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2020 
Energetic electron dynamics is highly affected by plasma waves through quasilinear and/or nonlinear interactions in the Earth s inner magnetosphere. In this letter, we provide physical explanations for a previously reported intriguing event from the Van Allen Probes observations, where bursts of electron butterfly distributions at tens of keV exhibit remarkable correlations with chorus waves. Both test particle and quasilinear simulations are used to reveal the formation mechanism for the bursts of electron butterfly distribution. The test particle simulation results indicate that nonlinear phase trapping due to chorus waves is the key process to accelerate electrons to form the electron butterfly distribution within ~30 s, and reproduces the observed features. Quasilinear simulation results show that although the diffusion process alone also contributes to form the electron butterfly distribution, the timescale is slower. Our study demonstrates the importance of nonlinear interaction in rapid electron acceleration at tens of keV by chorus waves. Gan, L.; Li, W.; Ma, Q.; Artemyev, A.; Albert, J.; Published by: Geophysical Research Letters Published on: 10/2020 YEAR: 2020 DOI: https://doi.org/10.1029/2020GL090749 butterfly distribution; chorus waves; Electron acceleration; Radiation belts; nonlinear interaction; Van Allen Probes 
2019 
Variability of the Proton Radiation Belt Significant steady but slow variability of radiation belt proton intensity, in the energy range \~19\textendash200 MeV and for L<2.4, has been observed in an empirical model derived from data taken by Van Allen Probes during 2013\textendash2019. It is compared to predictions of a theoretical model based on measured initial and boundary conditions. Two aspects of the variability are considered in detail and require adjustments to model parameters. Observed inward transport of proton intensity maxima near L=1.9 and associated increasing intensity are caused in the model by inward radial diffusion from an external source while conserving the first two adiabatic invariants. The diffusion coefficient is constrained by these observations and is required to have increased near the start of 2015 by a factor \~2. Observed decay of proton intensity at L<1.6 can be caused only in part by energy loss to free and bound electrons in the local plasma and neutral atmosphere. Another, unknown loss mechanism is required to match observed proton decay rates as a function of energy. Accounting for the expected influence of slow radial diffusion at low L, the additional loss should have a mean lifetime near 22 years, independent of L and energy in the range \~19\textendash70 MeV. Several candidate loss mechanisms are considered\textemdashadded plasma or neutral density, elastic Coulomb scattering, plasma wave scattering, fieldline curvature scattering, and collision with orbital debris\textemdashbut none are found viable. Published by: Journal of Geophysical Research: Space Physics Published on: 07/2019 YEAR: 2019 DOI: 10.1029/2019JA026754 
2016 
Electron precipitation down to the atmosphere due to waveparticle scattering in the magnetosphere contributes significantly to the auroral ionospheric conductivity. In order to obtain the auroral conductivity in global MHD models that are incapable of capturing kinetic physics in the magnetosphere, MHD parameters are often used to estimate electron precipitation flux for the conductivity calculation. Such an MHD approach, however, lacks selfconsistency in representing the magnetosphereionosphere coupling processes. In this study we improve the coupling processes in global models with a more physical method. We calculate the physicsbased electron precipitation from the ring current and map it to the ionospheric altitude for solving the ionospheric electrodynamics. In particular, we use the BATSRUS (Block Adaptive Tree SchemeRoe typeUpstream) MHD model coupled with the kinetic ring current model RAMSCB (Ring currentAtmosphere interaction Model with SelfConsistent Magnetic field (B)) that solves pitch angledependent electron distribution functions, to study the global circulation dynamics during the 25\textendash26 January 2013 storm event. Since the electron precipitation loss is mostly governed by waveparticle resonant scattering in the magnetosphere, we further investigate two loss methods of specifying