Effects of finite heat conductivity on instabilities in a rotating plasma

Abstract

Analytical theory of magnetorotational and convective instabilities in a rotating cylindrical plasma with finite heat conductivity is developed and discussed. The heat conductivity is incorporated into the standardized equations of the regular magnetohydrodynamic approach to studying these instabilities. A case of high-β plasma (β is the ratio of plasma pressure to the magnetic field pressure) and the modes with parallel phase velocity much smaller than the sound velocity is particularly emphasized and considered in the quasi-incompressible approximation. It is shown that this approximation is more adequate than the Boussinesq approximation. Both these approximations lead to the same results for aperiodical instabilities of the axisymmetric modes which are hybrids of the magnetorotational and convective instabilities. On the other hand, the Boussinesq approximation overlooks the heat-conductivity-induced instabilities predicted by the quasi-incompressible approximation describing the dissipative excitation of the slow magnetoacoustic and Alfvén waves. Non-axisymmetric aperiodical instabilities are considered. It is shown that, for such modes, the role of convective instabilities is greater than for the magnetorotational instability.