Theoretical and numerical analysis of radiation belt electron precipitation by coherent whistler mode waves

The interaction between coherent whistler mode waves and energetic radiation belt electrons can result in pitch angle scattering of electrons into the bounce loss cone and subsequent precipitation. In studying the effects of VLF transmitter signals on particle precipitation, past modeling efforts have focused on the computation of diffusion coefficients for a Fokker-Planck model. In contrast, to capture the nonlinear effects of large-amplitude coherent waves, we evaluate particle precipitation using a Vlasov-Liouville (VL) model which computes the phase space particle distribution function directly using a characteristic-based solution of the Vlasov equation. Previous work has shown that in the case of large-amplitude coherent waves, phase trapping can significantly perturb resonant particles from their adiabatic paths. We evaluate the importance of phase trapping over a range of wave amplitudes (up to 200 pT); the percentage of particles that precipitate after being phase trapped is computed over a phase space grid in the loss cone. The results demonstrate that phase trapping contributes significantly to precipitation when a large-amplitude wave (>100 pT) is present. Additionally, linear theory can be valid over a broad range of amplitudes and the relative accuracy of linear theory in calculating the precipitated flux depends strongly on the initial particle distribution. Additionally, we demonstrate the ability of the VL model to calculate the time evolution of the precipitated flux due to short-duration whistler mode pulses. The physical parameters used in this study are typical of those associated with the Siple Station wave injection experiment.