Radiation drive temperature measurements in aluminium via radiation-driven shock waves: Modeling using self-similar solutions

TL;DR

This paper develops a semi-analytic self-similar model to accurately relate radiation drive temperature to shock wave velocity in aluminium, reconciling discrepancies among previous experimental and simulation scaling relations.

Contribution

It introduces a detailed self-similar solution for radiative shock waves in aluminium, including transport effects, to derive a consistent $T_{Rad}(D_S)$ relation that explains existing data variations.

Findings

The model predicts a 40 eV spread in $T_{Rad}$ for given shock velocities.

It aligns well with experimental and simulation data.

The approach clarifies differences in previously reported scaling relations.

Abstract

We study the phenomena of radiative-driven shock waves using a semi-analytic model based on self similar solutions of the radiative hydrodynamic problem. The relation between the hohlraum drive temperature $T_{\mathrm{Rad}}$ and the resulting ablative shock $D_S$ is a well-known method for the estimation of the drive temperature. However, the various studies yield different scaling relations between $T_{\mathrm{Rad}}$ and $D_S$, based on different simulations. In [T. Shussman and S.I. Heizler, Phys. Plas., 22, 082109 (2015)] we have derived full analytic solutions for the subsonic heat wave, that include both the ablation and the shock wave regions. Using this self-similar approach we derive here the $T_{\mathrm{Rad}}(D_S)$ relation for aluminium, using the detailed Hugoniot relations and including transport effects. By our semi-analytic model, we find a spread of $\approx 40$eV in the $T_{\mathrm{Rad}}(D_S)$ curve, as a function of the temperature profile's duration and its temporal profile. Our model agrees with the various experiments and the simulations data, explaining the difference between the various scaling relations that appear in the literature.