Unified Framework for Ionization Balance and Equation of State in Partially Ionized Plasmas from Structure Factors

The ionization balance and charge state distribution of partially ionized plasmas are fundamental to predicting the key properties like the equation of state and transport properties. However, its determination remains contentious because of the ambiguous partitioning of electronic states into free and bound components. Here, we present a unified framework that rigorously connects the ionization potential depression, the ionization degree, and the equation of state through the structure factors. By incorporating thermal kinetic bottlenecks and pressure ionization via a modified partition function, and treating ionization potential depression through structure factors, the model resolves longstanding discrepancies in predicted ionization degrees. It accurately reproduces path integral Monte Carlo equations of state of hydrogen plasmas across a broad range of densities and temperatures, clarifies the competing roles of thermal and pressure ionization, and provides a clear link between microscopic electronic structure and macroscopic thermodynamics. This work offers a predictive and thermodynamically consistent foundation for modeling partially ionized plasmas in high energy density and astrophysical contexts.