The effect of sheared axial flow on the linear stability of the Z-pinch

A linear analysis of the ideal magnetohydrodynamic (MHD) stability of the Z-pinch is presented in which plasma flows are included in the equilibrium. With sheared axial flows it is found that substantial stabilization of internal modes is possible for some equilibrium profiles. For this to occur equilibria with a change in fluid velocity across the pinch radius of about Mach 2 are required. However, this ignores the surrounding vacuum and for the more realistic free boundary modes flows of about Mach 4 are required to stabilize all global MHD modes. This stabilization of MHD modes is not observed for all equilibria however. This fact, combined with the supersonic flow speeds required for stability, make it unlikely that a Z-pinch could in practice be stabilized by the introduction of sheared flow.