Boltzmann equation for a photon gas interacting with a plasma

Abstract

The dynamics of a photon gas is described in a Boltzmann-equation formulation for the rate of change of the photon occupation number. The interaction with the electron component of a hydrogen-helium plasma by Compton scattering is introduced as a Fokker-Planck operator. This operator, as well as the total energy exchange rate by Compton scattering, is derived by simple physical arguments from the limiting formula for the case of a zero-temperature nondegenerate electron gas; the effects of stimulated scattering are discussed. Photon production by various atomic processes (bremsstrahlung, direct radiative recombination, line emission, and 2 s-1 s two-photon continuum emission) is described as source terms in the Boltzmann equation. The spontaneous emission by these atomic processes is conveniently described in terms of the basic bremsstrahlung term which dominates the other atomic processes for kT e ≳ 1 Ry; at lower temperature the other processes, which involve bound atomic states, dominate. Absorption and stimulated emission by the atomic processes are discussed briefly. The process of radiative Compton scattering (double Compton scattering) is evaluated in the limit of low photon energies for interaction with a zero-temperature electron gas; this process is shown to be negligible compared with bremsstrahlung for the important application to the problem of the primordial plasma and photon gas.