Sheared flow stabilization of the m=1 kink mode in Z pinches

Abstract

The effect of a sheared axial flow on the 𝑚 = 1 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 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/kV0𝐴) was about 0.1.