Equation of state (EOS) is a necessary condition for studying the properties of plasma and fluid dynamics simulation under extreme conditions in astrophysics and laboratory. In inertial confinement fusion experiment (ICF), with the injection of laser energy, after a certain moment, the temperatures of ions, electrons and radiation field separate. It is generally considered that the free electrons in the plasma conform to the Maxwell distribution, and the ideal gas EOS is used for calculation. However, in the actual experimental environment, there are several non-thermal electron sources, which may cause errors in the theoretical simulation.
Previous experiments on microwaves and Thomson scattering have confirmed the existence of non-Maxwellian distributions. In the ICF black cavity, the main sources of non-thermal electrons include: super-thermal electrons generated by the laser-plasma interaction (LPI) process itself, preferential heating of low-energy electrons during laser inverse bremsstrahlung absorption, resulting in a super-thermal platform that satisfies the super-Gaussian distribution, and the high-energy tail that satisfies the kappa distribution due to the smaller collision cross-section between high-energy electrons, which corresponds to the quasi-steady-state solution of plasma Langmuir waves in kinetics. Therefore, it is necessary to construct a non-thermal equilibrium EOS when the microscopic statistical distribution of free electrons deviates from the Maxwell distribution.
Using the self-consistent field average atom model, this research constructs a quasi-steady EOS for non-thermal equilibrium gold plasma. We calculates the EOS when free electrons satisfy Maxwell-Boltzmann distribution, kappa-distribution, super-Gaussian distribution, and two-temperature distribution, respectively. Tsallis non-equilibrium statistical theory is employed to describe the kappa-distribution. The calculation results are significantly different from the ideal gas EOS. Additionally, the results indicate that the relativistic effect significantly modifies the EOS when the electron temperature exceeds 10keV. This model takes into account real experimental conditions and requires less computational time, contributes to deeper understanding of the physical mechanisms and influence of non-thermal electrons in EOS calculation. It also has certain reference value for future engineering applications of ICF.
 

Equation of state,,Non-equilibrium statistics,,non-local thermal equilibrium plasma,average atom model