electron precipitation loss associated with waveparticle interactions: (1) using pitch angle diffusion coefficients Dαα(E,α) determined from the quasilinear theory, with wave spectral and plasma density obtained from statistical observations (named as \textquotedblleftdiffusion coefficient method\textquotedblright) and (2) using electron lifetimes τ(E) independent on pitch angles inferred from the above diffusion coefficients (named as \textquotedblleftlifetime method\textquotedblright). We found that both loss methods demonstrate similar temporal evolution of the trapped ring current electrons, indicating that the impact of using different kinds of loss rates is small on the trapped electron population. However, for the precipitated electrons, the lifetime method hardly captures any precipitation in the large L shell (i.e., 4 < L < 6.5) region, while the diffusion coefficient method produces much better agreement with NOAA/POES measurements, including the spatial distribution and temporal evolution of electron precipitation in the region from the premidnight through the dawn to the dayside. Further comparisons of the precipitation energy flux to DMSP observations indicates that the new physicsbased precipitation approach using diffusion coefficients for the ring current electron loss can explain the diffuse electron precipitation in the dawn sector, such as the enhanced precipitation flux at auroral latitudes and flux drop near the subauroral latitudes, but the traditional MHD approach largely overestimates the precipitation flux at lower latitudes. Yu, Yiqun; Jordanova, Vania; Ridley, Aaron; Albert, Jay; Horne, Richard; Jeffery, Christopher; Published by: Journal of Geophysical Research: Space Physics Published on: 09/2016 YEAR: 2016 DOI: 10.1002/2016JA022585 Diffusion Coefficient; electron lifetime; electron precipitation; ionospheric conductivity; MI coupling; Van Allen Probes; waveparticle interactions 
2014 
Electron lifetimes from narrowband waveparticle interactions within the plasmasphere This paper is devoted to the systematic study of electron lifetimes from narrowband waveparticle interactions within the plasmasphere. It relies on a new formulation of the bounceaveraged quasilinear pitch angle diffusion coefficients parameterized by a single frequency, ω, and wave normal angle, θ. We first show that the diffusion coefficients scale with ω/Ωce, where Ωce is the equatorial electron gyrofrequency, and that maximal pitch angle diffusion occurs along the line α0 = π/2\textendashθ, where α0 is the equatorial pitch angle. Lifetimes are computed for L shell values in the range [1.5, 3.5] and energies, E, in the range [0.1, 6] MeV as a function of frequency and wave normal angle. The maximal pitch angle associated with a given lifetime is also given, revealing the frequencies that are able to scatter nearly equatorial pitch angle particles. The lifetimes are relatively independent of frequency and wave normal angle after taking into consideration the scaling law, with a weak dependence on wave normal angle up to 60\textendash70\textdegree, increasing to infinity as the wave normal angle approaches the resonance cone. We identify regions in the (L, E) plane in which a single wave type (hiss, VLF transmitters, or lightninggenerated waves) is dominant relative to the others. We find that VLF waves dominate the lifetime for 0.2\textendash0.4 MeV at L ~ 2 and for 0.5\textendash0.8 MeV at L ~ 1.5, while hiss dominates the lifetime for 2\textendash3 MeV at L = 3\textendash3.5. The influence of lightninggenerated waves is always mixed with the other two and cannot be easily differentiated. Limitations of the method for addressing effects due to restricted latitude or pitch angle domains are also discussed. Finally, for each (L, E) we search for the minimum lifetime and find that the optimal frequency that produces this lifetime increases as L diminishes. Restricting the search to very oblique waves, which could be emitted during the Demonstration and Science Experiments satellite mission, we find that the optimal frequency is always close to 0.16Ωce. Ripoll, J.F.; Albert, J.; Cunningham, G.; Published by: Journal of Geophysical Research: Space Physics Published on: 11/2014 YEAR: 2014 DOI: 10.1002/2014JA020217 DSX; electron; narrowband; plasmasphere; waveparticle interactions 
