Test particle simulations of resonant interactions between energetic electrons and discrete, multi-frequency artificial whistler waves in the plasmasphere

Modulated high frequency (HF) heating of the ionosphere provides a feasible means of artificially generating extremely low frequency (ELF)/very low frequency (VLF) whistler waves, which can leak into the inner magnetosphere and contribute to resonant interactions with high energy electrons. Combining the ray tracing method and test particle simulations, we evaluate the effects of energetic electron resonant scattering driven by the discrete, multi-frequency artificially generated ELF/VLF waves. The simulation results indicate a stochastic behavior of electrons and a linear profile of pitch angle and kinetic energy variations averaged over all test electrons. These features are similar to those associated with single-frequency waves. The computed local diffusion coefficients show that, although the momentum diffusion of relativistic electrons due to artificial ELF/VLF whistlers with a nominal amplitude of ~ 1 pT is minor, the pitch angle scattering can be notably efficient at low pitch angles near the loss cone, which supports the feasibility of artificial triggering of multi-frequency ELF/VLF whistler waves for the removal of high energy electrons from the magnetosphere. We also investigate the dependences of diffusion coefficients on the frequency interval (Δf) of the discrete, multi-frequency waves. We find that there is a threshold value of Δf for which the net diffusion coefficient of multi-frequency whistlers is inversely proportional to Δf (proportional to the frequency components Nw) when Δf is below the threshold value but it remains unchanged with increasing Δf when Δf is larger than the threshold value. This is explained as being due to the fact that the resonant scattering effect of broadband waves is the sum of the effects of each frequency in the ‘effective frequency band’. Our results suggest that the modulation frequency of HF heating of the ionosphere can be appropriately selected with reasonable frequency intervals so that better performance of controlled precipitation of high energy electrons in the plasmasphere by artificial ELF/VLF whistler waves can be achieved.