Analytic solutions are presented for inhomogeneous broadening effects in multimode cw chemical lasers. A Fabry-Perot (F.P.) resonator and a saturated amplifier are considered in the limits Δνh ≪ Δνd and Δνc ≪ Δνh, where Δνh, Δνd, and Δνc are homogeneous, Doppler, and longitudinal mode separation widths, respectively. The former inequality requires p(Torr) ⩽ 0(10). The results are believed valid for Δνc/Δνh ⩽ 0(1) and apply for resonator mirror separation lengths and amplifier lengths of the order of 10 m or more. The normalized frequency difference from line center is denoted X, and the value of X corresponding to the largest longitudinal mode frequency is denoted Xf. The quantity Xf is a measure of laser frequency bandwidth and the number of active longitudinal modes. For the case of an F.P. resonator, Xf varies with streamwise distance. The local value of Xf is independent of upstream conditions for the case of a saturated F.P. resonator. The variation of lasing intensity with X at each streamwise station is found to be a truncated Gaussian. The slope of the curve of η − 1 (anomalous index of refraction) vs X is positive in the lasing region |X| < Xf. The magnitude of η − 1 is proportional to the threshold gain. For a typical saturated cw chemical laser oscillator, the anomalous index of refraction is shown to be small, compared with the regular index, for medium pressures in the range p(Torr) ⩾ 0(1). The present analytic results are in good agreement with the numerical results of Bullock and Lipkis.
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