Radial diffusion simulations of the 20 September 2007 radiation belt dropout This is a study of a dropout of radiation belt electrons, associated with an isolated solar wind density pulse on 20 September 2007, as seen by the solidstate telescopes (SST) detectors on THEMIS (Time History of Events and Macroscale Interactions during Substorms). Omnidirectional fluxes were converted to phase space density at constant invariants M = 700 MeV G1 and K = 0.014 RE G1/2, with the assumption of local pitch angle α ≈ 80\textdegree and using the T04 magnetic field model. The last closed drift shell, which was calculated throughout the time interval, never came within the simulation outer boundary of L* = 6. It is found, using several different models for diffusion rates, that radial diffusion alone only allows the datadriven, timedependent boundary values at Lmax = 6 and Lmin = 3.7 to propagate a few tenths of an RE during the simulation; far too slow to account for the dropout observed over the broad range of L* = 4\textendash5.5. Pitch angle diffusion via resonant interactions with several types of waves (chorus, electromagnetic ion cyclotron waves, and plasmaspheric and plume hiss) also seems problematic, for several reasons which are discussed. Published by: Annales Geophysicae Published on: 11/2014 YEAR: 2014 DOI: 10.5194/angeo329252014 
Threedimensional stochastic modeling of radiation belts in adiabatic invariant coordinates A 3D model for solving the radiation belt diffusion equation in adiabatic invariant coordinates has been developed and tested. The model, named Radbelt Electron Model, obtains a probabilistic solution by solving a set of It\^o stochastic differential equations that are mathematically equivalent to the diffusion equation. This method is capable of solving diffusion equations with a full 3D diffusion tensor, including the radiallocal cross diffusion components. The correct form of the boundary condition at equatorial pitch angle α0=90\textdegree is also derived. The model is applied to a simulation of the October 2002 storm event. At α0 near 90\textdegree, our results are quantitatively consistent with GPS observations of phase space density (PSD) increases, suggesting dominance of radial diffusion; at smaller α0, the observed PSD increases are overestimated by the model, possibly due to the α0independent radial diffusion coefficients, or to insufficient electron loss in the model, or both. Statistical analysis of the stochastic processes provides further insights into the diffusion processes, showing distinctive electron source distributions with and without local acceleration. Zheng, Liheng; Chan, Anthony; Albert, Jay; Elkington, Scot; Koller, Josef; Horne, Richard; Glauert, Sarah; Meredith, Nigel; Published by: Journal of Geophysical Research: Space Physics Published on: 09/2014 YEAR: 2014 DOI: 10.1002/jgra.v119.910.1002/2014JA020127 adiabatic invariant coordinates; diffusion equation; fully 3D model; Radiation belt; stochastic differential equation 
Wave normal distributions of lowerband whistlermode waves observed outside the plasmapause exhibit two peaks; one near the parallel direction and the other at very oblique angles. We analyze a number of conjunction events between the Van Allen Probes near the equatorial plane and POES satellites at conjugate low altitudes, where lowerband whistlermode wave amplitudes were inferred from the twodirectional POES electron measurements over 30\textendash100 keV, assuming that these waves were quasiparallel. For conjunction events, the wave amplitudes inferred from the POES electron measurements were found to be overestimated as compared with the Van Allen Probes measurements primarily for oblique waves and quasiparallel waves with small wave amplitudes (< ~20 pT) measured at low latitudes. This provides plausible experimental evidence of stronger pitchangle scattering loss caused by oblique waves than by quasiparallel waves with the same magnetic wave amplitudes, as predicted by numerical calculations. Li, W.; Mourenas, D.; Artemyev, A.; Agapitov, O.; Bortnik, J.; Albert, J.; Thorne, R.; Ni, B.; Kletzing, C.; Kurth, W.; Hospodarsky, G.; Published by: Geophysical Research Letters Published on: 08/2014 YEAR: 2014 DOI: 10.1002/2014GL061260 chorus waves; electron precipitation; oblique whistler; pitch angle scattering 
2013 
