The greatly enhanced radiation pressure force felt by a relativistic plasma is accompanied by catastrophic Compton cooling and only in extreme conditions can it lead to acceleration to relativistic bulk velocities. We solve the equations of motion in the optimal case and find that the efficiency of acceleration is typically < 1 per cent (the energy lost being given to the scattered photons). The complicating effects of expansion of the plasma, finite source size and scattering above the Klein–Nishina limit are described. We end with a short list of situations in which the phenomenon may nevertheless be of importance
