Radiative transfer of excitation: Lévy flights and self-similarity

Abstract

The Green function of the Biberman–Holstein integral equation, both nonstationary (instantaneous point flash) and stationary (stationary point source) is studied. The point flash produces a self-similar spherical wave of excitation in homogenous gas medium. The transfer of excitation is due to the Lévy flights of resonance line photons. The properties of the wave – its shape, time evolution and propagation – are found for arbitrary line profile. The cases of Doppler, Lorentz and Voigt profiles are considered in some detail. For the Doppler broadened line, the structure of the self-similar wave is given by a rational function. The properties of the Green function of stationary Biberman–Holstein equation are reviewed. Some unexpected parallels with non-stationary case are found. The spherically-symmetric version of the longest flight approximation is discussed and the condition of its validity is formulated.