Statistical Mechanics of a Partially Ionized Hydrogen Plasma

Abstract

A generalized Saha equation for a partially ionized hydrogen plasma is derived and used for calculating the degree of ionization and the effective ionization potential for a wide range of electron densities and temperatures. The energy eigenvalues of the hydrogen atom in a plasma are obtained as solutions of the Schr\"odinger equation from a shielded potential $w(\mathcal{r})$. $w(\mathcal{r})$, determined by a self-consistent-field method, is found to be completely different from the Debye potential. A strong effect of the excited states at high temperatures is also established.