Ideal instabilities in a high-β rotating cylindrical plasma in the presence of an azimuthal magnetic field and a gravitational field

Magnetohydrodynamic (MHD) theory of ideal instabilities in a high-β rotating cylindrical plasma with an azimuthal magnetic field and a radial gravitational field is developed (β is the ratio of the plasma and magnetic field pressures). The basis of this theory is a system of two first-order differential equations for the Frieman–Rotenberg variable (the sum of the perturbed plasma and magnetic field pressures) and the radial plasma displacement, which leads to the second-order differential equation for the displacement. The sausage instability criterion is derived which generalizes the earlier results for a plasma without gravitation. It is shown that this instability can occur for both the decreasing and increasing plasma pressures. The non-axisymmetric modes are also considered. This analysis is related to the MHD instability theory in a nonrotating plasma dealing with snake instabilities. A number of rotational and gravitational effects on both the m = 1 and m > 1 modes are revealed, where m is the azimuthal mode number. The eigenmode equation describing the Suydam modes in the presence of rotational and gravitational effects is derived. These modes can be responsible, in particular, for the Velikhov and rotational-convective instabilities.