Comparison of bounce-averaged quasi-linear diffusion coefficients for parallel propagating whistler mode waves with test particle simulations

摘要

Quasi-linear bounce-averaged diffusion coefficients for interactions between electrons and parallel propagating whistler waves in a dipole field are compared with test particle simulations. We solve equations of motion for a large number of electrons interacting with waves with a Gaussian distribution of wave power. For broadband and small amplitude waves, which are assumed by the quasi-linear analysis, our test particle simulation results agree well with quasi-linear theory predictions. We then demonstrate the effect of the wave amplitude on diffusion coefficients. We show that as the amplitude increases, the bounce-averaged quasi-linear diffusion coefficients become invalid. Critical wave amplitudes for the breakdown of the bounce-averaged diffusion coefficients for a range of energies and pitch angles are calculated for the set of wave parameters we used. Finally, we investigate the effect of wave bandwidth on bounce-averaged diffusion coefficients. Consistent with a previous theoretical prediction, bounce-averaged quasi-linear diffusion coefficients are still valid for narrowband waves, as long as the wave amplitude is small. When the amplitude of the narrowband wavefield increases, nonlinear effects such as phase-bunching and trapping become dominant and correspondingly quasi-linear theory becomes invalid. Our results demonstrate the validity of applying quasi-linear theory to interactions between electrons and small amplitude plasma waves in the radiation belt.