Theory and simulations of nonlinear wave-particle interactions in planetary radiation belts

There has been significant progress in understanding the generation mechanism of whistler-mode chorus emissions in recent years. This is partly due to the successful reproduction of chorus emissions by computer simulations, and partly due to precise observations of the emissions by spacecraft in planetary radiation belts. We give a brief account of the nonlinear theory of the generation mechanism of chorus emissions, which has been revealed by the simulations and observations. 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. In contrast, falling-tone emissions are generated through the formation of electron “hills.” We also describe the mechanism of nonlinear wave damping due to quasi-oblique propagation, which results in the formation of a gap at half the electron cyclotron frequency. The nonlinear wave-growth theory of chorus emissions can also be applied to the generation mechanism of electromagnetic ion-cyclotron-(EMIC) triggered emissions, recently found in spacecraft observations. Hybrid code simulations have confirmed that coherent rising-tone emissions are generated by energetic protons at frequencies below the proton cyclotron frequency. Electromagnetic ion-cyclotron waves can also interact with relativistic electrons. Both chorus emissions and electromagnetic ion-cyclotron-triggered emissions play important roles in controlling radiation-belt particle dynamics.