Theory of flute instability of a non-homogeneous plasma

Abstract

In a geometrical-optics approximation we investigate the instability of an inhomogeneous low-pressure plasma located in a gravitational field that considers effectively the curvature of the magnetic field lines. We have analysed in detail the spectrum of the low-frequency plasma potential oscillations taking into account both gravitational and Larmor particle drifts as well as the non-potential oscillations propagating across the external magnetic field and across the particle drift.It has been shown that under conditions such that the velocity of gravitational particle drift approaches Larmor drift velocity, new modes of flute-like instability appear in the plasma; this is due to a resonance buildup of Larmor drift oscillations of the plasma from a gravitational ion drift leading to plasma instability virtually at any inhomogeneity. Special attention is paid to the analysis of long-wave plasma oscillations with a wavelength exceeding the Larmor ion radius. To our mind plasma instability with respect to long-wave oscillations is the most dangerous one. It is these oscillations that, embracing a large portion of the plasma-occupied region, can lead to breakup of the plasma as a whole. This paper elucidates the conditions under which long-wave instabilities can develop in plasma and discusses the possibility of such instabilities appearing in real experimental devices (mirror devices). It is shown that long-wave instabilities can develop in a plasma the longitudinal dimensions of which exceed transverse dimensions by (MR/mL)½ times if condition 2.4 is fulfilled, and also in a plasma in which m/M ≪ Te/Ti ≈ L/R. In the experimental devices discussed in this article, the first of these conditions is apparently not fulfilled, whereas the second can, generally speaking, be fulfilled. Plasma instability with respect to short-wave oscillations does not represent such a danger as it does with respect to long-wave oscillations, although such an instability can, as is shown in this paper, virtually appear at any plasma inhomogeneity and at any curvature of the magnetic field lines. Short-wave instability can lead to sharp noise increase in the plasma and as a result to the appearance of anomalously large plasma diffusion across the magnetic field.This paper shows also the possibility of plasma instability in devices with a negative curvature (cusped geometry) with respect to non-potential oscillations propagating across the magnetic field.