Equilibrium flow structures and scaling of implosion trajectories in wire array Z pinches

Abstract

The hypothesis that wire array Z-pinch radiation sources can be represented as an ablating mass source embedded within a Lorentz force field is examined and the effects that this has upon the trajectory and spatial structure of the ensuing implosion are studied. Two-dimensional (2D) resistive magnetohydrodynamic (MHD) simulations of the ablating core regions and of the array cross-section indicate that the core ablation rate is determined by force balance at the ablation surface. This implies a weak dependence of the ablation velocity (the ratio of the magnitude of the Lorentz force to the mass ablation rate) on the array parameters (current, radius, mass, etc.). In the case of a constant ablation rate, the radial profiles in the flow region between the wires and the axis are found to converge to a set of time independent equilibria. These profiles represent a unique solution to the ideal MHD equations for super-Alfvénic flow in cylindrical geometry. Comparisons of simulated implosion trajectories with experimental optical streak photography data are used as a code validation exercise and show important deviations from the scenario of invariant ablation velocity. The importance of the number of wires in the array in determining the ablation rate and thus the trajectory and structure of the implosion is highlighted. The effects upon the inferred implosion symmetry and the x-ray pulse shape and peak power are discussed.