Repeated Compton scattering in a strong magnetic field

Repeated scatterings of unpolarized photons by non-relativistic electrons in a static and uniform magnetic field are investigated by using the Boltzmann equation with quantum mechanical correction factors for the stimulated scattering effects. The resulting Kompaneets equation depends explicitly on the electron cyclotron frequency and the incidence angle of the incoming photons relative to the direction of the magnetic field. The evolutionary behavior of the photon spectrum and energy density is highly anisotropic with respect to the static external magnetic field. Possible applications of our results to the X-ray emission from compact and massive stellar objects are discussed in detail and those to the interaction of the microwave background radiation with the hot electrons in galactic clusters are discussed briefly.