2018; Colpitts et al., 2016; Shprits et al., 2008a, 2013, 2016, 2017; Hendry et al., 2016, 2019; Zhang et al., 2016; Aseev et al., 2017; Drozdov, Shprits, Usanova, et al., 2017; Capannolo et al., 2018, 2019; Denton et al., 2019; Qin et al., 2019), themselves related to the complex location and duration of these waves. EMIC waves are discrete electromagnetic emissions in multiple frequency bands (e.g., Saikin et al., 2015), which are observed across a large region of geospace (e.g., Saikin et al., 2016), including the ring current and the plasmasphere, dayside plumes, and the outer dayside magnetosphere (Engebretson et al., 2015; Engebretson et al., 2018; Engebretson et al., 2018; Tetrick et al., 2017). When EMIC emissions occur, they often spread over one (or a few) MLT sectors, which limits their effect. On the other hand, EMIC waves can be extremelly powerful (>~12 nT2) but they do not necessarily last long and the question of their duration remains open and fundamental for the characterization of their effect. The effect of EMIC waves is also highly dependent on the local ion plasma composition (H+, O+, and He+), which is important to accurately compute the wave‐particle interactions, for instance, based on measured local properties such as measured by the HOPE instrument (Funsten et al., 2013; Spence et al., 2013) of the Van Allen Probes. Knowledge of duration, spatial spread, and ion density is thus necessary to compute EMIC effects. EMIC wave scattering causes relativistic electron precipitation, but how important is it for radiation belt losses on the whole? For example, loss due to EMIC wave scattering appears to be localized spatially, from an observational standpoint. Do we understand quantitatively why that is the case? This aspect of EMIC wave loss thus makes it difficult to parameterize in radiation belt modeling, an issue that will be taken up in conjunction with section 5. Do EMIC waves only act on ultrarelativistic electrons (cf. Denton

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et al., 2019, in this collection and discussion in section 5)? Another question that warrants deeper investigation is whether EMIC scattering occurs significantly or not in the plasmasphere and inner zone. Finally, wave‐particle interactions are based on Doppler‐shifted local cyclotron (and Landau) resonance (Schulz & Lanzerotti, 1974), but,one may want to also assess the effect of all possible types of resonance phenomena; Blum et al. (2019) in this collection discuss the possible role of bounce resonance that is a current research interest (Cao et al., 2017; Cao et al., 2017; Shprits, 2016). 3.3.6. Whistler Mode Chorus Waves Whistler mode chorus waves are electromagnetic, right‐hand polarized whistler mode waves that are observed in two distinct frequency bands outside the plasmasphere up to geostationary orbits and beyond (e.g., Allcock, 1957; Bunch et al., 2013; LeDocq et al., 1998; Meredith et al., 2012; Meredith, Horne, Li, et al., 2014; Tsurutani & Smith, 1974). Chorus lower band ranges from about 0.1 to 0.5 of the electron cyclotron frequency (fce), and the upper band from about 0.5 to 0.8 fce. They have a coherent fine temporal structure, made of chorus elements with rising‐tone and falling‐tone frequency as well as short impulsive bursts, all with timescales lower than a second (e.g., Cully et al., 2011; Santolík et al., 2004; Santolík, Gurnett, et al., 2003; Yu et al., 2018). The origin and growth of the chorus fine structure is a current complex subject of research that involves nonlinear wave‐particle interactions (e.g., Omura et al., 2009; Tao et al., 2012; Omura et al., 2019) (cf. sections 4 and 5).

Whistler mode chorus waves have been the subject of a multitude of research studies as these powerful waves are responsible for intense and extreme electron acceleration, from a few tens of kiloelectron volts up to several megaelectron volts (e.g., Horne & Thorne, 1999; Horne et al., 2003, Horne et al., 2005, Horne et al., 2005; Shprits, Thorne, Horne, et al., 2006; Summers et al., 2007; Bortnik, Thorne, & Inan, 2008; Tao & Bortnik, 2010; Thorne et al., 2013; Su et al., 2014; Ma et al., 2018; Allison et al., 2019; Omura et al., 2019). Chorus emissions are also essential because of their strong interaction with electrons in the outer radiation belt, which leads to nonadiabatic scattering causing precipitation into the atmosphere and a net removal of energetic electrons from the outer radiation zone. This is a dominant scattering process outside of the plasmasphere leading to diffuse auroral precipitation (e.g., Johnstone et al., 1993; Miyoshi et al., 2010, 2015; Ni et al., 2011; Nishimura et al., 2010; Oyama et al., 2017; Thorne et al., 2010). We note the statistical databases of chorus wave properties generated from the Van Allen Probes (Li et al., 2016), from Cluster (Agapitov et al., 2013), and the compilation from multiple satellites (DE1, Combined Release and Radiation Effects Satellite [CRRES], Cluster, Double Star TC1, and THEMIS) by Meredith et al. (2012; Meredith, Horne, Li, et al., 2014). Wang et al. (2019) in this collection provide an analytical model of both amplitude and frequency for upper‐ and lower‐band chorus waves based on Van Allen Probes data (see also Zhu, Shprits, et al., 2019, and Agapitov et al., 2018). 3.3.7. 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 kiloelectron volts (Fennell et al., 2014; Lorentzen et al., 2001; Mozer et al., 2018). One major question is whether microbursts are actually significant at relativistic (e.g., Blum, Li et al., 2015; Breneman et al., 2017) or ultrarelativistic energies, or not, and whether they can be caused by waves other than whistler mode chorus waves, such as EMIC waves. Douma et al. (2018) in this collection used combined space and ground based observation to show that chorus waves are, most likely, the primary drivers of relativistic microbursts, but present some case studies that confirm the potential of EMIC waves as an occasional driver of relativistic microbursts. Additional questions regarding microbursts concern: How do microbursts contribute to the global flux decay of the outer belt during storms? How do they correlate with loss of outer belt electrons? Greeley et al. (2019) in this collection find that the microburst to global loss coupling is predominant in the quasi‐trapped population of radiation belt electrons (i.e., electrons performing less than one full drift before being precipitated) while having negligible influence on the untrapped and stably trapped populations. Previous estimates of microburst flux levels are not well constrained, and further studies are needed to refine these estimates, which can then be incorporated more accurately into radiation belt models (section 5). 3.3.8. Magnetosonic and Electrostatic Cyclotron Harmonic Waves Finally, magnetosonic waves (Russell et al., 1970) are extremely oblique waves (mean wave normal angle ~89°) with a relative effect in terms of loss that is rather small compared with other waves, with pitch

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angle diffusion concentrated around a narrow range of intermediate to high pitch angles at energies above 100 keV (e.g., Albert et al., 2016) and with some events responsible for particle acceleration (e.g., Horne et al., 2007). These waves were originally referred as magnetosonic equatorial noise (see also Perraut et al., 1982; Santolík et al., 2004; Thomsen et al., 2011). Wave particle interactions with magnetosonic waves via Landau resonance have been recently suggested to cause the so‐called “peculiar” pitch angle distributions (Li et al., 2016; Ni et al., 2016) with enhanced PSD at intermediate pitch angles and an abrupt decay around ~90° observed in the slot region and in the inner zone (Zhao et al., 2014a). But the competing process of cross diffusion (pitch angle and energy) involving chorus and hiss interactions could also explain such “peculiar” angular distributions (Albert et al., 2016). Lessard et al. (2019) in this collection propose EMIC waves as another contributor to the development of butterﬂy distributions. Research studies are ongoing to conﬁrm the mechanism that forms such “peculiar” pitch angle distribution, as it may 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 resonant interactions with radiation belt electrons and a contribution to diffuse aurora at L > 8 (Liu et al., 2018; Meredith et al., 2000; Meredith, Horne, Thorne, & Anderson, 2009; Shaw & Gurnett, 1975; Zhang et al., 2015).

