Power loss analysis for optical cavity of X-ray free-electron laser oscillator at 10 KeV

We investigate properties of optical elements in the optical cavity of an X-ray free electron laser oscillator with emphasis on power loss of a monochromatic Gaussian radiation beam upon passing through them using analytical and numerical approaches. Here we assume the optical cavity comprises of refractive lenses and Bragg crystals exploiting symmetric Bragg scattering. For lens, we include the focusing and curvature effects while we include the angular filtering due to finite Darwin width of Bragg crystals. Our results indicate feasibility of X-ray power outcoupling in the range of 0.5-28 % with intra-cavity reflectivity of 67-95 % at 10.321 KeV.