First-principles analysis of the warm dense plasma jets in Double-Cone Ignition experiments

Double-Cone Ignition (DCI) differs from the traditional laser-driven inertial confinement fusions by relying on gold cones for transverse filtering to achieve warm dense plasma, thereby reducing the energy required during the compression process. Thus, the state of the plasma ejected from the gold cones directly reflects the energy conversion efficiency and influences the subsequent fusion process. In this paper, we analyze the x-ray Thomson scattering data from the earlier stage DCI experiments \cite{zhang2020double}. We combine the imaginary-time correlation function method with first-principles methods to decouple the diagnosis of temperature and density and obtain the temperature and density diagnostic outputs: $25$ $\mathrm{eV}$ and $8\pm2$ $\mathrm{g/cc}$. In the analysis, we consider the effect of multi-element mixing and determine the gold impurity ratio to be $0.162 \pm 0.015 \%$ based on the experimental spectrum. These detailed analysis results demonstrate the role of the gold cone in achieving plasma compression and confirm that the gold impurities are within an acceptable range, providing valuable references for future experiments.