Consistent Solutions of the Radiation Diffusion Equation in Spherical and Cylindrical Geometries

TL;DR

This paper extends the radiation diffusion model to spherical and cylindrical geometries, enabling accurate modeling of small-scale systems like ICF capsules where previous models failed.

Contribution

The authors develop a new analytic model for radiation diffusion in diverging geometries, improving accuracy for small-scale spherical and cylindrical systems.

Findings

Model agrees with numerical solutions within specific ranges

Small geometries show increased effects of curvature on wavefronts

Rapid iteration benefits for small-scale spherical systems

Abstract

We have extended the radiation diffusion model of Hammer and Rosen to diverging spherical and cylindrical geometries. The effect of curvilinear geometry on the supersonic, expanding wavefront increases as the internal radius of a spherical or cylindrical shell approaches zero. Small spherical geometries are important for modeling systems at the size scale of ICF capsules, at these scales existing quasi-analytic models for planar geometry significantly disagree with the results of simulation. With this method, the benefits of rapid iteration can be applied to common spherical systems at much smaller length scales. We present comparisons between numerical diffusion solutions and the analytic model to give ranges of applicability for the model.