Thermal Ionization in a System with a Distribution of Ionization Potentials

In a hydrogen plasma, the microfields act upon the neutral atoms and cause Stark effects which result in a distribution of ionization potentials. The distribution function is derived and used with the Saha equation to calculate the electron densities which are then compared with those calculated from a single ionization potential derived from an average microfield given by Cen_e^⅔ where C = 4.2, 3.7, and 2.6, respectively, depending on the method of averaging. The temperature range considered is 5 750°K to 10 700°K in which the electron densities are between 10¹⁴ and 10¹⁷cm⁻³ when the neutral particle densities are 10¹⁷ – 10¹⁹cm⁻³. Within these ranges, whereas the electron density calculated from a single ionization potential based on an average field is up to about 1% greater than that given by the Saha equation using the ionization potential of an isolated atom, calculation using the distribution equation gives values up to about 2% greater.