High-Luminosity meV-Resolution Single-Shot Hard X-ray Spectrograph for Cavity-Based X-ray Free-Electron Lasers

Cavity-based x-ray free-electron lasers (CBXFELs) represent a possible realization of fully coherent hard x-ray sources having high spectral brilliance along with a narrow spectral bandwidth of $\simeq 1 - 50$~meV, a high repetition pulse rate of $\simeq 1$~MHz, and good stability. A diagnostic tool is required to measure CBXFEL spectra with meV resolution and high luminosity on a shot-to-shot basis. We have designed a high-luminosity single-shot hard x-ray spectrograph that images 9.831-keV x-rays in a $\simeq 200$~meV spectral window with a spectral resolution of a few meV. The spectrograph is designed around angular dispersion of x-rays in Bragg diffraction from crystals. It operates close to design specifications, exhibiting a linear dispersion rate of $\simeq$~1.4~$\mu$m/meV and a $\simeq$~200-meV window of high-fidelity spectral imaging. The experimentally demonstrated spectral resolution is $\simeq 20$~meV; this resolution is twice as low as expected from theory primarily because the spectrograph is highly sensitive to crystal angular instabilities. The experiment was performed at the bending magnet x-ray optics testing beamline 1-BM at the Advanced Photon Source.