Nonlinear Convective Growth of Whistler-mode Chorus and Electromagnetic Ion Cyclotron Rising-tone Emissions

Abstract

We give a brief review of the nonlinear wave growth theory of whistler-mode chorus emissions [1], [2]. We describe the nonlinear dynamics of resonant electrons, and the formation of the electromagnetic electron “hole” that results in resonant currents generating rising-tone emissions. We have theoretically derived threshold and optimum wave amplitudes for the nonlinear wave growth of rising-tone emissions. Nonlinear wave growth as an absolute instability takes place above the threshold amplitude near the magnetic equator, and the wave grows rapidly along with frequency increase. The nonlinear wave growth saturate around the optimum amplitude, and the wave amplitude damps to the level of the threshold amplitude. The nonlinear wave growth process is repeated, resulting in a series of sub-packets forming a rising-tone chorus element. As the wave packet propagates away from the equator, it undergoes nonlinear convective growth. The profiles of these wave amplitudes as functions of frequencies agree well with those from observations and simulations. As the wave packet propagates away from the equator, it undergoes efficient nonlinear convective growth. The wave normal angle gradually deviates from the parallel direction, and there occurs nonlinear wave damping at half the cyclotron frequency, separating the chorus element into lower-band and upper-band emissions [3]. At half the cyclotron frequency, the parallel phase velocity and parallel group velocity of a whistler-mode wave become nearly equal, enabling efficient nonlinear trapping of electrons by the wave fields through Landau resonance. The nonlinear wave growth theory of chorus emissions can be applied to the generation mechanism of electromagnetic ion cyclotron (EMIC) wave emissions [4]. Hybrid code simulations have confirmed that coherent rising-tone emissions are generated by energetic protons at frequencies below the proton cyclotron frequency through formation of electromagnetic proton holes [5]. Both chorus and EMIC emissions are generated near the magnetic equator, and some of them propagate along the magnetic field to the ground. Characteristics of these wave spectra are not affected much through propagation to the ground. The ground observations of these wave spectra can give us important clues for remote sensing of plasma conditions in the equatorial magnetosphere.