Optical Escape Factors for Bound‐bound and Free‐bound Radiation from Plasmas. I. Constant Source Function

Abstract

AbstractOptical escape factors for bound‐bound and free‐bound radiation have been calculated by solving the equation of radiative transfer with the assumption that the corresponding source functions are space‐independent. The general expression for bound‐bound transitions yields for large optical depths—within a correction factor of order unity—Holstein's asymptotic expressions for the two limiting cases of a Doppler and a dispersion profile. Application to the more general case of a Voigt profile leads to an analytical formula which permits a rapid estimate of the escape factor for any optical depth. Numerical application to the resonance lines of neutral helium‐which are broadened by Stark and Doppler effects—shows that under certain plasma conditions most of the higher members of the resonance series remain optically thin.—The general expression obtained for the escape factor of free‐bound radiation has been applied to the resonance continuum of neutral helium. The numerical results show that the resonance continuum remains optically thin as long as the optical depth in the center of the He resonance line (λ = 584 Å) remains smaller than 104 to 105. A similar result is obtained for atomic hydrogen.