Excitation of Upper‐Hybrid and Whistler‐Mode Waves by Electron Velocity Ring Distribution

Abstract The magnetospheres of the Earth and other magnetized planets are replete with high‐frequency fluctuations, which are sometimes accompanied by multiple‐harmonic electron cyclotron waves, and lower frequency waves of the whistler‐mode type. Such waves are presumed to be excited by energetic electrons trapped in the dipolar magnetic field, the so‐called loss‐cone electrons, the electron ring distribution being a highly idealized example. The present paper investigates the stability of electron ring distribution with respect to the excitation of quasi‐electrostatic upper‐hybrid wave instability as well as the quasi‐electromagnetic whistler mode instability that operates near electron cyclotron frequency. By employing a two‐dimensional particle‐in‐cell numerical simulation, it is demonstrated that the relatively early dynamics is dominated by the upper‐hybrid wave instability, but over a longer time period it is the whistler mode instability that ultimately determines the final relaxed state. The simulation results are interpreted with the quasilinear theoretical framework.