Van Allen Probes Bibliography is from August 2012 through September 2021 Notice:

Evolution of electron distribution driven by nonlinear resonances with intense fieldaligned chorus waves
Author  Vainchtein, D.; Zhang, X.J.; Artemyev, A.; Mourenas, D.; Angelopoulos, V.; Thorne, R.; 
Keywords  Van Allen Probes 
Abstract  Resonant electron interaction with whistlermode chorus waves is recognized as one of the main drivers of radiation belt dynamics. For moderate wave intensity, this interaction is well described by quasilinear theory. However, recent statistics of parallel propagating chorus waves have demonstrated that 5  20\% of the observed waves are sufficiently intense to interact nonlinearly with electrons. Such interactions include phase trapping and phase bunching (nonlinear scattering) effects not described by quasilinear diffusion. For sufficiently long (large) wavepackets, these nonlinear effects can result in very rapid electron acceleration and scattering. In this paper we introduce a method to include trapping and nonlinear scattering into the kinetic equation describing the evolution of the electron distribution function. We use statistics of Van Allen Probes and Time History of Events and Macroscale Interactions during Substorms (THEMIS) observations to determine the probability distribution of intense, long wavepackets as a function of power and frequency. Then we develop an analytical model of individual particle resonance with an intense chorus wavepacket and derive the main properties of this interaction: probability of electron trapping, energy change due to trapping and nonlinear scattering. These properties are combined in a nonlocal operator acting on the electron distribution function. When multiple waves are present, we average the obtained operator over the observed distributions of waves and examine solutions of the resultant kinetic equation. We also examine energy conservation and its implications in systems with nonlinear waveparticle interaction. 
Year of Publication  2018 
Journal  Journal of Geophysical Research: Space Physics 
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Number of Pages  
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Date Published  09/2018 
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URL  https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018JA025654 
DOI  10.1029/2018JA025654 