Modeling of the k-shell radiation production in stainless steel nested wire arrays on Z

Production of iron K-shell x-rays has been studied in a series of recent experiments on Z accelerator at Sandia. We present the results of 1-D RMHD numerical simulation of these experiments. Our simulations explicitly take into account detailed radiation hydro physics, and use a heuristic model to describe the 3-D effect of the outer-through-inner mass interpenetration and current splitting associated with it, which typically take place in the nested wire array implosions. The physical model of a two-temperature plasma includes electron and ion heat conduction, heat exchange between electrons and ions, magnetic field diffusion, Ohmic heating, radiation energy transport and losses. The radiation losses and the distribution of plasma ionization states are determined from the solution of the coupled equations of the nonstationary collisional-radiative model and radiation transport for spectral lines and continuum. We study the dependence of the radiation yields in the K- and L-lines of iron and the radiation pulsewidths on the masses and radii of the nested arrays, which were varied in the experiments on Z so that the implosion time was kept constant. Our results indicate that the observed yield dependence on mass/radius is probably a 1 -D effect, with radiative performance determined mainly by the stagnating load mass. For a high mass/small radius the yield is low because the eta parameter of the plasma is small-ions in the K-shell are few. For a low mass/large radius, the plasma density at stagnation is low, and it radiates a smaller fraction of its energy in all spectral ranges before bouncing back. We present the results of a similar modeling for a slighly different experimental configuration, with some mass added initially near the axis, as if more wires were initially placed there. Simulations predict some gain in the K-shell yield for this load configuration. Simulations done for the refurbished ZR machine predict very high iron K-shell yields-the increase is greater than the current-squared scaling would give-with an optimum radius extended to a larger value than on Z.