3.4. Determining Loss Processes From the great variety of electromagnetic waves aforementioned, one understands how important it is to determine quantitatively the relative contributions to relativistic electron loss from precipitation into the atmosphere due to wave‐particle interactions and from magnetopause shadowing, either statistically or in a given electron loss event, and over a variety of distinct energy and L‐shell ranges. 3.4.1. The Importance of the Plasmasphere In addition to the wave environment, we seek to understand the local plasma conditions (e.g., Thaller et al., 2019; Hwang & Yoon, 2018, in this collection) that lead to the enhancement or suppression of these various wave modes and the consequences therein for the precipitation of the trapped populations. For instance, Greeley et al. (2019) in this collection have found that the plasmapause is likely a better indicator of microburst location than L‐shell. Their results complement the study by Douma et al. (2017) in which it was shown that microbursts primarily occur outside of the plasmapause and follow the inward movement of the plasmapause with increasing geomagnetic activity. The density level becomes then the relevant spatial marker since wave particle interactions are very sensitive to the density. This thesis is supported by strong correlations that have also been found between plasma density and hiss wave amplitudes (Malaspina et al., 2018) or, similarly, with the plasmapause location (Malaspina et al., 2016). 3.4.2. Energy‐Dependent Structure of the Belts Measurements from the MagEIS instruments on board the Van Allen Probes show the flux level of electrons of energy above 1 MeV in the inner belt is below the instrument background level (Fennell et al., 2015). This suggests that the inner belt is devoid of megaelctron volt electrons and more generally reveals the absence of multi–megaelectron volt electrons below L = 2.8 (Baker et al., 2014), except for rare events (e.g., Claudepierre et al., 2019, in this collection). This discovery has changed our understanding of the inner belt and 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 energy dependent, and the morphological structure of these two belts has also been shown to be highly energy dependent. Thus, we seek to investigate if this energy‐dependent inner/outer 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 times, Turner et al. (2019) in this collection provide a statistical characterization of the energy‐dependent evolution of the radiation belts during 4 days after and before the storm. For quiet times, Ripoll et al. (2019) in this collection provide a complementary analysis (though not statistical) of the energy dependence of the radiation belts 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 agreement between the energy dependence of quasi‐linear hiss‐driven scattering and the energy dependence of the radiations belts during quiet times, from L = 1.3 to L = 5.5. It is important to globally investigate whistler

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mode hiss wave interactions with electrons, as it determines the energy‐dependent slot structure and radiation belt boundaries (Reeves et al., 2016; Ripoll, Reeves, et al., 2016).

Since VLF waves can resonate with ~0.1‐ to 2‐MeV electrons between L = 1.7 and L = 3, how do Earth ground‐based VLF transmitters affect energetic electron populations at low L? What is the relative importance of VLF transmitter waves and lightning‐generated whistlers, compared with whistler mode hiss waves, all three responsible for radiation belt electron precipitation? Are these waves responsible for some of the slot region formation or connected in any way to the lack of megaelectron volt electrons observed at low L‐shells? If so, then how can that be reconciled with the observed energy dependence of the location of the inner edge of the slot region? All of these questions regarding the energy‐dependent structure of the radiation belts, and the role that the various loss processes play therein should be more thoroughly investigated. In addition, among all of the plasma waves noted above, we seek to understand which ones contribute the most to the scattering of trapped particles, for both the kiloelectron volt and megaelectron volt populations, and where in near‐Earth space (inside the plasmasphere, at the plasmapause, outside the plasmasphere, at GEO orbits, etc.) they are most effective. 3.4.3. Inner Belt Dynamics and Active Experiments Acknowledging the absence of electrons above 1 MeV in the inner zone, how do we explain possible losses of the relativistic electrons from this region? Aside from Van Allen Probes, what other reliable observations can be brought to bear on the subject of electron loss from the inner zone or, more generally, at low L‐shells? Given observed interplanetary shock injections of multi–megaelectron volt electrons to low L, such as during the March 1991 event (Li et al., 1993), what processes would contribute to electron loss in the inner zone and 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 have been various anthropogenic manners to influence the ionosphere and the space environment, as presented in the review of Gombosi et al. (2017). Chang et al. (2018) in this collection address this aspect in investigating electron diffusion from the effect of controlled heating of the ionosphere. More generally, the Demonstration and Science Experiments mission (Adler et al., 2006; Fennelly, 2009; Moldwin, 2010) that was launched in May 2019 will use antennas to drive electromagnetic waves in the radiation belts and measure the propagation of these waves, and any resulting pitch angle diffusion of the trapped particles. In addition, there is an upcoming sounding rocket experiment named SMART (Space Measurement of Rocket Released Turbulence) to be launched in 2021 that will inject high‐speed Barium in the upper ionosphere that is unstable to lower‐hybrid waves that undergo a turbulent conversion to electromagnetic whistler waves that will propagate into the radiation belts and interact with trapped particles (Ganguli et al., 2015). Wave emission from pulsed electron beams either on board of a rocket or spacecraft is a third alternative that is currently under investiguation (e.g., Delzanno & Roytershteyn, 2019). Pulsed electron beams fired from a spacecraft and spotted at its magnetic footpoint in the ionosphere can also be used to follow the magnetic field lines and connect and map the magnetosphere to the ionosphere (e.g., Delzanno et al., 2015, 2016; Lucco Castello et al., 1968). What can we also learn from the systematic appearance of structured flux peaks and valleys called zebra stripes (Ukhorskiy et al., 2012; Lejosne & Roederer, 2016) that are observed in the spectrograms of energetic electrons and ions trapped in the inner belt below L ~ 3 and could be modified by active experiments? 3.4.4. Loss Observations An important topic concerns the observations and measurements of losses, independent of the associated processes. Specifically, we need to better identify the definitive observational signatures of atmospheric and magnetopause losses. For example, it is possible that loss signatures are misidentified since, as we know, not every decrease in flux is a real loss. Thus, it is crucial to take full advantage of multipoint observations combining those in space and on/near the ground, as in the research contained in this collection. Example measurements include NASA's Van Allen Probes, THEMIS, Magnetospheric Multiscale and SAMPEX; NOAA's GOES and Polar Orbiting Environmental Satellites constellations; LANL's GPS and GEO constellations; Japan Aerospace Exploration Agency's Arase mission; ESA's Cluster and Project for On‐Board Autonomy and Vegetation missions; the BARREL balloon campaigns; low‐altitude CubeSats; and ground‐based observatories, such as magnetometer arrays, broadband high‐frequency and VLF radio waves receivers (e.g., riometers in Canada and Finland, AARDDVARK), and radars. Small satellite missions will play a key role in the future (Millan et al., 2019).

