On the linear cross-field instability problem

Abstract

A re-examination of the linear E x B instability problem for infinite stratified media gives results differing from those published. The main point is to warn against the application to inhomogeneous media of the usual instability criterion, as developed for homogeneous media. The fact that the dispersion relation gives complex values of ω for real k does not always indicate the existence of an instabifity. It could also describe propagation of a constant wave energy through an inhomogeneous medium. It is demonstrated that in certain situations it is possible to choose dependent variables in such a way that these two effects disentangle, allowing for a definite solution of the instability problem.In this paper the linear stability' problem for an infinite inhomogeneous, partially ionized gas penetrated by crossed electric and magnetic fields, is re-examined. Several authors (e.g. Reid 1968; Whitehead 1967, 1971; Cunnold 1969; Chimonas 1969; Linson & Workman 1970; looper & Walker 1971; Sato 1971; Sato & Tsuda 1972; Kato 1972) have considered the possibility that the so-called cross-field instability exists in the ionosphere. Our reason for treating the problem again is to point out a deficiency in the literature.