Dispersion Relations for Electron Acoustic Waves in Plasmas with Anisotropic Power Law Distributions

Electron-acoustic waves (EAWs) exist in space and laboratory plasmas where two different electron populations, called cool and hot electrons, occur. It has been shown that the distribution functions of both populations of electrons frequently have non-Maxwellian form. In this paper, we investigate that how various plasma parameters change the structure of EAWs by using kinetic theory model. Different forms of kappa distributions are used to model the electron velocity distribution, corresponding to the range of temperatures and kappa values. Dispersion and damping curves illustrate the behavior of EAWs in plasma. The outcomes of these models depict that the cool and hot electron densities are almost equal in regions of weak damping of EAWs. Damping of EA Ws is strong due to hot electrons in low normalized wave number regime. A high normalized wave number regime involves the strong Landau damping due to cool electrons as thermal velocity of cool electrons decreases and become comparable to phase velocity of waves ($v_{\phi}\sim v_{th_{c}}$). It is predicted that the damping of EAWs is strong for high and low values of normalized wave numbers and waves are observable in the range of intermediate value of normalized wave number.

I. Introduction

In recent years, studies of linear and nonlinear Electron acoustic waves (EAWs) in plasmas with non-thermal electrons have become a great deal of interest [1]. The linear analysis of EAWs, gives heavily damped acoustic-like solution in addition to the Langmuir waves and ion-acoustic waves (IAWs). The electron acoustic waves can exist in, Radiation belts, planetary magneto sphere, Confinement of plasma for fusion purposes and shock waves in solar wind. Satellite observations have shown existence of electron acoustic waves in the Earth's magnetosphere, solar wind and in the distant magneto tail [2]. EAWs occur in plasma where two population of electrons co-exit called hot electrons and cool electrons having temperature and , respectively. These are high-frequency electrostatic waves as compared to ion acoustic waves. EAWs have phase velocity greater than thermal velocity () of cool electron and lesser than thermal velocity () of hot electron [3].