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4. The Role of Nonlinear Processes in the Global Variability of the Radiation Belts The development of nonlinear dynamics and plasma theory, dramatic increase in computational power and numerical simulation capability, and, most importantly, highly accurate in situ field and plasma measurements collected in the radiation belts since the Combined Release and Radiation Effects Satellite (CRRES) mission 30 years ago (e.g., Anderson et al., 1992; Vampola et al., 1992) have revealed a number of nonlinear acceleration and loss processes that cannot be described in the quasilinear diffusion approximation. Thus, we seek to advance our theoretical and experimental understanding of the role of the nonlinear processes in the global variability of the inner and the outer belt (see Sorathia et al., 2018 in this collection). We broadly classify these investigations into three categories: nonlinear particle dynamics, nonlinear particle interaction with quasi‐monochromatic waves, and weak‐turbulence effects. In the following, we list some of the outstanding science questions in each category. 4.1. Nonlinear Particle Dynamics Is radial diffusion appropriate for modeling radial transport in the outer belt, slot, and the inner belt region? The results of test‐particle simulations of radial transport in broadband ULF turbulence in Pc4 to Pc5 frequency range suggest that persistent phase correlations cause large deviation of the transport from the radial diffusion approximation. It is important to determine whether these deviations become less prominent in the 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 belt where the magnetic field becomes sufficiently compressed such that two local minima of the magnetic field intensity are formed above the equatorial plane, electron drift orbits exhibit bifurcations associated with second adiabatic invariant violation, producing rapid nondiffusive transport and strong enhancement of magnetopause losses (Ukhorskiy et al., 2011). Multispacecraft measurement analyses are required to address the overall importance of drift orbit bifurcations to radial transport and magnetopause losses. What role do kinetic Alfvén waves play in energetic particle acceleration and loss in the inner magnetosphere? Recent measurements from the Van Allen Probes have revealed that kinetic Alfvén waves (e.g., Chaston et al., 2015) can be commonly produced in the inner magnetosphere in association with injections from the magnetotail. For instance, Chaston et al. (2018) showed the simultaneous occurrence of broadband Alfvénic fluctuations observed by the Van Allen Probes and the multitimescale modulation of enhanced atmospheric X‐ray bremsstrahlung emission in the BARREL data. Pitch angle diffusion in the Alfvénic fluctuations that are time stationary on the electron timescale could cause the transport of electrons into the loss cone over an energy range from hundreds of kiloelectron volts to multi–megaelectron volts on diffusive timescales on the order of hours, which would constitute a significant loss process for the radiation belts. It was previously suggested that the ion gyroradii‐scale electric fields that they carry may be sufficient to demagnetize ion motion and allow stochastic acceleration in the wave's perpendicular electric field. Detailed numerical modeling and data analysis are required to determine what role kinetic Alfvén waves play in ion heating in the inner magnetosphere and whether these processes are significant at radiation belt energies. Finally, the role that nonlinear wave structures, commonly referred to as “time domain structures” (TDSs), play in relativistic electron dynamics in the outer zone is important to understand. One of the surprising results from the Van Allen Probes is the ubiquity of TDS observed in the inner magnetosphere (Mozer et al., 2015, 2017). Given the novelty of these radiation belt observations, the role of TDSs in radiation belt dynamics is underexplored and is rife for investigation and potential discovery. 4.2. Nonlinear Wave‐Particle Interactions What is the relative importance of nonlinear wave‐particle interactions of electrons with quasi‐coherent whistler mode waves in radiation belt acceleration and loss, and how do the inhomogeneities in the local environment affect them? Are the numerical simulation models used representative of reality? How does it compare with linear and quasilinear theory? Multiple theoretical analyses and numerical simulations (see reviews, Shklyar & Matsumoto, 2009; Nunn & Omura, 2015) show that phase trapping of electrons in large‐amplitude oblique whistler mode waves in an inhomogeneous magnetic field can result in rapid acceleration, as well as atmospheric loss, of radiation belt electrons on bounce timescales (few seconds). Recently, very large amplitude

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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 conditions is required to assess the global effects on acceleration and loss. Recent progress toward this goal has been made by the use of a numerical “Green's function” (Omura, Miyashita, et al., 2015; Kubota & Omura, 2018) that gives the nonlinear test‐particle response to a given subpacket of chorus and demonstrates that rapid acceleration to megaelectron volt energies is possible. A subpacket of chorus (Foster et al., 2017 and Santolík 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 5–10 wave periods and may itself be due to a higher‐order nonlinear resonance between the whistler mode wave and the electrons that generate the wave (Crabtree et al., 2017a, 2017b). What role do rising tone EMIC emissions play in radiation belt losses and ring current acceleration? Recent analysis (Kubota et al., 2015; Shoji & Omura, 2014) showed that rising tone EMIC emission can produce rapid heating of energetic protons around the equator because of the stable trapping, as well as the atmospheric losses of relativistic electrons inside the plasmasphere. Nakamura et al. (2019) presented direct Van Allen Probes observations of an event of rapid precipitation of relativistic electrons in timescale shorter than 1 min and in <1 hr of MLT, possibly through nonlinear trapping by EMIC rising tones. Quantitative assessment of the occurrence rates of EMIC rising tones is required to establish their importance to the ring current and radiation belts. 4.3. Nonlinear Weak‐Turbulence Effects Recent theoretical analysis (Crabtree et al., 2012) has shown that inside the plasmasphere the threshold for the nonlinear scattering of plasma waves with frequencies between the ion and the electron gyrofrequencies can be reached by waves with amplitudes as low as 50 pT in the magnetic field perturbation, which can be reached by powerful plasmaspheric whistler mode waves (Breneman et al., 2011; Cattell et al., 2008). The nonlinear scattering of these waves can lead to a preference for wave properties that can produce an enhanced precipitation rate. Can this effect be observed? Are weak turbulence effects important to inner radiation belt dynamics? Can this effect be incorporated into current models, for example, by incorporating the dependence of the statistical wave normal angle of waves with the amplitude? Are there other instances where wave–wave 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 radiation belts? Current theories of chorus generation mechanisms assume a coherent parallel‐propagating plane wave, which allows for the analytical solution to the nonlinear current and feedback mechanisms. Recent detailed analysis of wave data from EMFISIS (Crabtree et al., 2017) indicates that these assumptions may not be met and that chorus, as it grows in amplitude, may give rise to new secondary instabilities similar to weak turbulence interactions. Nonlinear wave growth and saturation (e.g., Summers et al., 2011) is expected to differ from the linear Kennel‐Petschek limit (Kennel & Petschek, 1966), but by how much? Recent laboratory experimental evidence demonstrates that nonlinear induced scattering and nonlinear three‐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 of Model Uncertainties Modeling is necessary to fully understand the physical mechanisms responsible for the observed dynamics of radiation belt particles. Nearly 20 years ago, the first detailed computer simulations of radiation belt dynamics were undertaken, modeling pitch angle and/or radial diffusion (see, for instance, review in Shprits et al., 2008a, 2008b). In order to model specific observed events, such modeling often relied on CRRES measurements of electromagnetic waves and plasma conditions, or CRRES and/or LANL GEO fluxes for providing the boundary conditions. Many of the codes in use then, which were developed into the end of the 1990s, were not particularly elaborate, but they ultimately proved to be useful in future studies, once the physical properties of the space environment were more fully understood. In those times, many of the physical parameters required for the initial and boundary conditions that are needed to run such models were sparse, often averaged, and sometimes relied on empirical models, while others were simply not known. Detailed observations for model validation were also sparse, available only over a limited

