Current-Driven Buneman Instability in Inhomogeneous Plasmas

Current-driven Buneman instability in inhomogeneous plasmas is investigated. Considering the continuity, momentum transfer, and Poisson’s equations, an eikonal equation is derived. The dispersion relation is obtained using the approximation of geometrical optics in two cases. In the first case, the electron density has linear inhomogeneity while other parameters are homogeneous. In another case, only the collision frequency is inhomogeneous and the inhomogeneity is a parabolic function. Moreover, the eikonal equation and the dispersion relation are studied in the nonresonant and resonant conditions. Results indicate that for the nonresonant condition, by increasing the electron velocity and n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} parameter, discrete values of the growth rate increase. By increasing the collision frequency, the growth rate of the Buneman instability decreases. It is found that the amount of the growth rate in the second case is greater than in the first one. In the resonant condition, the growth rate increases, reaches its maximum and then decreases.