Multi-dimensional radiation transport for modeling axisymmetric Z pinches: Ray tracing compared to Monte Carlo solutions for a two-level atom

Radiation plays a critical role in the dynamical evolution and energetics of Z pinches and a dominant role for those loads designed as radiation sources in the keV photon energy region. Therefore, in modeling such plasmas it is essential to employ an accurate and realistic calculation of radiation generation and transport. This study presents a straightforward method to carry out three-dimensional radiation transport calculations in an azimuthally symmetric cylindrical geometry for use in magnetohydrodynamic simulations of high energy Z-pinch plasma radiation sources. The present approach is based on the integral solution of the radiative transfer equation using long characteristics with equal weight angular quadratures, and uses either a multifrequency grid or probability-of-escape-based zone-to-zone coupling. Using previously published Monte Carlo calculations of a two-level atom in cylindrical geometry as a benchmark, the accuracy of the approach is assessed as a function of the frequency grid, number of rays employed, and spatial grid. An analytic expression for the frequency averaged escape probability of an emission line is found to be as accurate for the population kinetics as the multifrequency method. While the escape probability description sacrifices information on the line profile, it is far more computationally efficient yet sufficiently accurate for line dominated plasmas such as Z-pinch radiation sources.