Nonlinear pitch angle scattering of energetic electrons near the loss cone by whistler mode chorus emissions

Chorus emissions are coherent whistler mode waves observed in the inner magnetosphere and scatter the pitch angle of energetic electrons, while the precipitation of energetic electrons into the atmosphere contributes to diffuse and pulsating aurora. Conventionally, it has been considered that particles that satisfy the cyclotron resonance condition in the energy range from a few keV to tens of keV are scattered toward the loss cone by whistler mode waves. While the nonlinear motion of resonant particles encountering a coherent wave has been studied more than 40 years (cf. Omura et al., 1991), in the derivation of the equations, previous studies assumed small wave amplitude compared to the ambient magnetic field B0 (Dysthe, 1971) and large pitch angle of energetic electrons (Nunn, 1974). In this study, we derive the equations without both of the assumptions, and theoretically evaluate the additional term related to the Lorentz force caused by the wave magnetic field and the parallel velocity of particles. Furthermore, we carry out a test particle simulation and reproduce that the additional term plays a role of the pitch angle scattering away from the loss cone. In the simulation results of parallel propagating coherent waves with constant frequency, diffusion-like scattering of resonant electrons is observed in the case of waves with weak amplitude (0.1 % of B0). On the contrary, all of resonant electrons are scattered in the pitch angle away from the loss cone in the case of waves with larger amplitude (more than 0.5 % of B0). We also carry out simulations for the case of waves with frequency sweeping and find that particles near the loss cone are more effectively scattered away from the loss cone by the wave with large amplitude (more than 0.7 % of B0). These results suggest that the relation between chorus wave intensity and the flux of auroral electron precipitation is not straightforward and should be investigated by considering the nonlinear effects.