Role of “positive phase bunching” effect for long-term electron flux dynamics due to resonances with whistler-mode waves

Abstract

Resonant interactions with electromagnetic whistler-mode waves are a primary driver of energetic electron dynamics in the Earth's radiation belts. The most intense waves can resonate with electrons nonlinearly, and effects of such nonlinear resonant interactions significantly differ from the classical quasi-linear diffusion. There have been continuous efforts on the theoretical investigation and implementation of these effects into radiation belt models, but not all nonlinear effects have been revealed yet. The two most investigated effects are phase trapping and phase bunching, which are responsible for electron acceleration and precipitation into the Earth's atmosphere, respectively, i.e., for the first cyclotron resonance with waves generated at the equator and propagating to higher latitudes, phase trapping increases electrons' energy, whereas phase bunching decreases the electron pitch-angle (and magnetic moment). However, recent studies reported a new effect called positive phase bunching, which may increase the electron pitch-angle and move them away from the loss-cone. This paper aims to characterize possible contributions of this effect to long-term electron dynamics, including multiple resonant interactions. Using an iterated mapping technique, we show that although the positive phase bunching effect can modify electron trajectories, it does not change the average rate of electron mixing in phase space. Thus, this effect may be safely neglected in long-term simulations of radiation belt dynamics. We also discuss possible verification of the positive phase bunching effect using short (single resonance), bursty electron precipitation events.