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Application of one-dimensional stagnation solutions to three-dimensional simulation of compact wire array in absence of radiation

We investigate the stagnation phase of a three-dimensional (3D), magnetohydrodynamic simulation of a compact, tungsten wire-array Z pinch, under the simplifying assumption of negligible radiative loss. In particular, we address the ability of one-dimensional (1D) analytic theory to describe the time evolution of spatially averaged plasma properties from 3D simulation. The complex fluid flows exhibited in the stagnated plasma are beyond the scope of 1D theory and result in centrifugal force as well as enhanced thermal transport. Despite these complications, a 1D homogeneous (i.e., shockless) stagnation solution can capture the increase of on-axis density and pressure during the initial formation of stagnated plasma. Later, when the stagnated plasma expands outward into the imploding plasma, a 1D shock solution describes the decrease of on-axis density and pressure, as well as the growth of the shock accretion region.