Photoionization fronts play a dominant role in many astrophysical situations, but remain difficult to achieve in a laboratory experiment. We present the results from a computational parameter study evaluating the feasibility of the photoionization experiment presented in the design paper by Drake, R. P., Hazak, G., Keiter, P. A., Davis, J. S., Patterson, C. R., Frank, A., Blackman, E. G., & Busquet, M. 2016, ApJ, 833, 249 in which a photoionization front is generated in a nitrogen medium . The nitrogen gas density and the Planckian radiation temperature of the x-ray source define each simulation. Simulations modeled experiments in which the x-ray flux is generated by a laser-heated gold foil, suitable for experiments using many kJ of laser energy, and experiments in which the flux is generated by a z-pinch device, which implodes a cylindrical shell of conducting wires. The models are run using CRASH, our block-adaptive-mesh code for multi-material radiation hydrodynamics. The radiative transfer model uses multi-group, flux-limited diffusion with thirty radiation groups. In addition, electron heat conduction is modeled using a single-group, flux-limited diffusion. In the theory, a photoionization front can exist only when the ratios of the electron recombination rate to the photoionization rate and the electron impact ionization rate to the recombination rate lie in certain ranges. These ratios are computed for several ionization states of nitrogen. Photoionization fronts are found to exist for laser driven models with moderate nitrogen densities ($sim$10$^{21}$ cm$^{-3}$) and radiation temperatures above 90 eV. For z-pinch driven models, lower nitrogen densities are preferred ($<$10$^{21}$ cm$^{-3}$). We conclude that the proposed experiments are likely to generate photoionization fronts.
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