Abstract
Nonlinear processes associated with the generation process of whistler-mode chorus emissions are summarized. The nonlinear dynamics of energetic electrons interacting with a coherent whistler-mode wave and the formation of electromagnetic electron holes or hills in the velocity phase space are described. The condition for resonant electrons to be free from the anomalous trapping at low pitch angles is obtained. In the presence of the inhomogeneity due to the frequency variation and the gradient of the magnetic field, the electron holes or hills result in resonant currents generating rising-tone emissions or falling-tone emissions, respectively. After formation of a coherent wave at a frequency of the maximum linear growth rate, triggering of the nonlinear wave growth takes place when the wave amplitude is above the threshold amplitude. The wave grows to a level close to the optimum wave amplitude as an absolute instability near the magnetic equator. The nonlinear growth rate at a position away from the equator is derived for a subtracted Maxwellian momentum distribution function with correction to the formulas in the past publications. The triggering process is repeated sequentially at progressively higher frequencies in the case of a rising-tone emission, generating subpackets forming a chorus element. With a higher plasma density as in the plasmasphere, the triggering of subpackets takes place concurrently over a wide range of frequency forming discrete hiss elements with varying frequencies. The mechanism of nonlinear wave damping due to quasi-parallel propagation from the equator is presented, which results in the formation of a gap at half the electron cyclotron frequency, separating a long rising-tone chorus emission into the upper-band and lower-band chorus emissions. The theoretical formulation of an oblique whistler mode wave and its interaction with energetic electrons at the n-th resonance is also presented along with derivation of the inhomogeneity factor.
Highlights
Whistler-mode chorus emissions have been studied for more than half a century, and their generation mechanism has not been clarified completely yet
We have introduced some randomness assuming that there exist fluctuations of the electromagnetic fields which are radiated from counter-streaming energetic electrons, which are modulated in their wave phases through interaction with foregoing waves
Studied the effect of the gradient of the magnetic field on generation process of chorus and broadband hiss-like. The generation of these emissions with frequency variation is due to a coherent wave that modify the velocity distribution function F (v ) with its wave potential formed at the cyclotron resonance velocity VR as we studied in the previous sections
Summary
Whistler-mode chorus emissions have been studied for more than half a century, and their generation mechanism has not been clarified completely yet. Along with the gradient of the background magnetic field, the trapped electrons are accelerated by the parallel and perpendicular electric fields of the wave, while the waves near half the cyclotron frequency undergo damping giving energy to the electrons This results in the formation of a gap separating chorus elements into the lower-band and upper-band emissions. Review papers on chorus emissions (Tao et al 2020) and on controlled excitation of nonlinear wave-particle interactions (Golkowski et al 2019) were published recently Thanks to these comprehensive review papers, I can focus on providing a consistent summary of the nonlinear wave growth theory developed in recent years in an attempt to understand results of simulations and observations of whistlermode chorus and hiss emissions.
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