Gain models for source-flow chemical lasers

Abstract

Four gain models are developed for use in analyzing source-flow chemical laser resonators. The first is a rotational nonequilibrium (RNE) model which traces the evolution of each vibrational-rotational state of the lasing molecule. The second is a less detailed model based on the assumption that each vibrational level is in rotational equilibrium (RE). In the third model, in addition to the rotational equilibrium assumption, the gain is assumed to be the same for all the vibrational transitions. The equations then become identical in form to those describing single-line (SL) lasing from a two-level system. The RE and RNE models solve the chemical kinetics equations for the gain self-consistently with the gasdynamic equations describing the flow field. In the SL model coupling between the gasdynamics and the laser kinetics is eliminated by using the gasdynamics from a simple Fabry–Perot calculation at a representative value of the threshold gain to provide the flow field conditions for the resonator calculation. A fourth gain model investigates the effect of using the gasdynamic calculation from the simpler SL model in a rotational nonequilibrium kinetics model. The objectives of the study are to determine how well the more computationally efficient RE and SL models can reproduce the predictions of the RNE model, and to determine the error introduced by decoupling the solutions to the gasdynamic and laser kinetic equations. The impact of rotational nonequilibrium phenomena on lasing performance is also assessed. Comparisons for the specific case of a HF laser indicate that both the RE and SL models predict output powers and peak-power mode widths which are in good agreement with those predicted by the RNE model over a wide range of values for the resonator gain. Furthermore, the RE model well approximates the power distribution among the vibrational levels, although only the RNE model is capable of providing detailed spectral information. We also find that decoupling the gasdynamic and kinetic equations does not significantly impact the accuracy of the resonator calculation. The utility of the more computationally efficient models in the design of source-flow chemical laser resonators is discussed.