Radiation trapping in 1D using the Markov chain formalism: a computational physics project

A computational model study for atomic radiation trapping is presented with an audience non-specialized in radiation transport in mind. The level of presentation is adequate for a final undergraduate or beginning graduate project in a computational physics instruction. The dynamics of resonance radiation transport is discussed using a theoretical model known as the multiple scattering representation. This model is compared with the alternative Holstein's ansatz, reinterpreting the fundamental mode as the one associated with a relaxed stationary spatial distribution of excitation. Its computational implementation is done making use of the stochastic Markov chain formalism. A comprehensive discussion of its rationale as well as fine implementation details are presented. The simplest case of complete frequency redistribution in a two-level system is considered for a unidimensional geometry. Nevertheless, the model study discusses at length the influence of the spectral distributions, overall opacity and emission quantum yield for trapping distorted ensemble quantities stressing physical insight and using only straightforward algorithmic concepts. Overall relaxation parameters ( ensemble emission yield and lifetime) as well as steady-state quantities (spectra and spatial distribution) are calculated as a function of intrinsic emission yield, opacity and external excitation mode for Doppler, Lorentz and Voigt lineshapes, respectively, with the fundamental mode contribution singled out.