Supersonic-subsonic transition region in radiative heat flow via self-similar solutions

TL;DR

This paper develops approximate self-similar solutions to model the transition between supersonic and subsonic radiative heat flows in plasmas, validated against numerical simulations and experimental data.

Contribution

It introduces a generalized analytical approximation for self-similar solutions in radiative heat flow, bridging the gap between pure regimes and matching numerical and experimental results.

Findings

Good agreement with numerical simulations for thermodynamic profiles.

Accurate energy absorption estimates for gold and Ta2O5.

Experimental data aligns with the intermediate regime predictions.

Abstract

We study the radiative hydrodynamics flow of radiation-driven heat waves in hot dense plasmas, using approximate self-similar solutions. Specifically, we have focused on the intermediate regime between pure radiative supersonic flow and the pure subsonic regime. These two regimes were investigated both using exact self-similar solutions and numerical simulations, however, most of the study used numerical simulations, mainly because the radiative heat wave and the shock regions are not self-similar altogether. In a milestone work [J. Garnier et al., Phys. Plas., 13, 092703 (2006)], it was found that for a specific power law dependency temperature profile, a unique exact self-similar solution exists, that is valid for all physical regimes. In this work we approximate Garnier's exact solution for a general power-law temperature-dependency, using simple analytical considerations. This approximate solution yields a good agreement compared to numerical simulations for the different thermodynamic profiles within the expected range of validity. In addition, we offer an approximate solution for the energies absorbed in the matter, again, for a general power-law temperature profile. Our approximate self-similar solution for the energy yields very good results comparing to exact numerical simulations for both gold and $\mathrm{Ta_2O_5}$. We also set a comparison of our self-similar solutions with the results of an experiment for radiation temperature measurement in a hohlraum in low-density foams that is addressed directly, to the intermediate regime, yielding a good agreement and similar trends. The different models as well as the numerical simulations are powerful tools to analyze the supersonic-subsonic transition region.