Photon plasma--wave interaction via Compton scattering

The Kompaneets theory of photon kinetic evolution due to the Compton effect in the absence of absorption and emission is extended to the case of the Vlasov plasma wave oscillations. Under the assumption that the electron distribution function at equilibrium is perturbed by a solution of the linearised Vlasov equation in the long-wavelength limit, a solution of the Kompaneets kinetic equation for the photon distribution function is found and discussed.