Comparison of two equation-of-state models for partially ionized aluminum: Zel’dovich and Raizer’s model versus the activity expansion code

Abstract

Two equation-of-state (EOS) models for multipy ionized matter are evaluated for the case of an aluminum plasma in the temperature range from about one eV to several hundred eV, spanning conditions of weak to strong ionization. Specifically, the simple analytical mode of Zel’dovich and Raizer and the more comprehensive model comprised by Rogers’ plasma physics avtivity expansion code (ACTEX) are used to calculate the specific internal energy ε and average degree of ionization Z̄*, as functons of temperature T and density ρ. In the absence of experimental data, these results are compared against each other, covering almost five orders-of-magnitude variation in ε and the full range of Z̄* We find generally good agreement between the two sets of results, especially for low densities and for temperatures near the upper end of the rage. Calculated values of ε(T) agree to within ±30% over nearly the full range in T for densities below about 1 g/cm3. Similarly, the two models predict values of Z̄*(T) which track each other fairly well; above 20 eV the discrepancy is less than ±20% fpr ρ≲1 g/cm3. Where the calculations disagree, we expect the ACTEX code to be more accurate than Zel’dovich and Raizer’s model, by virtue of its more detailed physics content.