A note on MHD instability of a compressible gravitational streaming fluid cylinder

Abstract

The fundamental equations are formulated using cylindrical polar coordinates and then solved in the unperturbed state. The perturbation equations are determined, simplified, integrated and the constants of integrations are identified by applying appropriate boundary conditions across the perturbed fluid interface. A cumbersome stability criterion for MHD inviscid compressible self-gravitating streaming fluid cylinder is derived. The magnetic field is stabilizing, the streaming is destabilizing while both of the self-gravitating and compressibility are stabilizing or not according to restrictions and that the gravitational instability of sufficiently long waves will persist. Several approximations are required to obtain Chandrasekhar's and Fermi's dispersion relation (Chandrasekhar and Fermi, 1953).