Averaged collision model in the theory of the polarizability of the active medium of a ring laser

An analysis is made of a collision model based on averaging the Keilson–Storer kernel and capable of describing elastic atomic collisions with an arbitrary velocity persistence. The properties of the averaged collision operator are analyzed and an analytic quadrature solution is derived for the kinetic equation for the velocity distribution of the excited atoms. An investigation is made of the influence of elastic collisions with an arbitrary persistence on the velocity distribution profile and nonlinear interaction parameters of the opposite waves in a ring laser with an active medium. The results are compared with the numerical solution based on the Keilson–Storer model and it is shown that, in typical laser problems, the averaged collision model is almost equivalent to the Keilson-Storer model.