Diffusive and non-diffusive behavior of electron interaction with quasi-coherent and quasi-parallel chorus emissions

Numerical models used to study the Earth’s outer radiation belt dynamics are often based on the diffusive Fokker-Planck equation derived from the quasilinear theory of wave-particle interactions. However, this stochastic approach fails at short time scales due to nonlinear interactions with high-amplitude waves, which can result in a rapid directional transport of particles in the phase space. An example of strong waves that facilitate nonlinear transport is the chorus emission, which often forms discrete, rising-tone elements with a high degree of phase coherence.It is expected that after multiple resonant interactions of electrons with the chorus waves, the stochastic description of scattering becomes applicable. However, it is unclear how this convergence towards stochastic and diffusive behavior depends on the wave parameters. We, therefore, construct a realistic model of chorus elements parametrized by bandwidth, wave normal distribution, frequency range, and amplitude. With this model, we numerically investigate the evolution of electron pitch angle and energy over multiple bounces. We use the backward-in-time test-particle mapping of phase space density for each element separately, and obtain the long-term evolution with a variable train of chorus elements by combining the individual mappings. We analyze the onset of stochasticity in dependence on the wave parameters and compare the phase space density evolution with the VERB-2D (Versatile Electron Radiation Belt code) implementation of the diffusive Fokker-Planck equation.