Flow effects on the stability of Z-pinches

Abstract

Summary form only given, as follows. The effect of an axial flow on the m=1 kink instability in Z-pinches is studied numerically by reducing the linearized ideal MHD equations to a one-dimensional eigenvalue equation for the radial displacement. The derivation of the displacement equation for equilibria with axial flows will be presented. A diffuse Z-pinch equilibrium is chosen that is made marginally stable to the m=0 sausage mode by tailoring the pressure profile. The principle result reveals that a sheared axial flow does stabilize the kink mode when the shear exceeds a threshold value. Additionally, the m=0 sausage mode is driven from marginal stability into the stable regime which suggests that the equilibrium pressure profile control can be relaxed. The amount of axial flow that is necessary for stability depends on the ratio of the radius of the conducting wall, r/sub w/, to the characteristic plasma radius, a. For reasonable values of r/sub w//a, the threshold shear can be obtained with flow velocities less than the Alfven speed. This stabilization effect has important implications to fast Z-pinches, as well as steady-state flow-through Z-pinches. Fast Z-pinches such as liner implosions are plagued by the Rayleigh-Taylor instability which destroys the liner and disrupts the current path before the liner arrives on axis. A sheared axial flow in a liner may quench the Rayleigh-Taylor instability in the same way that it quenches MHD instabilities in a diffuse Z-pinch. Simulation results will be presented showing the effect of a sheared axial flow on the Rayleigh-Taylor instability in a fast liner implosion. Liners of infinite length with and without flow will be compared. A liner geometry that develops an axial flow will also be presented as a stable liner implosion configuration.