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2018 
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. Vainchtein, D.; Zhang, X.J.; Artemyev, A.; Mourenas, D.; Angelopoulos, V.; Thorne, R.; Published by: Journal of Geophysical Research: Space Physics Published on: 09/2018 YEAR: 2018 DOI: 10.1029/2018JA025654 
2015 
In the present paper, we investigate the trapping of relativistic electrons by intense whistlermode waves or electromagnetic ion cyclotron waves in the Earth\textquoterights radiation belts. We consider the nonresonant impact of additional, lower amplitude magnetic field fluctuations on the stability of electron trapping. We show that such additional nonresonant fluctuations can break the adiabatic invariant corresponding to trapped electron oscillations in the effective wave potential. This destruction results in a diffusive escape of electrons from the trapped regime of motion and thus can lead to a significant reduction of the efficiency of electron acceleration. We demonstrate that when energetic electrons are trapped by intense parallel or very oblique whistlermode waves, nonresonant magnetic field fluctuations in the whistlermode frequency range with moderate amplitudes around 315 pT (much less intense than the primary waves) can totally disrupt the trapped motion. However, the trapping of relativistic electrons by electromagnetic ion cyclotron waves is noticeably more stable. We also discuss how the proposed approach can be used to estimate the effects of wave amplitude modulations on the motion of trapped particles. Artemyev, A.; Mourenas, D.; Agapitov, O.; Vainchtein, D.; Mozer, F.; Krasnoselskikh, V.; Published by: Physics of Plasmas Published on: 08/2015 YEAR: 2015 DOI: 10.1063/1.4927774 Cyclotron resonances; magnetic fields; Particle fluctuations; Plasma electromagnetic waves; Whistler waves 
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