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Modeling of static K and Rb diode pumped alkali lasers (DPAL) and ion-electron recombination processes in these lasers is reported. The cases of He/CH4 and pure He buffer gases are investigated and the output power and optical efficiency calculated for various pump powers, mole fractions of methane, buffer gas pressures and flow velocities. The model considers the processes of excitation of high levels of K and Rb, ionization, ion-electron recombination and heating of electrons which affect the diffusion coefficient of K and Rb ions. It explains the experimentally observed sharp increase in power in static K DPAL caused by the addition of a few percent of methane to He buffer gas and its decrease with further increase in the methane percentage [B.V. Zhdanov et al, Opt. Exp. 25, 30793 (2017)]. The predictions of the model for different He/CH4 mixtures are presented and verified by comparing them with experimental results for K flowing-gas DPAL [A. J. Wallerstein, Ph.D. dissertation (Air Force Institute of Technology, 2018)] and with the calculated results obtained using a simplified three-level model based on one-dimensional gas dynamics approach reported by A. Gavrielides et al [J. Opt. Soc. Am. B 35, 2202 (2018)]. Calculations of potential energy curves of the 2 K + and 2 Rb + molecular ions and of the diabatic 1ε+, 3ε+, 1Δ, 3Δ, 1 Π 3Π, 1Φ and 3Φ valence states of 2 K + and 2 Rb + that provide the routes for dissociative recombination (DR of the ions are performed. These curves are required for subsequent calculations of DR rate constants. The excited states of K atoms produced by DR are 42P and 52P. Most of the Rb atoms produced by DR are in the 62P excited state. This conclusion contradicts the kinetic scheme for K and Rb DPAL proposed elsewhere, and thus the kinetic schemes of these DPALs should be modified according to the present results.
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