Equilibrium Theory of a Partially Ionized Plasma

A detailed study is made of the use of the Debye potential as the effective interaction between the electron and proton of a hydrogen atom in a partially ionized plasma. The chemical potentials of the constituents are calculated and examined in the light of the requirement that they be consistent with a single free-energy function. On this basis a Saha equation is derived which is consistent and correct up to terms of the order of the Debye-H\"uckel energy. It is further shown that the next order, obtained by expanding the effective potential in powers of the Bohr radius divided by the Debye length, is incorrect.