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energy/pitch angle range, and usually available over limited periods of time. Data from the CRRES satellite was typically regarded as the gold standard at the time, but unfortunately CRRES survived only 14 months before 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 in many aspects of radiation belt physics. For example, many research groups now develop and run codes that model multiple wave particle interactions (e.g., energy and pitch angle diffusion); dynamic magnetic field configurations; coupled ring current codes; coupling between radial diffusion and pitch angle diffusion and other cross term effects; coupling with global magnetohydrodynamic (MHD; e.g., Sorathia et al., 2018 in this collection); and 2‐D and 3‐D particle‐in‐cell (PIC) simulations (e.g., Chang et al., 2018 in this collection). We briefly review in the following paragraphs the state of the art of modern computational tools for solving the radiation belts and their environment. 5.1. Modern Computational Tools 5.1.1. The Fokker‐Planck Formalism The primary radiation belt models currently use a Fokker‐Planck formalism based on quasilinear diffusion of radiation belt particles. These codes have tremendously improved over the last 15 years, thanks to two parallel efforts relative to theory and model validation. First, the theory of quasilinear pitch angle diffusion of the 1970s (e.g., Roberts, 1969; Lyons et al., 1971, 1972; Lyons, 1974a; Schulz & Lanzerotti, 1974) has been deeply revisited, rederived, and modernized to be more easily understood and implemented in modern codes (e.g., Albert, 2005, 2007, 2010, 2012; Glauert & Horne, 2005; Summers, 2005). Such a task was needed and difficult, as illustrated by the various missing factors of 2 that were tracked within the various formalisms from 2005 to 2012 (e.g., Albert, 2012; Summers, 2005; Tu et al., 2013). Theoretical understanding also made great progress thanks to the derivation of simplified models, whose accuracy turned out to be sufficient to understand the main physical drivers and to allow the derivation of scaling laws. Among them, there is the parallel approximation (Summers, 2005), the mean value approximation (Albert, 2007; Albert, 2008a), the analytical approximation of lifetime (Albert & Shprits, 2009), and various other analytical approximations of pitch angle diffusion and lifetime (e.g., Mourenas & Ripoll, 2012; Albert, 2017). The solidity of the theoretical framework directly benefitted the Fokker‐Planck numerical codes that were developed simultaneously by numerous research groups around the world. These codes are all based on an equation that takes the form of a linear diffusion equation and on bounce and drift averaging procedures, well adapted to the dynamics of the particles trapped into the radiation belts, making use of the periodic motion of trapped particles. Bounce and drift averaging helps by reducing the dimension to three (radial distance, energy, and pitch angle, or, equivalently, three adiabatic invariants 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 calculation of various diffusion coefficients that represent the effect of small‐amplitude waves (from millihertz to kilohertz frequency range) on the particle distribution function. All the effects induced by the electromagnetic waves are included in these diffusion coefficients, which are calculated in the framework of quasilinear theory (e.g., Fälthammar, 1965; Kennel & Petschek, 1966; Lerche, 1968; Lyons et al., 1971, 1972; Lyons, 1974a, 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 simulations. Quasilinear theory nevertheless requires that the waves have random phases and small amplitudes and are based on cold plasma linear theory (Stix, 2006) (i.e., neglecting thermal effects) and that the particles are in (cyclotron and Landau) resonance with the wave spectrum. Tao et al. (2012) have, for instance, verified 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 (e.g., Schulz & Lanzerotti, 1974), most early formulations were based on the unidimensional Fokker‐Planck equation that solves for radial diffusion and approximates pitch angle diffusion (or any other diffusion phenomenae) thanks to loss terms (that do not involve partial derivatives). Derivation and limitation of this method are, for instance, discussed 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‐Planck formulation has been commonly used since the 1970s for Earth's (and other planets) radiation belts (e.g.,

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Spjeldvik & Thorne, 1975, 1976; Spjeldvik & Lyons, 2013; Brautigam & Albert, 2000; Shprits et al., 2005; Shprits, Thorne, Horne, et al., 2006; Tu et al., 2009; Ozeke et al., 2014; Li, Millan, et al., 2014; Ripoll, Loridan, 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 and/or the lifetime model, 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 & Newman, 1988; Walt, 1970). Tridimensional full Fokker‐Planck codes only became readily available and operational in a common manner in the years 2005–2010 (e.g., Albert et al., 2009; Subbotin & Shprits, 2009; Varotsou et al., 2005, 2008). This is due to the complexity of different technical aspects, such as the coupling between radial diffusion (solved in the invariant space) and the other diffusion processes (solved in the physical space), cross diffusion (such as mixed pitch angle and energy diffusion terms), the lack of knowledge of the wave and plasma properties that serve for the diffusion coefficients as well as for the initial and boundary conditions, and the computational cost. For instance, cross diffusion is still nowadays not necessarily included in all 3‐D simulations (e.g., Glauert et al., 2018) and there are debates on the appropriate numerical schemes that should be used (Albert, 2013; Albert & Young, 2005; Camporeale et al., 2013a, 2013b). We also emphasize that no modern model is free running based only on knowledge of the Sun's behavior; all the current models require the imposition of preverified outer boundary conditions. With a full Fokker‐Planck code, one can solve today simultaneously the following processes: radial diffusion, pitch angle diffusion, energy diffusion, cross energy and pitch angle diffusion, Coulomb collision, and anomalous diffusion. Among the most well‐established Fokker‐Planck codes are the ONERA Salammbô code (e.g., Beutier & Boscher, 1995; Bourdarie et al., 1996, 2000, 2005; Pugacheva et al., 2000; Beutier et al., 2005; Varotsou et al., 2005, 2008; Maget et al., 2015; Herrera et al., 2016), the British Antarctic Survey (BAS) Radiation Belt Code (e.g., Glauert et al., 2014a, 2014b; Glauert & Horne, 2005; Horne et al., 2013; Meredith et al., 2016, 2018), the VERB 3‐D code (e.g., Subbotin & Shprits, 2009; Shprits et al., 2009; Subbotin et al., 2010, 2011; Kim et al., 2011, Kim et al., 2012; Drozdov et al., 2015) recently extended to a 4‐D version (e.g., Aseev et al., 2016; Shprits et al., 2015) to soon incorporate models of nonlinear wave‐particle interactions, the University of California, Los Angeles (UCLA) 3‐D diffusion code (e.g., Tao et al., 2011; Li et al., 2014; Li, Ma, et al., 2016; Ma et al., 2015, 2016, 2016, Ma et al., 2017 that incorporates the (UCLA) Full Diffusion Code (e.g., Ni et al., 2008, Ni et al., 2011; Shprits & Ni, 2009) in order to compute diffusion coefficients (similarly to VERB 3‐D/4‐D), the radiation belt code of the Space Vehicles Directorate of the U.S. Air Force Research Laboratory (AFRL) (e.g., Albert, 2005, 2008b; Albert et al., 2009; Albert & Young, 2005; Selesnick, Albert, & Starks, 2013), the LANL Dynamic Radiation Environment Assimilation Model (DREAM) 1‐D (e.g., Tu et al., 2009; Reeves et al., 2012; Welling et al., 2013) and 3‐D codes (Camporeale et al., 2013a, 2013b; Cunningham, 2016; Cunningham et al., 2018; Tu et al., 2013), the Commissariat à l'Energie Atomique (CEA) CEVA code (Réveillé, 1997; Ripoll & Mourenas, 2012; Ripoll, Chen, et al., 2014, Ripoll, Reeves, et al., 2016, Ripoll et al., 2017, 2019), and the STEERB code developed in China (e.g., Su et al., 2010; Su, Zheng, et al., 2011; Su et al., 1984).

The second effort made to develop Fokker‐Planck codes is the successive tests and validations of these codes that have been carried along the years against various types of events, such as fast dropout and strong enhancement of megaelectron volt electrons during storms with DREAM 3‐D (e.g., Tu, Cunningham, et al., 2014), local acceleration by chorus waves with the UCLA diffusion code (Li, Thorne, et al., 2014; Li, Millan, et al., 2014; Thorne et al., 2013), electron radiation belt dropout event during storms with the U.S. AFRL (e.g., 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 EMIC waves with STEERB (Su et al., 2017) and VERB 3‐D (Drozdov, Shprits, Usanova, et al., 2017), nonstorm time and quiet dynamics of electron radiation belts with STEERB (e.g., Su et al., 2014), UCLA (Ma et al., 2015; 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), internal acceleration and continuous losses with the BAS code (Glauert et al., 2014b), early storm recovery phases with the UCLA code (Ma, Li, Thorne, Nishimura, et al., 2016), ﬂux enhancements during both the storm and the nonstorm times with the UCLA code (Ma et al., 2018), deep injection of ~1‐MeV electrons into the slot region with VERB 3‐D (Kim et al., 2016), the atmospheric scattering and decay of inner radiation belt electrons (Selesnick, 2012) and inner radiation belt dynamics (Selesnick, Albert, & Starks, 2013)

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with the U.S. AFRL code, and the DREAM (Cunningham et al., 2018) codes. Long periods of radiation belts dynamics that combine successively various types of events, with the complexity of cumulating the error as time increases, have been simulated for 6 months with DREAM 3‐D (Tu, Cunningham, et al., 2014), 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 but also often reveal lacking pieces and the need to continue the effort of validation.

