X-ray Scattering Measurement of the Heat Capacity Ratio in Shock Compressed Matter*

We developed accurate x-ray scattering techniques to measure properties of matter under extreme conditions of density and temperature in intense laser-solid interaction experiments. We report on novel applications of x-ray scattering to measure the heat-capacity ratio $\gamma=c_p/c_v$ of a Be plasma which determines the equation of state of the system. Ultraintense laser radiation is focussed onto both sides of a Be foil, creating two counterpropagating planar shock waves that collide in the target center. A second set of lasers produces Zn He-$\alpha$ radiation of 8.9 keV energy that scatters from the shock-compressed matter. We observe temperatures of $10\,\textrm{eV}$ and $15\,\textrm{eV}$ and mass densities of $5\,\textrm{g/cm}^{3}$ and $11\,\textrm{g/cm}^{3}$ before and after the shock collision. Applying the Rankine-Hugoniot relations for counterpropagating shocks we then infer $\gamma$ as a function of density using only the measured mass compression ratios. Our results agree with equation of state models and DFT simulations.