Statistical Ionization Equilibrium in Partially Degenerate Plasmas

The thermal ionization equilibrium in plasmas is considered at pressures for which the electron gas is partially to considerably degenerate. An ionization equation is derived which takes into account that i) the electron energies are distributed according to Fermi statistics and ii) the (heavy) ions and atoms obey Boltzmann statistics which is valid up to pressures at which the wave functions of the atoms begin to overlap. A comparison of the quantum statistical and Saha ionization equations indicates that the degeneracy effects in the electron gas suppress somewhat the ionization. It is remarkable that the Saha equation describes, approximately, the thermal ionization equilibrium up to the critical pressure at which the wave functions of the atoms begin to overlap (e.g., up to P ~ 103 Bar and P ~ 106 Bar in the cases of Cs and H plasmas, respectively), although the electrons are noticeably degenerate.