Radiation drive temperature measurements in aluminum 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 Rad and the resulting ablative shock DS is a well-known method for the estimation of the drive temperature. However, the various studies yield different scaling relations between T Rad and DS based on different simulations. In T. Shussman and S. I. Heizler, Phys. Plasmas 22, 082109 (2015), we have derived full analytic solutions for the subsonic heat wave, which include both the ablation and the shock wave regions. Using this self-similar approach, we derive here the T Rad (D S) relation for aluminum, using the detailed Hugoniot relations and including transport effects. By our semi-analytic model, we find a spread of ≈ 40 eV in the T 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.