Formulations and analysis of Compton scattering for deterministic thermal radiation transport
In high-energy-density physics at low densities and high temperatures, Compton scattering can be the dominant interaction mechanism between thermal radiation and the material. Boson statistics leads to induced scattering, where the rate of scattering is proportional to the square of the photon intensity. To explore the importance of this nonlinear effect in the context of thermal radiative transfer, in this work we formulate several linear approximations to the scattering rate and compare them to the proper nonlinear rate in an infinite-medium setting. With the goal of implementing Compton scattering in a radiation transport code, we study heating-rate accuracy and iterative convergence properties for the linear methods as we vary the fidelity of the discretization in photon frequency. We find the equilibrium out-scattering formulation to be the most accurate linear method, with heating rate errors around 15% when the radiation is heating the material and up to 50% when the radiation is cooling the material.