Markov Chain Modeling of Nonlinear Electron Scattering by Rising‐Tone Chorus Waves

Abstract Whistler‐mode chorus waves play a central role in energetic electron dynamics in Earth's inner magnetosphere. Although test‐particle simulations can directly model these interactions, their high computational cost limits phase space resolution and hinders tracking of long‐term phase space density (PSD) evolution. Here, we present a new Markov chain method to simulate PSD evolution in a realistic rising‐tone chorus wave packet model. The wave model is constructed using ray‐tracing techniques (the method of characteristic curves), and Green's functions derived from test‐particle simulations are used to build the Markov transport matrix, enabling efficient computation of PSD evolution. Our results reproduce the characteristic butterfly pitch‐angle distributions of electrons above 20 keV. Sub‐10 keV electrons are efficiently scattered at intermediate pitch angles through nonlinear phase bunching, and exhibit negative PSD gradients when they are scattered into loss cone. These findings highlight the significant role of rising‐tone chorus waves in energetic electron scattering and establish the Markov chain approach as an efficient framework for investigating long‐term nonlinear wave–particle interactions.