Evolution of electron distribution driven by nonlinear resonances with intense field-aligned chorus waves

TL;DR

This paper develops a new kinetic model incorporating nonlinear wave-particle interactions, such as trapping and scattering, to better understand electron dynamics in Earth's radiation belts driven by intense chorus waves.

Contribution

It introduces an analytical framework for nonlinear resonant interactions and integrates observational statistics to improve modeling of electron acceleration and scattering.

Findings

Nonlinear effects can cause rapid electron acceleration.

A nonlocal operator models trapping and scattering in the kinetic equation.

The model aligns with observational data from Van Allen Probes and THEMIS.

Abstract

Resonant electron interaction with whistler-mode chorus waves is recognized as one of the main drivers of radiation belt dynamics. For moderate wave intensity, this interaction is well described by quasi-linear 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 the quasi-linear diffusion. For sufficiently long (large) wave-packets, 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 wave-packets as function of power and frequency. Then we develop an analytical model of particle resonance of an individual particle with an intense chorus wave-packet 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 the nonlinear wave-particle interaction.