The Electric Field and Waves (EFW) Instruments on the Radiation Belt Storm Probes Mission The Electric Fields and Waves (EFW) Instruments on the two Radiation Belt Storm Probe (RBSP) spacecraft (recently renamed the Van Allen Probes) are designed to measure three dimensional quasistatic and low frequency electric fields and waves associated with the major mechanisms responsible for the acceleration of energetic charged particles in the inner magnetosphere of the Earth. For this measurement, the instrument uses two pairs of spherical double probe sensors at the ends of orthogonal centripetally deployed booms in the spin plane with tiptotip separations of 100 meters. The third component of the electric field is measured by two spherical sensors separated by \~15 m, deployed at the ends of two stacer booms oppositely directed along the spin axis of the spacecraft. The instrument provides a continuous stream of measurements over the entire orbit of the low frequency electric field vector at 32 samples/s in a survey mode. This survey mode also includes measurements of spacecraft potential to provide information on thermal electron plasma variations and structure. Survey mode spectral information allows the continuous evaluation of the peak value and spectral power in electric, magnetic and density fluctuations from several Hz to 6.5 kHz. Onboard crossspectral data allows the calculation of fieldaligned wave Poynting flux along the magnetic field. For higher frequency waveform information, two different programmable burst memories are used with nominal sampling rates of 512 samples/s and 16 k samples/s. The EFW burst modes provide targeted measurements over brief time intervals of 3d electric fields, 3d wave magnetic fields (from the EMFISIS magnetic search coil sensors), and spacecraft potential. In the burst modes all six sensorspacecraft potential measurements are telemetered enabling interferometric timing of smallscale plasma structures. In the first burst mode, the instrument stores all or a substantial fraction of the high frequency measurements in a 32 gigabyte burst memory. The subintervals to be downloaded are uplinked by ground command after inspection of instrument survey data and other information available on the ground. The second burst mode involves autonomous storing and playback of data controlled by flight software algorithms, which assess the \textquotedbllefthighest quality\textquotedblright events on the basis of instrument measurements and information from other instruments available on orbit. The EFW instrument provides 3d wave electric field signals with a frequency response up to 400 kHz to the EMFISIS instrument for analysis and telemetry (Kletzing et al. Space Sci. Rev. 2013). Wygant, J.; Bonnell, J; Goetz, K.; Ergun, R.E.; Mozer, F.; Bale, S.D.; Ludlam, M.; Turin, P.; Harvey, P.R.; Hochmann, R.; Harps, K.; Dalton, G.; McCauley, J.; Rachelson, W.; Gordon, D.; Donakowski, B.; Shultz, C.; Smith, C.; DiazAguado, M.; Fischer, J.; Heavner, S.; Berg, P.; Malaspina, D.; Bolton, M.; Hudson, M.; Strangeway, R.; Baker, D.; Li, X.; Albert, J.; Foster, J.C.; Chaston, C.C.; Mann, I.; Donovan, E.; Cully, C.M.; Cattell, C.; Krasnoselskikh, V.; Kersten, K.; Brenneman, A; Tao, J.; Published by: Space Science Reviews Published on: 11/2013 YEAR: 2013 DOI: 10.1007/s1121401300137 
2008 
Relativistic electron precipitation by EMIC waves from selfconsistent global simulations [1] We study the effect of electromagnetic ion cyclotron (EMIC) wave scattering on radiation belt electrons during the large geomagnetic storm of 21 October 2001 with minimum Dst = 187 nT. We use our global physicsbased model, which solves the kinetic equation for relativistic electrons and H+, O+, and He+ ions as a function of radial distance in the equatorial plane, magnetic local time, energy, and pitch angle. The model includes timedependent convective transport and radial diffusion and all major loss processes and is coupled with a dynamic plasmasphere model. We calculate the excitation of EMIC waves selfconsistently with the evolving plasma populations. Particle interactions with these waves are evaluated according to quasilinear theory, using diffusion coefficients for a multicomponent plasma and including not only fieldaligned but also oblique EMIC wave propagation. The pitch angle diffusion coefficients increase from 0\textdegree to \~60\textdegree during specific storm conditions. Pitch angle scattering by EMIC waves causes significant loss of radiation belt electrons at E >= 1 MeV and precipitation into the atmosphere. However, the