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 $T_{\text{Rad}}$ 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 $T_{\text{Rad}}$ and D_S 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 $T_{\text{Rad}}(D_S)$ relation for aluminum, using the detailed Hugoniot relations and including transport effects. By our semi-analytic model, we find a spread of $\approx 40$ eV in the $T_{\text{Rad}}(D_S)$ 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.

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通过辐射驱动的冲击波测量铝中的辐射驱动温度：使用自相似解的建模

我们使用基于辐射流体动力问题自相似解的半解析模型研究辐射驱动冲击波的现象。Hohlraum驱动器温度之间的关系${Ť}_{\text{拉德}}$产生的烧蚀冲击D _S是用于估计驱动器温度的众所周知的方法。然而，各种研究得出了不同的比例关系${Ť}_{\text{拉德}}$和D _S基于不同的模拟。在T. Shussman和SI Heizler，物理学。等离子体22，082109（2015），我们已经导出了亚音速热浪充分解析解，其包括消融和冲击波区域。使用这种自相似的方法，我们在这里得出${Ť}_{\text{拉德}}（d_{\mathrm{小号}}）$使用详细的Hugoniot关系并包括传输效应来确定铝的关系。通过我们的半解析模型，我们发现$\approx 40$ 中的eV ${Ť}_{\text{拉德}}（d_{\mathrm{小号}}）$温度曲线的持续时间及其时间曲线的函数。我们的模型与各种实验和模拟数据相吻合，解释了文献中出现的各种比例关系之间的差异。