Radiation belt particles are tied to the Earth's magnetic field, itself responding to both external and internal forces. The ring current dominates the plasma influence on the near‐Earth electric and magnetic fields and is, therefore, a strong internal driver of the variation of the Earth's magnetic field. Rather than solving the radiation belt particle dynamics within a modeled and prescribed inner magnetosphere, an alternative is to model the dynamics of the inner magnetosphere magnetic and electric fields and to include the trapped radiation belt particles within the inner magnetosphere model. Such an approach is favored by the fact that the ring current and its interactions (cf. review in Daglis et al., 1999; Liemohn, 2006; Ganushkina et al., 2017, and references within) can also be computed similarly with a bounce‐averaged kinetic Fokker‐Planck equation that describes the evolution of the PSD as an advection–diffusion process in coordinates consisting of radial distance, kinetic energy, cosine of the equatorial pitch angle, and, as fourth variable driving advection, the 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‐Consistent Magnetic Field model, RAM provides the anisotropic pressure that calculates self‐consistently the magnetic field topology for the ring current (RAM) plasma (Jordanova et al., 1996, 1997, 2006; Zaharia et al., 2006, 2010; Jordanova & Miyoshi, 2005, Miyoshi et al., 2006; Jordanova et al., 2010; Welling et al., 2011; Yu et al., 2011; Yu, Jordanova, et al., 2017). Recent extensions of RAM‐SCB include the generalization to relativistic energies and radial diffusion such that the radiation belt electrons can now be included and well solved (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 particles. The CIMI model (Fok et al., 2014) was developed by merging the Comprehensive Ring Current Model (Fok et al., 2001; Fok & Moore, 1997) and the Radiation Belt Environment (Fok et al., 2008, 2011; Glocer et al., 2011; Kang et al., 2016) models. CIMI solves for both ion and electron distributions in the ring current and radiation belts, electron precipitation in the ionosphere, plasmaspheric density, subauroral convection fields, convection potential, and Region 2 field‐aligned currents. These global and self‐consistent approaches are highly promising, in particular for storm times (and at L > 3) that are vastly driven by the strongly variable and non dipolar magnetic field. These models, however, usually lack a full resolution of wave particle interactions that focus first on a correct resolution of the inner magnetosphere itself, whose dynamics is independent of radiation belts particles. Recently, the CIMI model incorporated pitch angle, energy, and cross 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 therefore only just now starting, and sparse for that reason, although encouraged by successful simulations of storm time dynamics with RAM‐SCB (e.g., Jordanova et al., 2016), of rapid dropout event for highly relativistic electrons with Radiation Belt Environment (Kang et al., 2016), of drift‐resonant interaction with ULF 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 & Seki, 2010). In a similar effort to account for the variability of the magnetic field, or for the inclusion of nonlinear effects, or, again, for describing the azimuthal dynamics of trapped particles, advection terms have begun to be added into regular radiation belts Fokker‐Planck codes; this is the case of the VERB 3‐D code evolving into VERB 4‐D (e.g., Aseev et al., 2016; Shprits et al., 2015).

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

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magnetic field because that would require dynamically computing diffusion coefficients as the nondipolar magnetic field changes. Not only is such computation highly computer time‐consuming, but also a robust theory and its associated numerical recipe are currently lacking to compute diffusion coefficients in the case of a general non dipole magnetic field, which may experience drift‐orbit bifurcations and/or complex Shabansky 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 of pitch 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 of Summers (2005) and the Tsyganenko 04 (T04) magnetic field model (Tsyganenko & Sitnov, 2005). With the same motivation, Cunningham (2016) has proposed a new theoretical formalism, this time, for radial diffusion coefficients, that accounts for the variability of the magnetic field, yet this is very new and complex and has yet to be broadly tested or used. Thus, today, the full coupling between a disturbed and dynamic magnetic field and wave‐particle interactions remains yet unsolved (independently of what transport code is used). How does that matter? Will the variability of the magnetic field soon be included in the computation of wave‐particle interactions? The availability of magnetic field models and software as, for instance, LANLGeoMag (https://github.com/drsteve/LANLGeoMag/), as well as the availability of supercomputer power that allows the computation of event‐driven diffusion coefficients over thousands of processors (cf. Ripoll et al., 2019, in this collection) shows we are now ready to make better couplings between wave‐particle interactions and the magnetic field. To which extent will we try to conserve this coupling? Would it be enough to use a Kp‐variable T89 magnetic field, as in Orlova and Shprits (2014)? Or can we eliminate the problem and assume the variability of the magnetic field is already accounted for in wave‐particle interactions 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 magnetic field when these properties are generated (as, for instance, the Olson‐Pfitzer quiet time field model of Olson &Pfitzer, 2009, in Malaspina et al., 2018) and the magnetic field model that is used within the computation of the diffusion coefficients or/and within the (diffusion or advection–diffusion) Fokker‐Planck model? At which L‐shell and energy could these effects become important? In conclusions, there remain a great amount of physical and technical questions for including a dynamic magnetic field in wave‐ particle interactions. 5.1.2. 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 in global Earth electric and magnetic fields that are generated from MHD codes (e.g., Elkington et al., 2002, 2004; Ukhorskiy et al., 2008; Ukhorskiy & Sitnov, 2012; Kress et al., 2012; Sorathia et al., 2018). They rely on solving for the Full Liouville's equation and Hamiltonian theory of the guiding‐center motion (e.g., Cary & Brizard, 2009). The formulation can be gyroaveraged, for instance, for limiting the computational cost for electrons For instance, since the variation of the gyroradius among the particle species varies as 1∶40∶160 (e−:H+:O+), it is necessary to keep the gyrotrajectory when computing particle loss of heavy ions through the magnetopause (e.g., Sorathia et al., 2015). Global coupled MHD/test particle codes are well adapted, for instance, for azimuthal transport, that is, solving for particle gradient‐curvature drift motion, for rapid particle energization occurring during interplanetary shocks on the front end of coronal mass ejections (e.g., Hudson et al., 1997; Kress et al., 2007, 2008), for drift‐orbit bifurcation trajectory (Ukhorskiy et al., 2011), for acceleration at dipolarization fronts (Ukhorskiy et al., 2018 in this collection), for solar wind ion entering the magnetosphere (Sorathia et al., 2000), for energetic particle injections in the inner magnetosphere during substorms (e.g., Gkioulidou et al., 2015), or O+ ion outflow directly injected within the radiation belts (Gkioulidou et al., 2019), or for the sudden depletion (e.g., Ukhorskiy et al., 2015) and rapid recovery of the outer belt (e.g., Sorathia et al., 2018, in this collection). These codes can also be used to generate diffusion coefficients (e.g., Ukhorskiy & Sitnov, 2008). The main drawback of global test‐particle codes is their high computational cost in 3‐D and the current lack of inclusion of wave‐particle interactions such as pitch angle or energy diffusion, in particular energization from wave‐particle interaction with chorus waves that competes with the adiabatic energization from the magnetic field. Both of these currently limit the usability of these codes for studying radiation belts electron dynamics during long time periods (e.g., >2 days). Test‐particle codes are used to investigate the self‐consistent nonlinear mechanism of wave generation and growth in the radiation belts (e.g.,

