Amplitude dependence of frequency sweep rates of whistler mode chorus emissions

The frequency and amplitude characteristics of chorus emissions are studied by performing electron hybrid code simulations with different initial number densities of energetic electrons. Chorus emissions with rising tones are generated in all simulation runs except for the simulation assuming the lowest number density. The frequency sweep rates of reproduced chorus vary depending on the variation of the wave amplitude of respective chorus elements. We find that the theoretically estimated frequency sweep rates are consistent with the simulation results. The simulation results reveal that the characteristic frequency variation of chorus elements showing rising tones are formed at the region very close to the magnetic equator while the wave amplitudes of chorus elements are significantly amplified through their propagation away from the equator. The spatial scale of the region where the observed explosive wave growth varies in each simulation run, corresponding to the difference of the wave amplitudes of reproduced chorus elements. We estimate the spatial scale h_c, a measure of the spatial extent of the generation region derived from the nonlinear wave growth theory, using parameters of the simulation runs and find its consistency with the simulation results. We also analyze the energy spectra of reproduced chorus elements in the simulation results and find that the spectra of chorus are essentially different from those predicted by the linear growth rates in the frequency domain. These results clearly demonstrate that the nonlinear wave-particle interaction governs the chorus generation mechanism.