On multiple Compton scattering in plasma clouds

Inverse Compton scattering of low energy photons in a nonrelativistic electron gas is considered. The angle dependence in the Thomson cross section is neglected and spatial and energy transport are separated in a multiple scattering development of the emerging spectrum. The energy transport is determined by a Green function G which may be obtained from the single scattering spectrum for small optical depth or from the Kompaneets equation in the optically thick medium (τ ? 1). The electron cloud is assumed to be spherical and homogeneous with constant temperature $\text{?}{}_{\mathrm{e}}\text{=}\text{kT}{}_{\mathrm{e}}\text{m}{}_{\mathrm{e}}\text{c}{}^2$. Photon escape probabilities P_N from the cloud after N scatterings are calculated from a random flight problem with absorbing walls and alternative methods are mentioned and compared in the limit of large optical depth.