Cross section of curvature radiation absorption

When treating the absorption of light, it is instructive to focus on the absorption coefficient related to the probability of photons to survive while traversing a layer of material. From the point of view of particles doing the absorption, however, the elementary interaction of the particle with the photon is best described by the corresponding cross section. We revisit curvature radiation in order to find the absorption cross section for this process, making use of the Einstein coefficients and their relations with spontaneous and stimulated emission and true absorption. We derive the cross section as a function of the emission angle ψ (i.e. the angle between the instantaneous velocity vector and the direction of the photon) and the cross section integrated over angles. Both are positive, contrary to the synchrotron case for which the cross section can be negative for large ψ. Therefore, it is impossible to have curvature radiation masers. This has important consequences for sources of very large brightness temperatures that require a coherent emission process, such as pulsars and fast radio bursts.