Asymptotic Properties of Complete and Partial Frequency Redistribution

Abstract

Radiative transfer problems with frequency redistribution may be investigated by asymptotic methods when the mean number of scatterings undergone by photons is very large. These methods, which rely on the existence of a small parameter ε, which can be the probability of collisional destruction, provide scaling laws for characteristic parameters of the line radiation field, such as the thermalization length, the thermalization frequency or the saturation intensity of the radiation field. These methods also provide asymptotic transfer equations which describe the large scale behaviour of the radiation field away from boundaries. Boundary layers equations valid close to surfaces can also be obtained. Complete redistribution and the four standard types of partial redistribution will be discussed. It will be shown that resonance line partial redistribution (R_II) is a scattering process of the diffusive type, the diffusion being not only in space but also in frequency, while the other partial redistribution mechanisms are of the complete redistribution type and not diffusive. The origin of these drastically different behaviours will be explained in physical terms. Implications for numerical calculations will be briefly discussed.