Normal modes of an expanding plasma shell

We present a cold plasma, two-fluid electromagnetic theory of the normal modes of a plasma shell expanding, at sub-Alfvenic velocities, into a magnetic field. A two-fluid approach is used in order that the specific effects of plasma and magnetic field geometry can be considered. Three main results are obtained. First, a general normal mode equation for lower-hybrid frequency range oscillations is derived which is more accurate in its treatment of the plasma and magnetic field geometry than previous published normal mode equations. The higher accuracy accrues because no a priori assumptions are made about the ratio of perturbation and equilibrium scale lengths. The second set of results is the establishment of specific criteria for the existence of localized solutions of the lower-hybrid drift normal mode equation and the development of analytical formulae which describe the dispersive properties of this instability. These are useful because results concerning lower-hybrid drift instability growth rates and maximal growing wave numbers are usually given in the context of the local approximation without specifying where the normal modes are localized within the highly inhomogeneous plasma profile. The third result is a cautionary one. Two equilibrium models are constructed with identical magnetic field profiles, similar density profiles, but distinctive electron cross-field velocity profiles. The localization criteria and analytical formulae for lower-hybrid drift dispersive properties are found to be quite accurate for one equilibrium model but to be inappropriate for the other.