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

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.