relativistic electron flux dropout during the main phase at large L >= 5 is due mostly to outward radial diffusion, driven by the flux decrease at geosynchronous orbit. We show first results from global simulations indicating significant relativistic electron precipitation within regions of enhanced EMIC instability, whose location varies with time but is predominantly in the afternoondusk sector. The precipitating electron fluxes are usually collocated with precipitating ion fluxes but occur at variable energy range and magnitude. The minimum resonant energy increases at low L and relativistic electrons at E <= 1 MeV do not precipitate at L < 3 during this storm. Jordanova, V.; Albert, J.; Miyoshi, Y.; Published by: Journal of Geophysical Research Published on: 03/2008 YEAR: 2008 DOI: 10.1029/2008JA013239 
2007 
[1] Prior to 2003, there are two known cases where ultrarelativistic (≳10 MeV) electrons appeared in the Earth\textquoterights inner zone radiation belts in association with high speed interplanetary shocks: the 24 March 1991 and the less well studied 21 February 1994 storms. During the March 1991 event electrons were injected well into the inner zone on a timescale of minutes, producing a new stably trapped radiation belt population that persisted for \~10 years. More recently, at the end of solar cycle 23, a number of violent geomagnetic disturbances resulted in large variations in ultrarelativistic electrons in the inner zone, indicating that these events are less rare than previously thought. Here we present results from a numerical study of shockinduced transport and energization of outer zone electrons in the 1\textendash7 MeV range, resulting in a newly formed 10\textendash20 MeV electron belt near L \~ 3. Test particle trajectories are followed in timedependent fields from an MHD magnetospheric model simulation of the 29 October 2003 storm sudden commencement (SSC) driven by solar wind parameters measured at ACE. The newly formed belt is predominantly equatorially mirroring. This result is in part due to an SSC electric field pulse that is strongly peaked in the equatorial plane, preferentially accelerating equatorially mirroring particles. The timescale for subsequent pitch angle diffusion of the new belt, calculated using quasilinear bounceaveraged diffusion coefficients, is in agreement with the observed delay in the appearance of peak fluxes at SAMPEX in low Earth orbit. We also present techniques for modeling radiation belt dynamics using test particle trajectories in MHD fields. Simulations are performed using code developed by the Center for Integrated Space Weather Modeling. Kress, B.; Hudson, M.; Looper, M.; Albert, J.; Lyon, J.; Goodrich, C.; Published by: Journal of Geophysical Research Published on: 09/2007 YEAR: 2007 DOI: 10.1029/2006JA012218 ShockInduced Transport. Slot Refilling and Formation of New Belts. 
2006 
Energetic outer zone electron loss timescales during low geomagnetic activity Following enhanced magnetic activity the fluxes of energetic electrons in the Earth\textquoterights outer radiation belt gradually decay to quiettime levels. We use CRRES observations to estimate the energetic electron loss timescales and to identify the principal loss mechanisms. Gradual loss of energetic electrons in the region 3.0 <= L <= 5.0 occurs during quiet periods (Kp < 3) following enhanced magnetic activity on timescales ranging from 1.5 to 3.5 days for 214 keV electrons to 5.5 to 6.5 days for 1.09 MeV electrons. The intervals of decay are associated with large average values of the ratio fpe/fce (>7), indicating that the decay takes place in the plasmasphere. We compute loss timescales for pitchangle scattering by plasmaspheric hiss using the PADIE code with wave properties based on CRRES observations. The resulting timescales suggest that pitch angle scattering by plasmaspheric hiss propagating at small or intermediate wave normal angles is responsible for electron loss over a wide range of energies and L shells. The region where hiss dominates loss is energydependent, ranging from 3.5 <= L <= 5.0 at 214 keV to 3.0 <= L <= 4.0 at 1.09 MeV. Plasmaspheric hiss at large wave normal angles does not contribute significantly to the loss rates. At E = 1.09 MeV the loss timescales are overestimated by a factor of \~5 for 4.5 <= L <= 5.0. We suggest that resonant waveparticle interactions with EMIC waves, which become important at MeV energies for larger L (L > \~4.5), may play a significant role in this region. Meredith, Nigel; Horne, Richard; Glauert, Sarah; Thorne, Richard; Summers, D.; Albert, Jay; Anderson, Roger; Published by: Journal of Geophysical Research Published on: 05/2006 YEAR: 2006 DOI: 10.1029/2005JA011516 
