  The Saha equation describes the relative number density of consecutive
ionization levels of a given atomic species under conditions of thermodynamic
equilibrium in an ionized gas. Because the number density in the denominator
may be very small, special steps must be taken to ensure numerical stability.
In this paper we recast the equation into a form in which each ionization
fraction is normalized by the total number density of the atomic species,
analogous to the Boltzmann equation describing the distribution of excitation
states for a given ion.
