Towards x-ray free-electron laser oscillators

Free-electron lasers generating x-ray wavelengths typically operate in the self-amplified spontaneous emission (SASE) regime. Self-seeding by filtering an SASE pulse and subsequently amplifying the filtered optical pulse can be used to improve the coherence properties of the light produced. To obtain fully coherent optical pulses would require an oscillator configuration. At these wavelengths, single-crystal diamond can be used as a highly reflecting Bragg reflector. Here we consider 6 Bragg reflectors and 2 compound refractive lenses to create a stable ring resonator. To avoid excessive heating of the mirrors, we consider a so-called RAFEL configuration where a large fraction of the light is extracted from the resonator. Wavelength tuning is obtained by rotating the mirrors to change the Bragg condition. Assuming LCLS-II like parameters, we show lasing at 3.05 keV photon energy with substantial output power and high degree of coherence.