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Omura et al., 2009; Hikishima et al., 2009; Omura & Zhao, 2012, 2013; Chen et al., 2016; Katoh et al., 2018; Omura et al., 2019). Nevertheless, wave particle interaction in this context is at the forefront of the ﬁeld, with, for instance, Omura et al. (2019) using test particle simulation for studying energetic electrons 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 to fields (e.g., Camporeale, 2015; Delzanno et al., 2013; Meierbachtol et al., 2017), allow the self‐consistent generation of the wave spectrum and no further assumption is required. PIC codes are used to investigate the self‐consistent mechanism of wave generation and growth in the radiation belts, such as chorus generation and enhancement (Fu et al., 2014, 2017; Lu et al., 2019), whistler instability effects (Fan et al., 2019; Yoon et al., 2019) and saturation (Wu et al., 2019), and magnetosonic wave excitation (Chen et al., 2018) and propagation (Min et al., 2019). PIC codes are also used to test the validity of the quasilinear theory (e.g., Camporeale, 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 treated as 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 cold components of electrons are treated as particles. Hybrid codes are used to investigate the self‐consistent generation of whistler waves in the inner magnetosphere, such as the nonlinear generation and growth mechanisms of chorus waves (e.g., Katoh & Omura, 2004, 2006, 2007, 2013; Wu et al., 2015; da Silva et al., 2017) and EMIC waves (e.g., Hu & Denton, 2009; Hu et al., 2010; Denton et al., 2019, in this collection). These methods have significant potential. For instance, Denton et al. (2019) in this collection showed that nonlinear interactions with EMIC waves can cause precipitation of sub–megaelectron volt electrons, while the general assumption based on quasi‐linear resonant interactions is that the dominant interactions occur for >~2‐ MeV electrons (e.g., Kersten et al., 2014, and references within). Recent multi‐instrument observations from Hendry et al. (2019) corroborate this finding, showing one event of nonlinear EMIC‐driven electron precipitation at sub–megealectron volt energies. The comparative role of resonant and nonresonant interactions is still a widely open subject (e.g., Camporeale, 2015; Chen et al., 2016; Denton et al., 2019; Hendry et al., 2019). Full Vlasov simulations are generally not carried out for radiation belt dynamics due to their prohibitive computational cost, and this type of simulation is, for instance, restricted to the Earth's foreshock upstream of the terrestrial bow shock (e.g., Kempf et al., 2015; Palmroth et al., 2015) or to reconnection rates at the magnetopause (Hoilijoki et al., 2017). Preliminary results of modeling of electron precipitation computed with the full Vlasov Vlasiator code are presented in Palmroth and the Vlasiator team (2019) in this collection. 5.1.3. MHD As an alternative to kinetic theory, the MHD approach consists of neglecting all single particle aspects and focus on the whole collective behavior of the magnetospheric plasma that is treated as a conducting fluid, being described through its macroscopic variables, that are, the moments of the distribution function. MHD simulations have the ability to give a description of the dynamics over large spatiotemporal scales, for example, the interaction of the solar wind with the bow shock and the impact on the entire magnetosphere over many days. The American Block‐Adaptive‐Tree‐Solarwind‐Roe‐Upwind‐Scheme code (Powell et al., 1999; De Zeeuw et al., 2000; Gombosi et al., 2004) today embedded within the Space Weather Modeling Framework (Ellington et al., 2016; Glocer et al., 2013; Haiducek et al., 2017; Morley, Welling, & Woodroffe, 2018; Tóth et al., 2005, 2012), the Open Geospace General Circulation Model (Raeder et al., 2001), and the Coupled Magnetosphere‐Ionosphere‐Thermosphere model, also referred to by the magnetospheric Lyon‐Fedder‐Mobarry component (Lyon et al., 2004; Wiltberger et al., 2015), and most recently GAMERA (Zhang et al., 2018) models are all four state‐of‐the‐art MHD codes made for the computation of the dynamics of the magnetosphere and magnetosphere/solar wind interaction. At high spatial resolution they can solve for fine filamentary structure of the electric field in the nightside that dynamically changes with a turbulent nature. These codes can generate MHD low‐frequency waves (mHz) (e.g., Claudepierre et al., 2016) and can be used to generate radial diffusion coefficients (e.g., Tu et al., 2012) but fail to treat higher‐frequency waves (kHz) that would be needed for computing consistently the wave‐particle interactions that play a fundamental role in radiation belt dynamics. MHD models are commonly used to provide the magnetic and electric fields in the magnetosphere and on the ground and are also used to compute geomagnetic indices, such as Dst (e.g.,

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Liemohn, McCollough, et al., 2018; Liemohn, Ganushkina, et al., 2018). They are mandatory for realistic test‐particle simulations that use these fields. MHD models can also be coupled to a Fokker‐Planck radiation belt code (e.g., Glocer et al., 2009, 2011). 5.1.4. Empirical Models Extensive empirical models of the radiation belts have also been developed over the years, from AE4 (Singley & Vette, 1972) to AE8 (Fung, 1996; Vette, 1991) and IRENE/AE9/AP9 (Ginet et al., 2013), incorporating satellite measurements that date back into the 1960s from many orbital regimes (e.g., LEO, MEO, HEO, and GEO). We note also the IGE‐2006 model for electrons of 1 keV to 5.2 MeV (Sicard‐Piet et al., 2008), the two‐Maxwellian ATS‐6 model for electrons of less than 50 keV for charging spacecraft surfaces (Purvis et al., 1984), and the empirical Low‐Earth‐Orbit Electron Environment Model of radiation belt electron below ~600 km (Chen et al., 2012). Precomputed empirical models for electron pitch angle distribution can be useful for initial and boundary conditions, analytical estimates, etc. PSD models are legion in the literature (e.g., Vampola, 1997; Horne, Meredith, et al., 2003; Gannon et al., 2007; Xudong et al., 2011; Zhao et al., 2014a, 2014b; Chen et al., 2014; Ni et al., 2015; Shi et al., 2016; Allison et al., 2018, 2019). For instance, Denton 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 (between 1990 and 2007) made by LANL/GEO data. These empirical models are an invaluable tool for both the scientific and spacecraft engineering communities. 5.2. Accuracy, Uncertainty Quantification, and Forecasting Today, with the Van Allen Probes, we have entered a new era for which we now have at our disposal nearly full coverage of the waves and plasma properties, precise measurements of particle fluxes by multiple instruments, very fine energy resolution, and simultaneous measurements of magnetic and electric fields. Other satellite missions deliver relevant measurements for both model validation and model boundary conditions. The amount of information now available is considerable and allows for realistic simulations over long time intervals (e.g., years); detailed simulations dedicated to specific events, such as quiet time decays or strong magnetic storms; and performing real‐time computations that can be used for space weather predictions and situational awareness. We are indeed at a golden era in radiation belt modeling, owing to the convergence of both the dramatic increase in computational power and numerical simulation capability, along with the highly accurate in situ field and plasma measurements collected in the radiation belts. Thus, radiation belt modelers are now faced with new challenges, such as addressing the important physical effects 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 capabilities should be enhanced, described in greater detail below. 5.2.1. Accurate Modeling of Acceleration, Transport, and Loss Processes As described above in section 2, in the radiation belts, the two primary sources of new outer radiation belt electrons are less energetic electrons from larger L‐shells, energized by inward radial transport as they enter the inner magnetosphere, or less energetic electrons on the same L‐shell, energized locally by wave‐particle interactions. In both cases, lower‐energy electrons usually have a substantially larger PSD and thus can be a source of the more energetic electrons. However, the relative contribution of these two acceleration mechanisms is unclear. A priority is to differentiate between these (and other) acceleration mechanisms. Radiation belt models are in a unique position to address this question, as they provide a natural testbed to artificially turn on, and turn off, contributions from the relevant wave modes. For instance, distinguishing acceleration due to ULF waves from acceleration due to chorus waves is essential (e.g., debate in Loridan et al., 2019, and in Ozeke et al., 2019, both in this collection). This is something that is not entirely possible in observational studies, because both mechanisms often operate at the same time and in conjunction with the various loss processes, 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 the loss physics incorporated into one's model. Similar to the questions surrounding the acceleration and transport processes, our current understanding of the relative contributions between loss due to precipitation into the atmosphere and loss to the magnetopause is still lacking (see section 3). In particular, it is important to understand if our theoretical modeling of particle precipitation matches observational reality, and if not, by

