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The electron resonant interaction with whistler‐mode waves is characterized by transport in pitch angle–energy space. We calculate electron diffusion and advection coefficients (a simplified characterization of transport) for a large range of electron pitch angle and energy using test particle simulations. Nonlinear effects are analyzed by comparing the diffusion coefficients using test particle simulations and quasilinear theory, and by evaluating the advection rates. Dependence of nonlinear effects on the wave amplitude and bandwidth of whistler‐mode waves is evaluated by running test particle simulations with a broad range of wave amplitude and bandwidth. The maximum amplitudes where the quasilinear approach is valid are found to increase with increasing bandwidth, from 50 pT for narrowband waves to 300 pT for broadband waves atL‐shell of 6. Moreover, interactions between intense whistler‐mode waves and small pitch angle electrons lead to large positive advection, which limits the applicability of diffusion‐based models. This study demonstrates the parameter range of the applicability of quasilinear theory and diffusion model for different wave amplitudes and frequency bandwidths of whistler‐mode waves, which is critical for evaluating the effects of whistler‐mode waves on energetic electrons in the Earth’s magnetosphere.

Radiation belt electrons are strongly affected by resonant interactions with cyclotron‐resonant waves. For broad band, small amplitude waves the interactions are well described by quasi‐linear diffusion in pitch angle and energy, but coherent, large amplitude waves such as strong whistler mode chorus call for a different treatment. The standard nonlinear framework reduces the problem to that of a classical pendulum. This picture has generally been confirmed by many numerical simulations, but recent studies have uncovered additional, complex behavior, not captured by the pendulum model, for particles with low pitch angle. We show that avoiding a commonly made approximation leads to a more general but still tractable “second fundamental model” Hamiltonian, which involves not one but two regions of phase trapping. We analyze its phase portraits in detail, and perform representative test particle simulations with slowly changing parameters. We find that the trajectories encompass traditional phase bunching and phase trapping as well as additional behavior best understood using the new model.

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.

The “Quantitative Assessment of Radiation Belt Modeling” focus group was in place at Geospace Environment Modeling from 2014 to 2018. The overarching goals of this focus group were to bring together the current state‐of‐the‐art models for the acceleration, transport, and loss processes in Earth's radiation belts; develop event‐specific and global inputs of wave, plasma, and magnetic field to drive these models; and combine all these components to achieve a quantitative assessment of radiation belt modeling by validating against contemporary radiation belt measurements. This article briefly reviews the current understanding of radiation belt dynamics and related modeling efforts, summarizes the activities and accomplishments of the focus group, and discusses future directions.

We use test particle simulations to model the interaction between radiation belt electrons and whistler mode chorus waves by focusing on wave amplitude modulations. We quantify the pitch angle and energy changes due to phase trapping and phase bunching (including both advection and scattering) for electrons with various initial energies and pitch angles. Three nonlinear regimes are identified in a broad range of pitch angle‐energy space systematically, each indicating different nonlinear effects. Our simulation results show that wave amplitude modulations can extend the nonlinear regimes, while significantly reducing electron acceleration by phase trapping. By including amplitude modulations, the “advective” changes in pitch angle and energy caused by phase bunching are reduced, while the “diffusive” scattering due to phase bunching is enhanced. Our study demonstrates the importance of wave amplitude modulations in nonlinear effects and suggests that they need to be properly incorporated into future theoretical and numerical studies.