Design of Radiation Transport through Heterogeneous, Stochastic Media

Radiation flow through media containing optically thick particulates dispersed in an optically thin background can challenge high energy density physics models. Typically available transport models depend on a single material equation of state and opacity per spatial cell, such that the solutions may have to average over heterogeneous regions using atomic mix schemes. Direct numerical simulation (DNS) at sufficient resolution can model a particular small-scale stochastic-medium configuration, but many DNS calculations are required to obtain an average solution where stochastic media are defined only probabilistically. Levermore-Pomraning models and extensions are somewhat mature for linear, uncoupled transport, but less so for thermal radiation transport with hydrodynamics. The X-ray Flow Over Lumps (XFOL) experiment at the OMEGA facility seeks to use the COAX spectral diagnostic to measure, in more detail than ever before, radiation flow through stochastic media. In this work, we present design considerations for these experiments using Cassio simulations of radiation flow through optically thin Sc-Si-aerogel foams containing optically thick V-oxide particulates. We compare averaged homogeneous calculations with DNS calculations of the heterogeneous stochastic media.