Nonlocal theory of lower-hybrid drift instability for a plasma shell expanding into a magnetic field

A two-fluid, nonlocal theory of the lower-hybrid drift instability is developed for a plasma shell expanding into a magnetic field. The plasma is assumed cold and the induced cross-field current is entirely due to the deceleration of the plasma by the magnetic field. Attention is focused on physically realistic cases where the cross-field electron velocity has a single-jet or double-jet profile. Lower-hybrid drift eigenmodes are found to be localized where the transverse wave velocity is resonant with the cross-field electron velocity. This is markedly different from previously analyzed cases where the cross-field velocity is constant and eigenmode localization is near the maximum of ‖d ln n(x)/dx‖. For double-jet cross-field velocity profiles there is a rich set of eigenmodes associated with the double-well localizing structure. Despite the different localizing mechanism and more complicated nature of eigenmodes, the parametric dependencies of the frequency and growth rate are quite similar to those obtained for constant cross-field velocity profiles. Specifically, it is found that the transverse wave number of the most rapidly growing eigenmode generally scales as kmax∼V−1/2, where V is a measure of the magnitude of the cross-field electron velocity. This scaling is approximately the same for constant, as well as single and double-jet cross-field velocity profiles. The robustness of this weak scaling of kmax with V implies that the long wavelength structures experimentally observed on expanding plasma shells are not likely to be explained by including realistic geometry effects within linear lower-hybrid drift instability theory.