Generation mechanism of VLF chorus emissions and relativistic electrons in the magnetosphere

Summary form only given. We first study the generation mechanism of whistler mode chorus emissions. The essential mechanism of the frequency change is due to the inhomogeneity of the geomagnetic field in the equatorial region. A whistler mode wave can trap electrons near the cyclotron resonant velocity. The trapping is only possible near the equator where the Lorentz force due to the magnetic field component of the whistler mode wave is larger than the magnetic mirror force due to the inhomogeneity of the geomagnetic field. The electrons approaching the equator get into resonance with the wave when the parallel velocity increases to the resonance velocity of the wave due to the adiabatic motion. Most of the resonant electrons, however, do not enter the trapping region, because the separatrix of the trapping region is closed. Only a fraction of the resonant electrons near the separatrix get into the trapping region because of the enlargement of the separatrix as the particles approaches to the equator. Consequently, there arises a deficit of trapped particles in the velocity phase space, giving rise to a resonant current causing wave growth and frequency increase. Since the resonant current changes its polarization to cause wave damping on the other side of the equator, the rising tone emissions with increasing amplitudes are only possible when the coherent wave propagates away from the equator interacting with counter-streaming resonant electrons. The relativistic electrons with relatively high pitch angles can readily get into resonance with such a coherent whistler wave, if their parallel velocities satisfy the relativistic cyclotron resonance condition. We performed test particle simulations where we solved relativistic equations of motion for high energy electrons under the electromagnetic fields of a coherent whistler mode wave and the dipole geomagnetic field. We find that resonant trapping of relativistic electrons by a whistler mode wave with a rising tone results in efficient acceleration of resonant particles to relativistic energy.