Accurate ionization balance of gold plasmas in nonlocal thermodynamic equilibrium is essential for understanding the physics involved in inertial confinement fusion (ICF) hohlraums, where the persistent “drive deficit” issue may stem from an overestimation of the emission and absorption opacity of gold plasmas. Predicting the charge state distribution (CSD) of gold plasmas at temperatures of several keV poses considerable challenges as the ionization stages with open N and M shells are predominantly populated. In this study, we performed benchmark calculations for the CSD of gold plasmas at extremely high temperatures up to 8 keV. We used a rate equation based on the relativistic configuration approximation, taking into account electronic configurations with electron excitations up to a principal quantum number of $n=12$, resulting in over 10 million atomic states, which have not been previously achieved. A Monte Carlo algorithm was developed to efficiently solve these large-scale rate equations under the steady-state approach. By carefully considering the highly excited atomic states, we achieved convergence in the CSDs. The highly excited atomic states with maximum principal quantum numbers $n=8–12$ provide crucial dielectronic recombination channels and have a substantial impact on the ionization balance at a temperature of 8 keV and an electron density of ${10}^{21}{\mathrm{cm}}^{-3}$. This research lays the groundwork for accurately determining CSDs of gold plasmas in ICF hohlraums, contributing to a better understanding of the physical origins of the “drive deficit” problem.

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• Atomic orbital
• Inertial confinement fusion
• Plasma opacity
• Spontaneous emission