Solutions for ion-electron-radiation coupling with radiation and electron diffusion

We present semi-analytic solutions to the equations for radiation-electron-ion coupling, the so-called 3-T equations. Our solutions use a linearization based on Pomraning's form for the heat capacity given by Cv∝Te3 with additional stipulations for the electron heat conduction and ion-electron coupling coefficients. To solve the linearized equations we use integral transform techniques and compute a Fourier integral numerically. We give solutions for a 3-T version and a 2-T with heat conduction version of the Su-Olson problem as well as solutions for spherical and spherical shell sources. We use the xRage radiation hydrodynamics code to demonstrate that our solutions are useful for code verification in multiple dimensions and axisymmetric geometries.

Research Highlights► Verification solutions for 3-T equations. ► Diffusion theory for radiation and heat conduction. ► Solutions in slab and spherical geometry. ► Comparison between solutions and production code.