Finite-temperature relativistic fluid equations and scaling of high-current beams

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Abstract
Two sets of finite-temperature relativistic fluid equations are obtained by taking moments of the Vlasov equation, using equilibrium and monoenergetic distribution functions. The closed sets of fluid-Maxwell equations are reduced to a simple set of equations under steady-state conditions, using two fluid constants of the motion derived for each set. The set obtained using the monoenergetic distribution is parametrized in cylindrical coordinates for high-current diode studies. The radial scale length for a radial equilibrium superpinch is obtained in terms of macroscopic diode parameters, and radial profiles of the pinch are obtained by solution of the one-dimensional system. It is found that high-current superpinches are characterized by a hot uniform-density core surrounded by a hollow current sheet, and that there is a limit to the current which can be propagated for a given pinch radius, given the macroscopic diode parameters. The minimum pinch radius obtainable in a diode in the steady state is obtained from the hot pinch limit, and diode scaling laws are presented, assuming Child-Langmuir or parapotential flow.