Electron-acoustic waves by (modified) Zakharov–Kuznetsov equation and their multi-dimensional instability in the auroral zone

Abstract

The feature of electron-acoustic waves (EAWs) in a magnetized plasma composed of stationary ions, nonthermal electrons and cold electron fluids is presented. The Zakharov–Kuznetsov (ZK) equation and modified Zakharov–Kuznetsov (mZK) equation are derived via reductive perturbation technique. The solitary wave solutions of ZK and mZK equations and the corresponding growth rates of multi-dimensional instability are given via small k perturbation method. The instability criterion and growth rate rely on obliqueness, magnetic field strength, temperature and density ratios of the hot-to-cold electron species, nonthermal parameter and direction cosines. It is apparent that, in the dayside auroral zone, there only exists negative potential solitary waves, and when the external magnetic field is larger and obliqueness is smaller, EAWs by mZK equation are more unstable than that by ZK equation. The results are beneficial to understand different nonlinear characteristics of unstable electrostatic disturbances in laboratory and space plasmas.