Kinetic Theory of an Electron-Photon Gas

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Abstract
An extension of the Boltzmann equation for plasmas is presented, including interactions between the electrons and the photons which populate the radiation field. This development results in those electron‐photon collision integrals which are required to describe relaxation towards equilibrium of both particles and radiation field as a result of radiative interactions alone. Single‐photon emission and absorption as well as Compton scattering are treated. The equation derived is specialized to the case of electrons orbiting in a steady magnetic field, and is used to follow the relaxation of a test electron which is interacting with a thermal radiation field via the emission and absorption of cyclotron radiation. It is also used to study the saturation properties of the cyclotron radiation maser. In the case of Compton scattering by free electrons a clear separation between these electron‐photon collision terms and the usual electric field term in the Boltzmann equation is shown to exist. Collision terms are also derived for the photon transport equation, with particular attention paid to the effect of enhanced scattering when more than one mode of the radiation field is simultaneously occupied. This equation is then used to evaluate a new type of light scattering experiment, one which involves the enhanced Compton scattering by free electrons traversing an intense radiation field excited in two of its modes. The entire treatment is based upon independent particle behavior. Many‐body collective effects are ignored.