Enhanced energy coupling and x-ray emission in Z-pinch plasma implosions

Abstract

Recent experiments conducted on the Saturn pulsed-power generator at Sandia National Laboratories [R. B. Spielman et al., in Proceedings of the Second International Conference on Dense Z Pinches, Laguna Beach, CA, 1989, edited by N. R. Pereira, J. Davis, and N. Rostoker (American Institute of Physics, New York, 1989), p. 3] have produced large amounts of x-ray output, which cannot be accounted for in conventional magnetohydrodynamic (MHD) calculations. In these experiments, the Saturn current had a rise time of ∼180 ns in contrast to a rise time of ∼60 ns in Saturn’s earlier mode of operation. In both aluminum and tungsten wire-array Z-pinch implosions, 2–4 times more x-ray output was generated than could be supplied according to one-dimensional (1D) magnetohydrodynamic calculations by the combined action of the j×B acceleration forces and ohmic heating (as described by a classical Braginskii resistivity). In this paper, we reexamine the problem of coupling transmission line circuits to plasma fluid equations and derive expressions for the Z-pinch load circuit resistance and inductance that relate these quantities in a 1D analysis to the surface resistivity of the fluid, and to the magnetic field energy that is stored in the vacuum diode, respectively. Enhanced energy coupling in this analysis, therefore, comes from enhancements to the surface resistivity, and we show that plasma resistivities approximately three orders of magnitude larger than classical are needed in order to achieve energy inputs that are comparable to the Saturn experiment x-ray outputs. Large enhancements of the plasma resistivity increase the rate of magnetic field and current diffusion, significantly modify the qualitative features of the MHD, and raise important questions as to how the plasma fluid dynamics converts enhanced energy inputs into enhanced x-ray outputs. One-dimensional MHD calculations in which resistivity values are adjusted phenomenologically are used to illustrate how various dynamical assumptions influence the way enhanced energy inputs are channeled by the fluid dynamics. Variations in the parameters of the phenomenological model are made in order to determine how sensitively they influence the dynamics and the degree to which the calculated x-ray outputs can be made to replicate the kinds of large variations in the experimental x-ray power data that were observed in three nominally identical aluminum wire shots on Saturn.