Bent crystal spectrometer for both frequency and wavenumber resolved x-ray scattering at a seeded free-electron laser

We present a cylindrically curved GaAs x-ray spectrometer with energy resolution $\Delta E/E = 1.1\cdot 10^{-4}$ and wave-number resolution of $\Delta k/k = 3\cdot 10^{-3}$, allowing plasmon scattering at the resolution limits of the Linac Coherent Light Source (LCLS) x-ray free-electron laser. It spans scattering wavenumbers of 3.6 to $5.2/$\AA\ in 100 separate bins, with only 0.34\% wavenumber blurring. The dispersion of 0.418~eV/$13.5\,\mu$m agrees with predictions within 1.3\%. The reflection homogeneity over the entire wavenumber range was measured and used to normalize the amplitude of scattering spectra. The proposed spectrometer is superior to a mosaic HAPG spectrometer when the energy resolution needs to be comparable to the LCLS seeded bandwidth of 1~eV and a significant range of wavenumbers must be covered in one exposure.