Higher-order contribution to obliquely nonlinear electron-acoustic waves with electron beam in a magnetized plasma

Abstract

Propagation of electron-acoustic waves in a strongly magnetized four-component plasma consisting of cold and hot electrons, a warm electron beam, and stationary ions is investigated. The present model considered weakly dispersive and strongly magnetized plasma in the limit of long wavelengths. The introduction of an electron beam allows the existence of electron-acoustic solitons with velocity related to the beam velocity. With increasing the beam velocity and the beam temperature, both the soliton amplitude and the width increase. Applying a reductive perturbation theory, a nonlinear Zakharov-Kuznetsov (ZK) equation for the first-order perturbed potential and a linear inhomogeneous Zakharov-Kuznetsov (ZK-type) equation for the second-order perturbed potential are derived. Stationary solutions of these coupled equations are obtained using a renormalization method. These solutions admit either compressive or rarefactive soliton type depending on the electron-beam parameters. Moreover, the dependence of the solution on the beam parameters, obliqueness on the magnetic field, and the magnetic field itself is also investigated. The application of the present investigation to the broadband electrostatic noise in the dayside auroral zone of the Earth’s magnetosphere is considered.