辐射热流中超音速-亚音速转捩区的自相似解
Supersonic-subsonic transition region in radiative heat flow via self-similar solutions
摘要：
利用近似自相似解研究了热稠密等离子体中辐射驱动热波的辐射流体力学流动。具体地说，我们已经集中在纯辐射超音速流和纯亚音速制度之间的中间制度。这两个区域都使用精确自相似解和数值模拟进行了研究，然而，大多数研究都使用数值模拟，主要是因为辐射热波和激波区域并不完全自相似。在一项里程碑式的工作中[J. Garnier等人，物理学，13，092703（2006）]，发现对于特定的幂律依赖性温度分布，存在唯一的精确自相似解，其对于所有物理状态都有效。在这项工作中，我们近似卡尼尔的精确解的一般幂律温度依赖性，使用简单的分析考虑。这种近似的解决方案产生了良好的协议相比，数值模拟的不同的热力学配置文件在预期的有效性范围内。此外，我们提供了一个近似的解决方案，在物质中吸收的能量，再次，一般的幂律温度分布。我们的近似自相似的解决方案的能量产生非常好的结果相比，精确的数值模拟的黄金和$\mathrm{Ta_2O_5}$。我们还设置了一个比较我们的自相似的解决方案与辐射温度测量的实验结果，在一个黑腔中的低密度泡沫，直接解决，到中间政权，产生了良好的协议和类似的趋势。不同的模型以及数值模拟是分析超音速-亚音速转捩区的有力工具。
英文摘要：
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.
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