Characterization of inverted populations in chemical lasers by temperaturelike distributions: Gain characteristics in the F + H2 → HF + H system

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Abstract
With the aid of the temperature parameters characterizing product state distributions in a number of chemical reactions, frequently used concepts in chemical laser studies can be expressed in a compact form. The assumption of a rotational‐translational microcanonical equilibrium in the product atom‐diatom system leads to simple expressions for population inversions and gain factors. (However, the equilibrium assumption is not necessary; the expressions will retain their simple form also when the vib‐rotational distributions are more specific.) The main advantage is that of using only one or two parameters instead of different vibrational and rotational temperatures for every transition. Two special situations are considered in detail: (a) a nonrelaxed initial product population and (b) a vibrationally nonrelaxed but rotationally thermal population. As a specific example, the HF laser with F + H2 → HF + H as the pumping reaction is studied. Rate equations governing the emission of different laser transitions are solved. In the solution, cascading and pumping effects are considered but not rotational or vibrational relaxation. The detailed rate constants of HF formation in different vib‐rotational levels used in the calculation are those which lead to equipartition (microcanonical equilibrium) of rotational and translational energies. Comparison with experimental results indicates that the model calculations are in agreement with some chemical laser and trajectory studies which show initial population peaked at some high rotational states. The chemiluminescence measurements for low reagents energies show relatively lower peaks.