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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.

Plain Language Summary Whistler mode chorus waves are intense electromagnetic emissions that play an important role in pitch angle scattering and acceleration of electrons in the Earth's outer radiation belt. Particularly, large amplitude chorus waves can result in nonlinear interactions with electrons, known as phase trapping and phase bunching. Previous studies have shown that phase trapping can accelerate electrons rapidly while phase bunching can decelerate electrons. However, quantification of such nonlinear interactions and their dependence on chorus wave amplitude modulations have not been fully understood. In this paper, we use a set of parameters to quantify the nonlinear interactions between chorus waves and electrons in a wide range of energy (0.01-10 MeV) and equatorial pitch angle (0-90 degrees). We found that nonlinear interactions lead to different pitch angle and energy variations at different regions of the pitch angle-energy space. We also found that nonlinear interactions are in general reduced by the amplitude modulations of chorus waves, with phase trapping being most significantly affected. Our study suggests that the effects of wave amplitude modulations need to be properly included in future theoretical and numerical studies.