2005 
Techniques are presented for efficiently evaluating quasilinear diffusion coefficients for whistler mode waves propagating according to the full cold plasma index of refraction. In particular, the density ratio ωpe/Ωe can be small, which favors energy diffusion. This generalizes an approach, previously used for highdensity hiss and electromagnetic ion cyclotron waves, of identifying (and omitting) ranges of wavenormal angle θ that are incompatible with cyclotron resonant frequencies ω occurring between sharp cutoffs of the modeled wave frequency spectrum. This requires a detailed analysis of the maximum and minimum values of the refractive index as a function of ω and θ, as has previously been performed in the highdensity approximation. Sample calculations show the effect of lowdensity ratio on the pitch angle and energy diffusion coefficients modeling the effect of chorus waves on radiation belt electrons. The highdensity approximation turns out to be quite robust, especially when the upper frequency cutoff is small compared with Ωe. The techniques greatly reduce the amount of computation needed for a sample calculation, while taking into account all resonant harmonic numbers n up to \textpm$\infty$. Published by: Journal of Geophysical Research Published on: 03/2005 YEAR: 2005 DOI: 10.1029/2004JA010844 
2003 
Evaluation of quasilinear diffusion coefficients for EMIC waves in a multispecies plasma Quasilinear velocityspace diffusion coefficients due to Lmode electromagnetic ion cyclotron (EMIC) waves are considered in a multispecies plasma. It is shown, with slight approximations to exact cold plasma theory, that within EMIC pass bands the index of refraction is a monotonically increasing function of frequency. Analytical criteria are then derived which identify ranges of latitude, wavenormal angle, and resonance number consistent with resonance in a prescribed wave population. This leads to computational techniques which allow very efficient calculation of the diffusion coefficients, along the lines previously developed for whistler and ion cyclotron waves in an electronproton plasma. The techniques are applied to radiation belt electrons at L = 4, for EMIC waves in the hydrogen, helium, and oxygen bands representative of different phases of a magnetic storm. Finally, diffusion coefficients for recoveryphase heliumband EMIC waves are combined with those for typical whistler hiss, resulting in electron precipitation lifetimes substantially less than those due to hiss alone. Published by: Journal of Geophysical Research Published on: 06/2003 YEAR: 2003 DOI: 10.1029/2002JA009792 
2000 
The response of outer radiation belt relativistic electrons to the October 9, 1990, magnetic storm is analyzed in detail using a radial diffusion model and data from the Combined Release and Radiation Effects Satellite (CRRES) and the Los Alamos National Laboratory (LANL) geosynchronous satellite 1989046. Electron measurements are expressed in terms of phase space density as a function of the three adiabatic invariants determined from CRRES magnetic field data and the Tsyganenko 1989 Kpdependent magnetic field model. The radial diffusion model is implemented with a timedependent radial diffusion coefficient parameterized by Kp, and a timedependent outer boundary condition scaled by geosynchronous electron data. The results show that radial diffusion propagates outer boundary variations into the heart of the outer radiation belt, accounting for both significant decreases and increases in the <1 MeV electron flux throughout that region. It is further shown that the gradual increase throughout the recovery phase of the >1 MeV electrons is inconsistent with the radial diffusion model given the parameter regime chosen for this study. Greatly enhanced whistler chorus waves observed by CRRES throughout the recovery phase suggest that a possible explanation for the inconsistency may be electron acceleration via waveparticle interaction. Published by: Journal of Geophysical Research Published on: 01/2000 YEAR: 2000 DOI: 10.1029/1999JA900344 
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