Luminosity optimization schemes in Compton experiments based on Fabry-Perot optical resonators

The luminosity of Compton x-ray and gamma sources depends on the average current in electron bunches, the energy of the laser pulses, and the geometry of the particle bunch to laser pulse collisions. To obtain high power photon pulses, these can be stacked in a passive optical resonator (Fabry-Perot cavity) especially when a high average flux is required. But, in this case, owing to the presence of the optical cavity mirrors, the electron bunches have to collide at an angle with the laser pulses with a consequent luminosity decrease. In this article a crab-crossing scheme is proposed for Compton sources, based on a laser amplified in a Fabry-Perot resonator, to eliminate the luminosity losses given by the crossing angle, taking into account that in laser-electron collisions only the electron bunches can be tilted at the collision point. We report the analytical study on the crab-crossing scheme for Compton gamma sources. The analytical expression for the total yield of photons generated in Compton sources with the crab-crossing scheme of collision is derived. The optimal collision angle of the bunch was found to be equal to half of the collision angle. At this crabbing angle, the maximal yield of scattered off laser photons is attained thanks to the maximization, in the collision process, of the time spent by the laser pulse in the electron bunch. Estimations for some Compton source projects are presented. Furthermore, some schemes of the optical cavities configuration are analyzed and the luminosity calculated. As illustrated, the four-mirror two- or three-dimensional scheme is the most appropriate for Compton sources.