Effect of Reflecting Boundaries on the Transport of Resonance Radiation. II. Comparison with Diffusion Theory

Abstract

The generalized Holstein-Biberman transport theory developed in Part I is used to calculate the effect of reflecting walls in increasing the decay time of Doppler broadened resonance radiation in cylinders and slabs. The results are compared with the corresponding results obtained from the Cayless diffusion theory for optical thicknesses between about 20 and 3000. It is shown that the Cayless theory grossly underestimates the effect over the entire range, giving values for the fractional increase in decay time which are too small by about a factor of 3 at the smaller optical thicknesses, and too small by about a factor of 30 at the larger thicknesses. The discrepancy is shown to arise partly from the inaccurate boundary condition used in the Cayless theory and partly from the inapplicability of the mean free path concept to processes involving the transport of resonance radiation. The consequences for the behavior of low-pressure mercury rare-gas discharges are discussed, and it is estimated that wall reflectance must begin to have a significant effect on the characteristics of such discharges at reflectances as low as 20% rather than at the 50% reflectance predicted by the Cayless theory.