Novel opportunities for sub-meV inelastic X-ray scattering at high-repetition rate self-seeded X-ray free-electron lasers

Inelastic X-ray scattering (IXS) is an important tool for studies of equilibrium dynamics in condensed matter. A new spectrometer recently proposed for ultra-high-resolution IXS (UHRIX) has achieved 0.6~meV and 0.25~nm$^{-1}$ spectral and momentum transfer resolutions, respectively. However, further improvements down to 0.1~meV and 0.02~nm$^{-1}$ are required to close the gap in energy-momentum space between high and low frequency probes. We show that this goal can be achieved by further optimizing the X-ray optics and by increasing the spectral flux of the incident X-ray pulses. UHRIX performs best at energies from 5 to 10 keV, where a combination of self-seeding and undulator tapering at the SASE-2 beamline of the European XFEL promises up to a hundred-fold increase in average spectral flux compared with nominal SASE pulses at saturation, or three orders of magnitude more than possible with storage-ring based radiation sources. Wave-optics propagation shows that about $7\times 10^{12}$~ph/s in a $90$-$\mu$eV bandwidth can be achieved on the sample. This will provide unique new possibilities for dynamics studies by IXS.Comment: 17 pages, 14 figure

Transverse coherence properties of X-ray beams in third-generation synchrotron radiation sources

This article describes a complete theory of spatial coherence for undulator radiation sources. Current estimations of coherence properties often assume that undulator sources are quasi-homogeneous, like thermal sources, and rely on the application of the van Cittert-Zernike theorem for calculating the degree of transverse coherence. Such assumption is not adequate when treating third generation light sources, because the vertical(geometrical) emittance of the electron beam is comparable or even much smaller than the radiation wavelength in a very wide spectral interval that spans over four orders of magnitude (from 0.1 Angstrom up to 10^3 Angstrom). Sometimes, the so-called Gaussian-Schell model, that is widely used in statistical optics in the description of partially-coherent sources, is applied as an alternative to the quasi-homogeneous model. However, as we will demonstrate, this model fails to properly describe coherent properties of X-ray beams from non-homogeneous undulator sources. As a result, a more rigorous analysis is required. We propose a technique, based on statistical optics and Fourier optics, to explicitly calculate the cross-spectral density of an undulator source in the most general case, at any position after the undulator. Our theory, that makes consistent use of dimensionless analysis, allows relatively easy treatment and physical understanding of many asymptotes of the parameter space, together with their region of applicability. Particular emphasis is given to the asymptotic situation when the horizontal emittance is much larger than the radiation wavelength, and the vertical emittance is arbitrary. This case is practically relevant for third generation synchrotron radiation sources.Comment: 71 pages, 20 figures - Version accepted for publication in Nuclear Inst. and Methods in Physics Research,