Theory of ionization/recombination kinetics with application to recombination lasers and the optogalvanic effect

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Abstract
The effects of the complete system of electron-atom inelastic collisions are shown to reduce to a system nearly as simple as the well-known one-quantum model. As a consequence, the effects of other processes, such as recombination lasing and resonant radiation enhanced ionization (the optogalvanic effect), can be analyzed simply, analytically, and quantitatively. A number of well- known ionization-recombination approximations are limiting cases of this theory. The simplification in this theory is obtained from a separable feature of the electron-atom collisional transition rate constants for Maxwellian free electrons. This feature has both theoretical and experimental support. No further approximation is needed. The resulting equations are sufficiently simple that the effects of some other processes can be explicitly determined. For example, the behavior of a collisional recombination laser can be expressed explicitly in terms of the rate coefficients. The magnitude of a population inversion and the efficiency for the laser can be derived. Similarly, resonant radiation ionization enhancement can be analyzed and it is shown how large enhancements are possible. Effects of failure of the quasisteady approximation are also analyzed. Models to include other effects are easily developed. Specialization of the coefficients in this theory leads to various well-known ionization-recombination approximations. In the limiting case of an atomic level continuum with all processes other than electron-atom collisions neglected and with one further approximation, the Mansbach and Keck solution is obtained. Through other specializations, the bottleneck, block-of-excited states, one-quantum diffusion, and modified diffusion approximations can each be found.

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