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

Abstract

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.