Understanding stellar interiors, inertial confinement fusion, and Z pinches depends on opacity models for mid-Z plasmas in the 100–300 eV temperature range. These models are complex and experimental validation is crucial. In this paper we describe the diagnosis of the first experiments to measure iron plasma opacity at a temperature high enough to produce the charge states and electron configurations that exist in the solar interior. The dynamic Hohlraum x-ray source at Sandia National Laboratories’ Z facility was used to both heat and backlight Mg/Fe CH tamped foils. The backlighter equivalent brightness temperature was estimated to be $T_r\sim 314\text{eV}\pm 8\%$ using time-resolved x-ray power and imaging diagnostics. This high brightness is significant because it overwhelms the sample self-emission. The sample transmission in the $7–15.5\text{Å}$ range was measured using two convex potassium acid phthalate crystal spectrometers that view the backlighter through the sample. The average spectral resolution over this range was estimated to be $\lambda /\delta \lambda \sim 700$ by comparing theoretical crystal resolution calculations with measurements at 7.126, 8.340, and $12.254\text{Å}$ . The electron density was determined to be $n_e=6.9\pm 1.7\times {10}^{21}{\text{cm}}^{-3}$ using the Stark-broadened Mg $\text{He}\beta$ , $\text{He}\gamma$ , and $\text{He}\delta$ lines. The temperature inferred from the H-like to He-like Mg line ratios was $T_e=156\pm 6\text{eV}$ . Comparisons with three different spectral synthesis models all have normalized ${\chi }^2$ that is close to unity, indicating quantitative consistency in the inferred plasma conditions. This supports the reliability of the results and implies the experiments are suitable for testing iron opacity models.

A general method for the calculation of the partition function of a canonical ensemble of noninteracting bound electrons is presented. It consists in a doubly recursive procedure with respect to the number of electrons and the number of orbitals. Contrary to existing approaches, this recursion relation contains no alternate summation of positive and negative numbers, which was the main source of numerical uncertainties. It is accompanied with a normalization of partition function through the determination of a free parameter consistent with the zeroth-order saddle-point approximation. The recursion relation allows one to calculate accurately partition functions for ions with a large number of orbitals, and is therefore important for calculations relying on the superconfiguration approximation.