A simple model for plasma temperature in imploded hollow plasma liners

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Abstract
Existing theory for the Rayleigh-Taylor instability in imploding hollow plasma liners has assumed a constant electrical resistivity during most of the implosion. While this is qualitatively justified by the competition between joule heating and field-diffusion-driven expansion of the plasma shell; one, nevertheless, expects the temperature and, therefore, electrical conductivity to rise during the implosion. A simple model for plasma temperature as a function of time, based on the neglect of radiative losses and using approximate fits to equation-of-state information, is presented here. The results are used to compute the minimum allowed wavelength, a parameter used to assess instability effects, and agreement with magnetohydrodynamic calculations to well within a factor of 2 is obtained.