Dispersion relations for waves in visco-gravitating anisotropic magnetoplasmas

Abstract

The effect of Braginskii's full viscosity tensor on an infinite non-conducting, gravitating anisotropic plasma in which the medium is trapped in a strong magnetic field is discussed in the context of Braginskii's magnetohydrodynamic model with Chew–Goldberger–Low double adiabatic approximation and finite Larmor radius (FLR) correction. Through linearization of the perturbed equations, the general dispersion relation is derived for the separate compression, shear, and drift viscosity components as well as the FLR corrections. We investigate the stability for parallel and transverse perturbations with respect to the direction of the magnetic field, and both gravitational and fire-hose instabilities are found. The role of each viscous term is to suppress instability, but each component works in different ways. The FLR acts in a way that is very similar to the drift viscosity. The instability threshold is found to be independent of viscosity for compression and shear viscosity, but both the drift viscosity and FLR corrections can change the critical wavenumber for the instability. The compression viscosity is most effective at reducing the growth rate of the gravitational instability, whereas the shear viscosity works to suppress the fire-hose instability. The result of the present study may be useful for the study of large scale compression, shear, and drift plasma flow in and around clusters of galaxies and galactic disks and for the solar and stellar wind.