## 2. Free energy model for a H-He mixtureSince the main matter constituting the Sun is a mixture of hydrogen
and helium, we need an expression for the free energy including the
contribution of at least six chemical species with free and bound
state, i.e., electrons, ions , and
neutral particles . The total free
energy where is the ideal-gas contribution of the particles; , the contribution from the uniform electron gas; , the radiation term of free energy; , the excess free energy arising from nonideal effects. The pressure and ## 2.1. Plasma parametersThe behaviour of a H-He mixture manifests nonideal effects of
interacting charged particles. Degeneracy of electron, Coulomb
coupling and pressure ionization are important features of the plasma.
To describe nonideal effects of the plasma, it is convenient to
introduce dimensionless parameters to characterize the plasma. We
consider the plasma consisting of
ions of species , with charges
,
neutral particles of species , and
electrons in a volume In the multicomponent plasma, the averaged Coulomb coupling parameters for ions and for electrons are given by (Ichimaru et al. 1987; Stolzmann & Böcher 1996): and where is the mean ion-sphere radius, and is the Boltzmann constant. The total number of ions is . The charge neutrality condition requires . The dimensionless density parameter of electrons and the degree of Fermi degeneracy are described as, respectively and where is the mass of an electron. ## 2.2. Ideal part of the free energyThe main purpose of this work is the investigation of the thermodynamic functions of the plasma. We stress that charged and neutral particles behave classically. In this paper, we limit ourselves to the consideration of one-component plasma (OCP) where the particles are regarded as point particles while the electrons are assumed to form a uniform background of neutralizing space charges. Thus and can be given by Maxwell-Boltzmann statistic and Fermi-Dirac integrals. The ideal free energy of classical particles can be written as with the thermal de-Broglie wavelength of particles where For partially degenerate electrons, the ideal part of the free energy for electrons is where is the pressure of the
ideal Fermi gas. The pressure and
electron density , in turn, are
functions of chemical potential and
temperature and where the degeneracy parameter is defined as , and is the usual nonrelativistic Fermi-Dirac integral. The chemical potential is obtained from the relationship Furthermore, can be expressed in useful analytic formula (Ichimaru & Kitamura 1996): with , , and , as a function of the degeneracy parameter . The third term on the right of Eq. (1), i.e., radiative term , is where and The excess free energy, , from the contribution of nonideal effects, will be discussed in Sect. 3. © European Southern Observatory (ESO) 2000 Online publication: January 29, 2001 |