Nonlinear dynamics of electrons interacting with oblique whistler mode waves in the magnetosphere

We investigate the properties of whistler-mode wave particle interactions at oblique angles to the background magnetic field. We compare an exact formula of oblique whistler-mode dispersion relation with that of the quasi-longitudinal approximation. We derive a group velocity of an oblique whistler-mode wave as a function of wave frequency, wave vector, and wave normal angle. We find that the angle between the group velocity and the background magnetic field is always less than 30° even if the wave normal angle is up to 80° for the wave frequency less than 0.5 times the electron gyrofrequency. This relation points out that the wave energy is always transported parallel to the ambient magnetic field. Landau resonance, which appear in oblique whistler-mode waves but not in parallel waves, results in significant electron acceleration. To reveal the physical process and the efficiency of electron acceleration, we perform test particle simulations with electrons started at specific equatorial pitch angles and kinetic energies. By confirming that the group velocity is nearly parallel to the background magnetic field, we utilize gyro-averaging method, which averages the cyclotron motion at gyro-center and reduces the simulation from two-dimensional system to one-dimensional system. The simulation results show that 10-1000keV electrons can be accelerated to multi-MeV energy through Landau resonance as well as the cyclotron resonance.