Saha Equation

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Saha Equation


a formula for the degree of thermal ionization α of a gas—that is, for the ratio of the number of ionized atoms to the total number of atoms present. First stated by M. Saha in 1920 for the description of processes in stellar atmospheres, the equation was derived from general thermodynamic considerations and deals with the case of a weakly ionized gas in a state of thermodynamic equilibrium. The equation has the form

where T is the absolute temperature, p is the pressure of the gas, Wi is the ionization potential of the gas’ atoms, ga and gi are the statistical weights of the neutral atom and the ion, respectively, m is the mass of an electron, k is the Boltzmann constant, and h is Planck’s constant.

The Saha equation is only approximately valid because its derivation rests on the assumption that only three types of particles are present: neutral atoms, singly ionized ions, and electrons. Multiple ionization, excited atoms, and the presence of impurities are not taken into account. Also not considered is the interaction of the gas with the wall. Such interaction can result in surface ionization and in the ionization of the gas by electrons ejected from a hot wall. Despite these limitations, the Saha equation is applicable to many cases where α ≪ 1.


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Saha equation for two-temperature plasmas: Theories, experimental evidence, and interpretation.
Thermodynamic inconsistency of the modified Saha equation at high pressures.
Departures from the Saha equation under varying conditions of Lyman continuous opacity.
An approach to a non-LTE Saha equation based on Druyvesteyn energy distribution function: A comparison between electron temperature obtained from OES and the Langmuir probe analysis.