Modeling Energetic Electron Nonlinear Wave-Particle Interactions With Electromagnetic Ion Cyclotron Waves

Electromagnetic ion cyclotron (EMIC) waves in duskside plasmasphere and plasmaspheric plume scatter megaelectron volt electrons into the loss cone and are considered a major loss mechanism for the outer radiation belt. Wave-particle interaction between energetic electrons and EMIC waves has been studied extensively by the quasi-linear diffusion theory. However, EMIC waves are typically strong enough to trigger nonlinear wave-particle interaction effects and transport electrons in very different ways from quasi-linear diffusion. New mathematical method is therefore in demand to study the evolution of energetic electron distribution in response to nonlinear wave-particle interaction. In this work, we present a Markov chain description of the wave-particle interaction process, in which the electron distribution is represented by a state vector and is evolved by the Markov matrix. The Markov matrix is a matrix form of the electron response Green's function and could be determined from test particle simulations. Our modeling results suggest that electron loss rate is not significantly affected by phase bunching and phase trapping, but for strong EMIC waves, electron distribution is more saturated near loss cone than quasi-linear theory prediction, and negative electron phase space density slope develops inside loss cone.