Stability analysis of a cylindrical surface current plasma confined by a force-free magnetic field using dispersion relations

Abstract

A force-free magnetic field satisfies a relation Del *B= alpha B, where alpha is assumed a constant in space. For a surface current cylindrical main plasma confined by force-free fields, with tenuous plasma including small resistivity, the stability is investigated in detail numerically by evaluating the stable region and the growth rate of the unstable mode for parameters k, m, R0/r0, alpha r0, beta and ( mu 0r0)-1 from dispersion relations where k is a real wave number, m is an integer, r0 and R0 are the radii of the main plasma and the conducting wall, respectively, and beta and mu 0 are the plasma beta and reciprocal pitch on the main plasma surface, respectively. For negative ( mu 0r0)-1, positive k and m=1, the stable region is expanded by introducing the force-free magnetic field. The marginal stability curve of the main plasma with the force-free field approaches the curve for the vacuum field with the wall of R0/r0=1 as alpha r0 decreases from 0 to a minimum value. To stabilize the unstable mode by the force-free field and wall, the values of beta and ( mu 0r0)-1 must be chosen for the mode to vanish at k=- mu 0. The instability for the positive ( mu 0r0)-1 can be sufficiently suppressed by using the wall of R0/r0 approximately 1.5.