Towards ultimate bandwidth photon sources based on Compton backscattering: Design constraints due to nonlinear effects

Nuclear resonance fluorescence experiments typically require high rates of monochromatic photons due to the narrow linewidth of these resonances. Inverse Compton scattering sources are used to perform these experiments. Their intrinsic excellent monochromaticity is however spoiled by a variety of unavoidable imperfections related to the electron and laser beams. Some projects aim at reaching one per-mille of energy bandwidth, which requires attaining excellent brilliance of the electron beam but also a careful optimization of the laser-beam parameters. In particular, in such a situation, a careful accounting for the nonlinearities induced by a relatively large laser energy has to be considered. In this article, we revisit these nonlinearities with a quantum viewpoint with the goal to provide analytical expressions that can be employed for a very fast optimization of the performance of the source. These expressions were benchmarked against the CAIN event generator with an excellent accuracy in the parameters hypervolume that is of interest in this context. We also show that previously published expression often used to include laser nonlinearities in analytical bandwidth expressions significantly depart from the detailed CAIN simulations. The obtained expression are further used to optimize designs similar to those considered in on-going projects.