Analytic expressions for the angular and the spectral fluxes at Compton X-ray sources

The goal of this paper is to express simply the number of photons impinging on a target in the framework of accelerator-based Compton X-ray sources. From the basic kinematics of Compton sources, analytic formulas for the angular and the spectral fluxes are established as functions of the energy spread or/and the angular divergence of the electron and the laser beams. Their detailed predictions are compared with Monte Carlo simulations. These analytic expressions allow one to compute in a simple and precise way the X-ray flux in a given angular acceptance and a given energy bandwidth, knowing the characteristics of the incoming beams.