Investigation on equation of state and ionization equilibrium for aluminum in warm dense matter regime

Abstract

Warm dense matter is widely found in the high-energy-density-physics researches, such as inertial confinement fusion, X-ray source and wire-array Z-pinch. The equation of state and ionization equilibrium of material in warm dense matter regime play a significant role in explaining experimental results and simulations of physical process. In this paper, the Coulomb interaction between charged particles, and the excluded volume effect due to high density and polarization effect between neutral atoms and charged particles are considered in the equation of state for aluminum in warm dense matter regime. A non-ideal Saha equation is used to account for the ionization equilibrium. The data for pressure and concentration of particles of aluminum plasma are derived by iteration between equation of state and ionization equilibrium model. The pressure and average ionization degree of aluminum plasma are consistent with the calculation results from other models and relevant experimental data. The Coulomb interaction, which dominants the non-ideal effects, is insensitive to temperature and increases with density rising especially near the region of critical density. The excluded volume effect peaks at a density of ～0.5 g/cm<sup>3</sup>. The polarization effect first becomes stronger with density increasing and then decreases at a density of ～0.4 g/cm<sup>3</sup>. The ionization equilibrium results with density ranging from 1.0 × 10<sup>–4</sup> g/cm<sup>3</sup> to 3.0 g/cm<sup>3</sup> and temperature ranging from 1.0 × 10<sup>4</sup> K to 3.0 × 10<sup>4</sup> K reveal that the average ionization degree increases with density sharply increasing near the critical density. The non-ideal effects, which lead the ionization energy to decline and the effective ionization potential of specific ions in aluminum plasma to decrease substantially, are responsible for the sharp increase of average ionization degree near the region of critical density. When the temperature is lower than 12000 K, first and second stage of ionization occur in aluminum plasma, and the system is mainly composed of Al<sup>1+</sup>, Al<sup>2+</sup> and electrons. The average ionization degree can reach 2 at critical density. The third stage of ionization is dominant in the aluminum plasma when plasma temperature is higher than 12000 K. And then, the charged particles in the plasma are composed of Al<sup>3+</sup> and electrons, allowing the average ionization degree to reach 3 at critical density.