Sheared Flow Stabilization of them=1Kink Mode inZPinches

Abstract

The effect of a sheared axial flow on the $m=1\mathrm{}$ kink instability in $Z$ pinches is studied numerically by reducing the linearized magnetohydrodynamic equations to a one-dimensional displacement equation. An equilibrium is used that is made marginally stable against the $m=0\mathrm{}$ sausage mode by tailoring its pressure profile. The principal result reveals that a sheared axial flow stabilizes the kink mode when the shear exceeds a threshold that is dependent on the location of the conducting wall. For the equilibria studied here the maximum threshold shear ( $v_z^{\prime }/{\mathrm{kV}}_A^0$) was about $0.1$.