Stability of sub-Alfvénic plasma expansions

Abstract

A comprehensive theoretical treatment of the linear stability of a sub-Alfvénic plasma expansion is developed. The analysis is similar to those performed for the lower-hybrid-drift instability and the drift cyclotron instability. In addition to the diamagnetic drift (Vdi) that drives these instabilities, the gravitational drift (Vg) caused by the deceleration of the plasma shell, and the Pedersen drift (VP) caused by ion–neutral collisions and neutral gas flow, are included. The emphasis of the paper is on the instability driven by the gravitational drift. The theory is fully kinetic and includes finite-beta effects (i.e., electromagnetic coupling and electron ∇B drift-wave resonances), collisional effects (electron–ion, electron–neutral, and ion–neutral collisions), and neutral gas flow, effects that have not been considered to date. The analysis is carried out in a slab geometry although the applications are to spherical expansions. The main conclusions are as follows. In the strong drift limit (Vg>vi and Vdi∼vi, where vi is the ion thermal velocity) it is found that (1) finite-beta effects are stabilizing and reduce the wavelength of the maximum growth rate; (2) ion–neutral collisions are stabilizing and do not affect the wavelength of the maximum growth rate; (3) electron–neutral collisions are stabilizing and increase the wavelength of the maximum growth rate; (4) the gravitational drift driven mode maximizes the growth rate at longer wavelengths than the diamagnetic drift driven mode; (5) the Pedersen drift effectively reduces the gravitational drift, and is therefore a stabilizing influence; and (6) the instability splits into two modes for Te≫Ti in finite-beta plasmas: the lower-hybrid-drift instability at high frequencies and short wavelengths, and a gravitational mode at lower frequencies and longer wavelengths. In the weak drift regime (Vg<vi and Vdi<vi) it is found that (1) finite-beta effects are stabilizing and increase the wavelength of the maximum growth rate; (2) ion–neutral collisions are destabilizing and decrease the wavelength of the maximum growth rate; and (3) electron–ion and electron–neutral collisions are stabilizing, and increase the wavelength of the maximum growth rate. When the growth rate becomes less than the ion cyclotron instability (γ<Ωi), the growth rate as a function of wave number ‘‘breaks up’’ into a discrete set of modes which is associated with the coupling of the drift waves to ion cyclotron waves. These results are applied to the AMPTE magnetotail release [J. Geophys. Res. 92, 5777 (1987)], the Naval Research Laboratory laser experiment [Phys. Rev. Lett. 59, 2299 (1987)], and the upcoming CRRES GTO releases [D. Reasoner (private communication, 1989)].