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how much it differs. This quantitative comparison between observed and modeled particle precipitation usually 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 a task explains why there exist only a few studies that have been capable to tackle this hard subject (e.g., Clilverd et al., 2017; Woodger et al., 2018). We also continue further refining our models such that loss associated with EMIC wave scattering is incorporated in a realistic and quantitative manner. Furthermore, recent work has clearly shown that global MHD test particle simulations do produce the large‐scale dropout events over the wide range of L shells that is typically observed (Ukhorskiy et al., 2015; Sorathia et al., 2018, in this collection). Thus, we try to identify what is incorrect/missing with either our representation of radial diffusion (e.g., ULF enhanced outward transport) or the local magnetopause loss models. As noted above, a quantitative understanding of magnetopause particle loss is required for a quantitative understanding of the particle acceleration because the measured electron flux is the net result of a dynamic competition between loss and acceleration. Thus, advances in our modeling of loss processes are crucial for accurate radiation belt modeling on the whole. 5.2.2. Quantification of Model Uncertainties Quantitative assessments made with dedicated metrics allow us to understand the input conditions and expected output values for which a model has high or low performance capabilities. Doing so reveals strengths and weaknesses of the underlying methodology (Jolliffe & Stephenson, 2012; Liemohn, McCollough, et al., 2018). According to the accuracy of the numerical model, a specific physical process can be confirmed or disproved. Operational metrics are generally specifically designed for certain forecast types or user communities (Eastwood et al., 2017). The proper choice of metrics is also important for comparisons with the measurements made on a moving spacecraft (Gordeev et al., 2015). Different statistical metrics have been used through the field of the radiation belt physics and applied to radiation belts electron fluxes (unidirectional or omnidirectional). These metrics can be based on the forecast error (difference between the model and the reference), on a relative forecast error (normalized difference between the model and the reference), or on an accuracy ratio (ratio of the model with the reference). Mean or median of these quantities are made, in a linear or (Base 10) logarithmic scale. Advantages and drawbacks of error metrics of this type are given in Morley, Brito, and Welling (2018) (see also Liemohn, McCollough et al., 2018). Among the main radiation belt flux metrics, we note the normalized forecast error (e.g., Subbotin et al., 2010; Subbotin & Shprits, 2009; Subbotin & Shprits, 2001), the mean absolute percentage error (e.g., Kim et al., 2012; Ripoll et al., 2017; Tu et al., 2013), the prediction efficiency (e.g., Pulkkinen et al., 2011; Tu et al., 2013), and the median symmetric accuracy percent and the median accuracy ratio (e.g., Glauert et al., 2018 and Ripoll et al., 2019, in this collection).

However, there is currently not an overarching framework for evaluating and tracking radiation belt model predictions and uncertainties. For example, a typical modeling effort focuses on a specific event, and often, one looks for which correction of the main parameters (e.g., the wave amplitude, or the lifetime, or diffusion coefficients of any kind and MLT dependence) is required for the model to reach a good agreement with observations, 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 of the MLT dependence of whistler hiss mode amplitudes measured by Radiation Belt Storm Probes is discussed in Ripoll, Reeves, et al. (2016), in which these authors showed the lacking MLT dependence in their event‐driven approach accounted for a factor ranging from ~1 for L in (1.5, 3) up to ~4 for L in (4, 5.5). Or, similarly, one tries among all the various models available for one quantity to determine which one leads to the most accurate results. For instance, Ozeke et al. (2017) tested commonly used radial diffusion coefficient models during long‐lasting depletions of ultrarelativistic electrons in the outer radiation belt (see also Drozdov, 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 be corrected. Because even if we have at disposal high‐quality in situ measurements, this is most often from a limited number of locations at any one time, which, therefore, obliges modelers to introduce, at best, statistical models to describe the entire system (in MLT and L) or, at worst, when statistics are incomplete (or too inaccurate), empirical correction factors. Both ways are source of errors that are often hard to estimate. This also begs the question, if the same model and modeling parameters are applied to different events, how

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good would be the agreement? Still, more observations we have at our disposal and less calibration is required, 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? Which metrics should we use? Is one metric enough or should we use simultaneously many? We tend to run models, compare with observations, and try to conclude whether the model captures the dynamics reasonably well or not. As we improve and change our models, in order to better reproduce the missing phenomena, we rarely come back to older models and to the former agreement that was found. So what does that say about the “good agreement” we got with old models? There is a need to construct a community‐wide framework of metrics to enable unbiased and quantitative assessments of the various radiation belt models in use today. How can we establish a baseline set of statistical analysis metrics for benchmarking? Aware of these questions and needs, the research community is making progress, for instance, with the recent effort through the “Quantitative Assessment of Radiation Belt Modeling” focus group organized at the Geospace Environment Modeling workshop, sponsored by the National Science Foundation Division of Atmospheric and Geospace Sciences, from 2014 to 2018 (Tu et al., 2019). This group selected four distinct radiation belt dropout and buildup events with the goal of quantitatively assessing the relative importance of various acceleration, transport, and loss processes through rigorous validation against contemporary radiation belt measurements. To avoid calibration and/or have the least dependence on statistical models, great coordinated efforts have been put into the development of event‐specific and global model inputs of wave, plasma, and magnetic field conditions for each of the challenge events. As discussed above, the organization of quantitative comparisons has been made possible nowadays since radiation belt codes have reached a mature and robust stage. Another effort made by the space weather community is the organization of working groups to address the issue of metrics for space weather models. This community work led to standardizing assessment metrics for geomagnetic indices (Liemohn, McCollough et al., 2018). Nevertheless, more studies including and reproducing important geospace features are still needed to help improve the models and reveal their intrinsic limitations. These efforts are encouraged and can take place through space weather research plans or organizations, themselves inspired by governmental policies (cf. the National Space Weather Strategy and Action Plan in 2015 and in 2019 followed by U.S. Presidential Executive Orders). For instance, the Committee on Space Research contributes to coordinated actions on space weather research and has recently issued a plan for the development of small‐size satellites that will be key for future scientific missions related to the radiation belts (Millan et al., 2019). All the current research studies support the conclusion that more validation efforts will be needed, for the next 5 to 10 years, before radiation belt codes reach a good level of predictability. 5.2.3. 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 very few extreme cases, in terms of solar wind properties and geomagnetic indices, have been observed thus far. In comparison, mission like SAMPEX lasted two decades, covering two solar cycles, with periods of extreme activity such as the Halloween storms (e.g., Baker et al., 2004; Lopez et al., 2004). We know that energetic radiation belt electrons typically penetrate to lower L with more negative Dst. The low level of geomagnetic activity is thus certainly related to the fact that Van Allen Probes has not measured >1‐MeV electrons in the inner belt (Fennell et al., 2015) until 2015 (Claudepierre et al., 2017; Pierrard et al., 2019). However, we know from CRRES that such events do occur, for example the extreme March 1991 event (e.g., Baker et al., 2004; Blake et al., 1992; Li et al., 1993), which deposited multi–megaelectron volt electrons deep into the inner belt. Thus, we must carefully consider how we extrapolate or generalize Van Allen Probes results to other solar cycles or other parts of the solar cycle (Li, Baker, et al., 2017). We also need to anticipate what could be the next extreme events (e.g., Horne et al., 2018) and characterize the highest flux that could occur at LEO (e.g., Meredith et al., 2016) and at GEO (e.g., Meredith et al., 2015, 2017). In particular, it is important to understand these implications for empirical models of the radiation environment (e.g., AE9 in Ginet et al., 2013), which are used heavily in the spacecraft engineering and design communities (e.g., Hands et al., 2018). Furthermore, Van Allen Probes data will eventually be ingested into these empirical models and will be considered the gold standard data set for such models. Which techniques and/or data sets can thus be used to appropriately tie missions together into a climatological description of changing space weather? Another related question is how well can we forecast the inner and outer electron radiation belts without using Van Allen Probes as an input? (Van Allen Probes measurements are vital for driving current

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operational space weather models, but these observations just ended.) These are challenges that space weather and space climate modeling communities will face in the future, and now is the time to begin addressing them. Furthermore, recent works have started to incorporate radiation belt electron precipitation into climate modeling (e.g., Matthes et al., 2017), for instance, for multidecadal climate simulations (e.g., van de Kamp et al., 2018, 2016), addressing the questions of the impact of radiation belt electrons on the upper stratospheric and mesospheric composition (e.g., 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 time at which climate change is one of the most important scientiﬁc issues.

