The Kelvin-Helmholtz Instability in Compressible Plasmas

A. G. GONZÁLEZ; J. GRATTON

Tandil, Argentina

Workshop; VIII Latin-American Workshop on Plasma Physics; 1998

The hydromagnetic Kelvin-Helmholtz instability is relevant in manysituations of astrophysical and laboratory plasmas. Many of these are very complex, since they involve the combined role of velocity shear, ofdensity and magnetic field stratification, and of various geometries incompressible plasmas. We present an analysis of the influence of thevarious physical and geometrical parameters that characterize the plasma on the Kelvin-Helmholtz modes. We introduce the general dispersion relation for compressible hydromagnetic modes localized near a velocity discontinuity between two uniform plasmas. We study analytically the existence and characteristics of the modes and their stability, for any relative orientation of B, u and  k, (B, $\rho $ continuous). We show that the stability of a given configuration cannot be guessed by considering only special orientations of k (say flute or parallel modes). We also study the effect of a density jump (for any relative orientation of B, u and  k; B continuous). We analyze the stability and the boundaries between modes by means of a general procedure that al\-lows to consider any configuration and all kind of perturbations. In contrast to the case of uniform density, for a density jump there are no monotonically unstable modes, only overstabilities. The unstable modes belong to two types. Those with the largest growth rates tend to monotonically unstable modes in the limit of uniform density and are related to the torsional Alfvén mode. The other overstable modes have no analog among the purely incompressible modes and occur in a range of U that is stable in the incompressible limit. We give bounds for the growth rate of the instability.