Possibility of X-ray free electron laser with single crystal optical resonator for Bragg reflection

Noting the X-ray reflection coefficient of a single crystal as high as 90% at a Bragg angle, a possibility of X-ray free electron laser in a storage ring was investigated. An optical resonator composed of four Si single crystal mirrors with diffraction angle 45 degrees provides a light beam size in the optical resonator about 30 /spl mu/m rms at a wavelength of 0.217 nm. Assuming an electron beam emittance of 46 pm-rad at a beam energy of 3 GeV, and a peak current of 1200 A, we obtain an FEL gain of 39% for an undulator with a number of periods of 300, which is slightly higher than the radiation loss in the mirrors. At the same time a conceptual design of a storage ring with such a small emittance beam is presented.