6. What Can We Learn About Radiation Belt Dynamics From Laboratory Plasma Experiments? Much of our current understanding of radiation belt dynamics comes from comparing models with observed in 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 belts and we observe). This forces assumptions to be made about initial conditions and boundary conditions of the models and even applicability of the physics underlying the models.

In laboratory plasma experiments, on the other hand, repeatability and controllability are powerful tools that can be combined to lead to a detailed knowledge of the spatiotemporal structure of the entire experiment and thus can lead to a rigorous understanding of the physical processes under investigation. Repeatability allows one to overcome the stochastic nature of many of these processes and observe the underlying physics. This brings an accurate spatial as well as temporal resolution of the process. Controllability allows for a speciﬁc perturbation to be applied and the response to be observed, a powerful tool to test hypotheses. These abilities lead to rigorous testing of the underlying hypotheses of any given physical radiation belt model.

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

6.1. Understanding Nonlinear‐Wave Particle Interactions in the Radiation Belts Recent laboratory experiments have successfully generated whistler mode waves with frequencies that chirp, analogous to chorus emissions in the radiation belts, by injecting helical electron beams into a background plasma (Tejero et al., 2016; Van Compernolle et al., 2015). Triggered emissions and nonlinear amplification have also been demonstrated in the laboratory (Tejero et al., 2016). This allows for the possibility of rigorously 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 chirping whistler mode waves in radiation belt plasmas. Several related questions that have already been considered are as follows: What is the precise role of magnetic field inhomogeneity in chorus wave generation and propagation? What is the physics behind the fine structure of both chorus (e.g., Santolík et al., 2014) and hiss (e.g., Summers et al., 2014; Zhu, Liu, & Chen, 2019) waves that has recently been highlighted by EMFISIS observations from the Van Allen Probes? Is it related to the saturation of the nonlinear amplification of chorus? Can laboratory plasmas be used to investigate the role of particle energization and pitch angle scattering loss that is seen in association with chorus? How can we use laboratory plasmas to understand other nonlinear wave structures that are observed (e.g., 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 examples of wave‐particle interactions. Can we use measurements of radiation belt plasmas in conjunction with

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laboratory measurements (Doveil & Macor, 2006; Fasoli et al., 1994) to investigate nonlinear wave‐particle interactions in general? 6.2. 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 modeling of global variability of radiation belt intensities. However, theoretical plasma physics and laboratory plasma experiments have long studied nonlinear interactions between waves and particles, for example, three‐wave decay and coalescence and nonlinear Landau damping, as the logical next step beyond the quasilinear picture into the nonlinear regime. Many of these phenomena have been investigated (and are being investigated) in the laboratory (Tejero et al., 2015a, 2015b; Dorfman & 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 phenomena? What are the important nonlinear wave–wave and wave‐particle processes in the radiation belts? Under what conditions do they become indispensable to Van Allen Probe data analysis? Can laboratory experiments elucidate the plasma microprocesses and identify their measurable signatures in the in situ data? 6.3. 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 sensing devices and algorithms in laboratory plasmas. An example that has seen recent development is the laboratory verification of methods of determining the wave‐vector direction from single point measurements. In magnetospheric plasma, wave measurements by the Means method (Means, 1972) and the Singular Value Decomposition (SVD) method (Santolík, Parrot, & Lefeuvre, 2003) have seen widespread use; however, there are many cases where the assumptions of a single coherent plane wave are violated and more advanced techniques must be used. One is the wave distribution function technique (Storey & Lefeuvre, 1979; Santolík & Parrot, 2000), which was recently verified in laboratory experiments, where results of the wave distribution function technique could be directly compared to cross‐correlation measurements from multiple probes and its accuracy confirmed (Tejero et al., 2015b). 6.4. Understanding the Origin of Waves and Dynamics in Dipolarization Fronts Van Allen Probe observations show dipolarization fronts that move earthward and interact with the radiation belts, where there is plasma energization along with intense broadband electrostatic and electromagnetic wave activity. The dipolarization front is the boundary between the low‐pressure plasma of the lobe and the high‐pressure plasma of the plasmasheet and constitutes a layer (e.g., Fletcher et al., 2019, in this collection), which is characterized by strong inhomogeneity over a small‐scale size and includes highly localized static electric fields (e.g., Ukhorskiy et al., 2018, in this collection). Because the inhomogeneities are localized over very small‐scale sizes that can be easily scaled in a laboratory device, the dipolarization front is well suited for replication in the laboratory for detailed characterization of the physical process that lead to the 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 plasmasheet and the lobe have been studied both theoretically (Romero et al., 1990; Romero & Ganguli, 1994) and experi- mentally (Amatucci et al., 2003; DuBois et al., 2013; DuBois et al., 2014). Thus, laboratory experiments could significantly improve our understanding of the dynamics of dipolarization fronts and their interaction with the radiation belt plasma.

7. Summary and Perspectives With the NASA's Van Allen Probes, coupled with other satellite observations and recent advances in radiation belt theory and modeling, associated increases in computational power and numerical simulation capabilities, we are perhaps in a “golden era,” in radiation belt research. In following of this introductive article, we 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 Earth's Radiation Belts. These articles are related to current research questions and studies, discussed in this introduction, and all relative 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 quantification of model uncertainties, and (5) laboratory plasma experiments.

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With the end of the Van Allen Probes mission, we enter a new era during which the scientific community will have the opportunity to look further into the considerable amount of high‐quality observations that has been gathered along this 7‐year mission. The scientific measurements are available for many more event‐based studies or statistical studies of the near Earth space that will reveal in depth both the common and the rare behaviors of the radiation belts. Models will benefit from these data and progress either from validation that will become more and more systematic or from the increasing availability of more reliable ambient properties of plasma and waves generated from the Van Allen Probes observations. “Big data” and artificial intelligence methods should soon allow us to fully take advantage of all Van Allen Probes observations. All progress made will converge toward new advances in the hardening of electronic spacecraft systems in the coming years. The success of this mission certainly shows the human capability to put forth a set of modern, reliable, long‐life, and complementary particle and field sensors in a hostile environment. On the other hand, with the end of the Van Allen Probes mission, we will have a limited view of the response of the radiation belts to new magnetospheric storms impacting the Earth, for times that may be more active than the rather quiet Van Allen Probes time period. The last questions ending our record are certainly about what the future will be made of regarding the observation of the radiation belts that feed space weather studies and space science. The number of satellites launched has doubled over the last 2 years (~400 satellites per 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 a threat. Severe space weather is today recognized as a global threat that requires a coordinated global response 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 show how numerous, complex, and open remain the main scientific problems on radiation effects in the near Earth space. What will then be the next generation of scientific space observers that will both allow physics to 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 in commercial or institutional satellites? What observational coverage of the near Earth space do we need? What will be the main societal goals that the scientific community will be capable to put forward to justify the economical investment needed for such scientific missions, both from civilian and defense related perspectives?

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