Generalizations of the Saha Equation

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Abstract
The Saha equation, which relates temperature to ion densities, is sometimes used under circumstances that do not justify the assumptions of thermodynamic equilibrium upon which it is based. Astronomers have therefore made generalizations of this equation but have unfortunately assumed thermodynamic equilibrium energy distributions for the particles and the radiation field even though these may be at different temperatures. It is therefore interesting to know how the nonequilibrium steady‐state energy distributions affect the ionization densities. In the present treatment a general expression relating ion densities to the radiation and particle energy distributions is obtained. This equation reduces to Saha's equation in the limit of thermal equilibrium and gives numerical results in good agreement with other work based on entirely different considerations, thus providing a good check. We find that under certain conditions one would expect results that differ enormously from those predicted by the Saha equation.

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