Relativistic electron scattering by large amplitude electromagnetic ion cyclotron waves: The role of phase bunching and trapping

Test particle computations are performed to study the interactions of relativistic electrons with electromagnetic ion cyclotron waves propagating parallel to the background magnetic field in a homogeneous plasma. In addition to their pitch angle scattering, electrons experience phase bunching and trapping and become clustered in gyrophase angle when the wave amplitude is sufficiently large. The concepts of electron phase bunching and trapping are defined and first illustrated for electrons interacting with a monochromatic wave. When the wave amplitude is sufficiently large, the electrons in or nearly in resonance with the wave are mainly phase trapped while the off-resonance electrons are only phase bunched. Phase trapping of electrons leads to nonlinear advection of the electrons toward the resonant pitch angle, at which the electrons with a specified kinetic energy are in resonance with the wave. For a broadband spectrum of incoherent waves, these general trends of electron phase bunching and trapping remain qualitatively the same, but they are not as evident as in the monochromatic wave case due to phase mixing of the electrons. The pitch angle diffusion coefficient and advection rate are evaluated from test particle computations of relativistic electron scattering by broadband waves. The results agree well with quasi-linear results when the waves are sufficiently weak, as expected. When the waves become strong, however, the diffusion coefficient and advection rate deviate from the predictions of quasi-linear theory, due to electron phase bunching and trapping. The diffusion coefficient is a flatter function of pitch angle than that predicted by quasi-linear theory. Electron phase bunching and trapping introduce nonlinear advection of the electrons, which is additional to the inherent advection included in the diffusion equation of quasi-linear theory and shifts the electrons toward the pitch angle at which the electrons with a specified kinetic energy are in resonance with the wave at the spectral peak. Finally, our results suggest that electron phase bunching and trapping by large amplitude waves flatten the pitch angle distribution and reduce the loss rate for relativistic electrons trapped in the radiation belts, compared to the predictions of quasi-linear theory. The present study focuses only on local electron scattering in a homogeneous background magnetic field and the results are therefore subject to possible modification after bounce averaging.