Dynamics of high-energy electrons interacting with whistler mode chorus emissions in the magnetosphere

Close examination of whistler mode chorus emissions reveals that a chorus emission is a coherent monochromatic wave typically with a fast rising tone. The frequency of the emission increases rapidly along with growth of the wave amplitude. We first consider the generation mechanism of whistler mode chorus emissions. The essential mechanism of the frequency change is critically related to the inhomogeneity of the geomagnetic field in the equatorial region. The rising tone emission is only possible when the coherent wave propagates away from the equator interacting with a sufficient flux of counterstreaming resonant electrons. Depletion of the resonant trapped electrons from the wave phase space results in formation of an electromagnetic electron hole, which gives rise to a transverse resonant current causing both wave growth and frequency increase. The wave growth of a rising tone can elongate the nonlinear trapping zone, which works as an effective wave train that guides a fraction of the resonant electrons moving toward the equator. We perform test particle simulations where we solve the relativistic equations of motion for high-energy electrons under the action of the electromagnetic field of a coherent whistler mode wave and the assumed dipole geomagnetic field. We find that a fraction of weakly relativistic electrons are trapped by a coherent wave and that the trapped electrons are effectively accelerated by the chorus wave with a rising tone.