Models of collisional-radiative recombination

The physical basis of electron-ion recombination in tenuous plasmas as a result of electron collisions is reviewed. The theory is developed from the optically thin collisional-radiative model by a continuous representation of the discrete state. It is shown that for a collision-dominated cascade this leads to a Fokker-Planck equation for the distribution among the excited states, whose analytic solution is derived. In the radiation-dominated limit an equivalent equation is derived, and the solution obtained. The physical basis of these results is explored. The results are in good agreement with direct numerical evaluation of the collisional-radiative equations, where the effect of collision-rate approximations is explored. It is found that the conventional criterion for the local thermodynamic equilibrium limit in such systems may need modification.