Stabilizing and destabilizing influence of the Hall effect in a Z pinch with a step-like volume current profile

Abstract

A dispersion relation is derived for axisymmetric perturbations of an infinitely extended circular incompressible Z pinch with a step-like volume current profile. This profile is characterized by constant but different volume currents in different regions of the plasma and at the step surface there is a sheet current. The stability boundaries are shifted compared with stability limits in ideal MHD theory. For equilibria with no current reversal there is a new stable range whereas for equilibria with current reversal there is a new unstable range. The number of solutions of the dispersion relation depends on the equilibrium. The behaviour of the eigenvalues near the stability boundaries is treated in accordance with bifurcation theory.