The plasma composition, equation of state, and phase diagram of dense helium plasma were calculated for temperatures of 104...105 K, total atom densities of 1015... 1025 cm−3, and pressures up to 102 TPa, including the region of partial ionization and strong Coulomb coupling. The basic thermodynamic potential was chosen to be the free energy density with contributions due to Coulomb interaction, hard-core repulsion, and van der Waals-like attraction for a mixture of differently charged atoms and free electrons. For the first time, we show the potential occurrence of a sequence of plasma phase transitions. In helium, they correspond to the ionization steps He0→He+ and He+→He++ respectively. The properties of the coexisting phases were determined by a Maxwell construction based on the combined chemical potential.

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We present a theoretical approach to the thermodynamic properties of nonideal plasmas consisting of neutral atoms, multiply charged ions, and free electrons. Starting with the free energy, we describe the ionization equilibrium of this system by a coupled set of mass action laws (Saha equations). Our model of interaction takes into account Coulomb forces between all charged particles and hard-core forces between all heavy particles and the electrons. The influence of multiple ionization and different interaction parts on plasma composition, mean charge, and equation of state is discussed for xenon. Finally, we show the potential occurrence of the plasma phase transition.

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A b s t r a c tThe equilibrium properties of a multi-component plasma of charged particles that interact through the Coulomb potential and general short-range potentials are investigated at low density within the framework of classical statistics. In particular, this article presents density expansions of (1) the reduced distribution functions for two and more particles up to second order as obtained from the screened Bogoliubov-BornGreen-Kirkwood-Yvon hierarchy and (2) the interaction contribution to the Helmholtz free energy including a new closed representation of the fourth duster integral derived with the help of a usual charging procedure. '1 IntroductionThe calculation of the equilibrium properties of many-particle systems for a given type of microscopic interaction is one of the most fundamental problems in statistical physics. In this article I consider a classical multi-component plasma at low density as a fluid mixture of N charged particles belonging to different species and interacting through the two-body Coulomb potential and additional short-range potentials between two and more particles.The systematic approach adopted here follows the traditional route of first solving the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for the reduced distribution functions by formal density expansion where Debye-Hiickel screening is consistently introduced, and then determining thermodynamic quantities as, e. g., the Helmholtz free energy from both the distribution functions and the interaction potentials by a charging process. In this way I calculate in Sec. 2 the first three coefficients in the expansion of the s-particle distribution function and in Sec. 3 the excess free energy up to the fourth cluster integral, thereby correcting and completing previous work of SCHMITZ [l, 21 from the late sixties on the same subject. All results are expressed in terms of the Mayer functions for two-, three-, and four-particle interaction potentials which makes it clear that the present method may be regarded as closely related to the diagrammatical derivation of cluster expansions from the ionic solution theory developed by MAYER and FRIEDMAN (for adetailed review see [3]). Density expansion of t h e reduced distribution functionThe reduced distribution function f51...a, for s particles, s < N , of species {a;} at positions {r;} (i = 1,. . . , s) from an N-particle system in the volume V at temperature T is given by where the configuration integral QN insures normalization of f5,...5, to Vd, and P = l/kwT.For a shorter notation I drop the dependence on r; always implying that, e. g., 351 = 3a, (rl).The central quantity in Eq. (1) is the total interaction potential, or direct potential, w , ,~. . .~~