Statistical thermodynamics of strongly coupled plasma

Abstract

To analyze nonidealities inherent to degenerate plasma, a quantum collective approach is developed. Thermodynamic functions of a system of partially degenerate electrons and strongly coupled ions are derived from first principles. The model takes into account the energy eigenvalues of i) the thermal translational particle motions, ii) the random collective electron and ion motions, and iii) the static Coulomb interaction energy of the electrons and ions in their oscillatory equilibrium positions. These statistical thermodynamic calculations lead to simple analytical expressions for internal energy as well as an equation of state (EOS). A dispersion relation for the high frequency branch of the plasma oscillations is introduced to take into account the partial degeneracy character and thereby to quantify temperature finiteness effects on thermodynamic properties of a partially degenerate plasma. The present results are in good quantitative agreement with the existing models. These latter being based mainly on numerical experiments while in the present model more physical insight is explicitly stated. This makes a contribution to the theoretical knowledge of coupled plasma for thermonuclear fusion as well as of astrophysical interests.