Simple resistive MHD models for instability revisited

Abstract

Two MHD models for instability, viz., the Shafranov's [1] resistive free-boundary and resistive fixed-boundary step models have been revisited. In the former, a constant longitudinal current density passes through a cylindrical column of a resistive plasma of radius a separated by vacuum from a perfectly conducting wall at a radius b; in the latter, the current density has the same radial profile but the plasma fills the whole cylinder up to the conducting wall.For the former, the explicit dependence of resistivity η on the maximum normalized growth rate Γmax is exhibited showing a stabilizing effect on kinks. A fact that is overlooked by some authors is also pointed out here in the form of a correction of the original growth rate γmax. For the latter, a special code set up to solve the (stiff) system of differential equations for instability in the region a ⩽ r ⩽ b, together with a set of jump conditions at the current channel radius a, yield no solution satisfying the appropriate boundary conditions at the wall.