The effect of plasma flow on line-tied magnetohydrodynamic modes

The linear stability of a linear pinch to kink modes with line-tying boundary conditions and equilibrium axial flow is studied. Numerical results in visco-resistive magnetohydrodynamics show that for long plasmas, in which the line-tying stabilization effect is weak, plasma flow is stabilizing. For shorter plasmas, near the length at which line-tying stabilizes the mode for zero flow, the flow can be destabilizing. A simple model using reduced ideal magnetohydrodynamics with a step-function current density and an even simpler one-dimensional sound wave model with equilibrium flow elucidate these effects. It is concluded that: (1) The stabilization in long plasmas is due to convective stabilization; (2) the destabilization for short plasmas can be explained using a picture involving the coupling of two stable waves, one propagating in the forward direction and one in the backward direction; and (3) strong magnetic shear suppresses the flow destabilization for short plasmas.