Abstract
The stabilizing effect of an axial flow on the m=1 kink instability in z-pinches has been studied numerically by reducing the linearized ideal MHD equations to a one-dimensional eigenvalue equation for the radial displacement. A diffuse z-pinch equilibrium is chosen that is made marginally stable to the m=0 sausage mode by tailoring the pressure profile. The principal result reveals that a sheared axial flow does stabilize the kink mode when the shear exceeds a threshold value which is inversely proportional to the wavelength of the mode. This threshold value can be satisfied with a peak flow which is less than the Alfven speed for certain wavelengths. 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 flow stabilization agrees with experimental observations. The details of the theoretical development will be presented. The implications of this stabilizing effect are to be investigated with a flow-through Z-pinch experiment, ZaP.
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