  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.
