Scaling of (MHD) instabilities in imploding plasma liners

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Abstract
The dynamics of imploding foil plasmas is considered using first‐order theory to model the implosion and to investigate the effects of magnetohydrodynamic instabilities on the structure of the plasma sheath. The effects of the acceleration‐produced magnetohydrodynamic (MHD) Rayleigh‐Taylor instability and a wall‐associated instability are studied for a variety of plasma implosion times for several pulsed power drivers. The basic physics of these instabilities is identified and models are developed to explain both linear and nonlinear behavior. These models are compared with the results of detailed two‐dimensional magnetohydrodynamic simulations. Expressions for linear Rayleigh‐Taylor growth are developed showing its dependence on driving current, plasma conductivity, and density gradient scale length. A nonlinear saturation model, based on magnetic field diffusion, is developed. The model for a wall instability involves the interaction of the plasma sheath with the electrode wall and the material ablated from the electrode. The growth of this instability is shown to be limited by field diffusion. Comparison with two‐dimensional simulations has been excellent.