Resonance radiation transport in inhomogeneous media: Cylindrical glow discharges

Numerical simulations of radiation transport in cylindrical geometry are used to determine the effect of radially symmetric inhomogeneities. The focus of this study are inhomogeneities such as may be produced by radial cataphoresis or temperature gradients in cylindrical glow discharges, i.e., a quadratic profile of absorbing atoms which has a minimum on the axis of the cylinder. A propogator function analysis of the Holstein–Biberman equation and a Monte Carlo simulation of resonance photon scattering are simultaneously used to examine three limiting cases of interest: (i) a pure Doppler broadened atomic lineshape, (ii) a pure Lorentz atomic lineshape produced by foreign gas broadening, and (iii) a pure Lorentz atomic lineshape produced by resonance collision broadening. The fundamental mode distribution of excited atoms, the fundamental mode trapped decay rate, and the volume-averaged escape rate for a homogeneous production rate per unit volume are calculated for each of these cases. The trapped decay rates are found to change modestly (depending upon lineshape) as the degree of inhomogeneity is increased, if the volume integral of the absorbing atom density remains fixed. Correction factors for the fundamental mode trapped decay rate are reported.