Tunable optical cavity for an x-ray free-electron-laser oscillator

An x-ray free-electron laser oscillator proposed recently for hard x rays [K. Kim, Y. Shvyd'ko, and S. Reiche, Phys. Rev. Lett. 100, 244802 (2008)] can be made tunable by using an x-ray cavity composed of four crystals, instead of two. The tunability of x-ray energy will significantly enhance the usefulness of an x-ray free-electron laser oscillator. We present a detailed analysis of the four-crystal optical cavity and choice of crystals for several applications: inelastic x-ray scattering, nuclear resonant scattering, bulk-sensitive hard x-ray photoemission spectroscopy, other high-energy-resolution ($\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{meV}$) spectroscopic probes, and for imaging with hard x rays at near-atomic resolution ($\ensuremath{\simeq}1\text{ }\text{ }\mathrm{nm}$).