Growth of the Rayleigh–Taylor instability in an imploding Z-pinch

Abstract

Rayleigh–Taylor (RT) instability of cylindrical, imploding plasma liners in a Z-pinch is analyzed. The reduction in total perturbation growth for multicascade systems (multiple imploding shells) is presented. This reduction is effective if the pressure produced by the impacting shell exceeds the magnetic pressure at the time of impact. Analytical and numerical solutions are also obtained for the RT instability of an imploding plasma liner accelerated into undisturbed plasma. The snowplow model is used in which the mass encountered by the imploding magnetic piston is swept into an infinitely thin sheath. A shock front launched ahead of the liner is shown to reduce the growth rate. It is also shown that accumulating the mass increases the growth rate. However, the total perturbation growth can be reduced if the liner accumulates the mass during the implosion compared to a liner with the same mass imploding into vacuum. Finally, it is shown that the final kinetic energy density for a given shell nonuniformity is largest if the final liner mass is accumulated during the implosion.