Global modes of flute instability of a rotating cylindrical plasma

Abstract

The influence of rotation on the flute instability of a cylindrical gravitating plasma in a straight inhomogeneous magnetic field is studied in the framework of one-fluid magnetohydrodynamics. The dispersion relation and integral expression for the instability growth rate of eigenmodes are derived. It is shown that, in the framework of the given problem, rotation is a destabilizing factor, and the corresponding theorem is proved for the general case. For a linear radial profile of the rotation frequency, the structure of eigenmodes is calculated. The growth rate of these modes is shown to increase with increasing rotation velocity and azimuthal mode number. It is found that plasma rotation in the eigenmode localization region leads to the displacement of perturbation from the rotation region, which results in a decrease in the instability growth rate. The absence of eigenmodes (i.e., exponential instability of the system) for certain profiles of the density and rotation frequency is demonstrated.