Conditions for supersonic bent Marshak waves

TL;DR

This paper derives conditions for supersonic radiation diffusion in bent Marshak waves, highlighting the dependence on Mach number, optical depth, and temperature, with numerical examples for SiO2 and gold.

Contribution

It extends the theory of supersonic radiation diffusion to 2D bent Marshak waves, establishing specific conditions involving Mach number and optical depth, and analyzes temperature constraints.

Findings

Supersonic diffusion requires Mach number > 8(1+√ε)/3 and optical depth > 1.

Proper source temperature is crucial for satisfying diffusion conditions.

Numerical examples for SiO2 and Au illustrate the feasible parameter regions.

Abstract

Supersonic radiation diffusion approximation is a useful way to study the radiation transportation. Considering the bent Marshak wave theory in 2-dimensions, and an invariable source temperature, we get the supersonic radiation diffusion conditions which are about the Mach number $M>8(1+\sqrt{\ep})/3$, and the optical depth $\tau>1$. A large Mach number requires a high temperature, while a large optical depth requires a low temperature. Only when the source temperature is in a proper region these conditions can be satisfied. Assuming the material opacity and the specific internal energy depend on the temperature and the density as a form of power law, for a given density, these conditions correspond to a region about source temperature and the length of the sample. This supersonic diffusion region involves both lower and upper limit of source temperature, while that in 1-dimension only gives a lower limit. Taking $\rm SiO_2$ and the Au for example, we show the supersonic region numerically.