Chubar, O.V. Geloni, G. Kocharyan, V. Madsen, A. Saldin, E. Serkez, S. Shvyd'ko, Yu. Sutter, J. MOP086 undulator radiation photon optics scattering 2015 2015-12 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 spectral and momentum Transfer resolutions, respectively*. However, further improvements down to 0.1 meV and 0.02/nm 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 improvements in 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 SASE2 beamline of the European XFEL promises up to a hundred-fold increase in average spectral flux compared to 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 7·10¹² ph/s in a 90-microeV bandwidth can be achieved on the sample. This will provide unique new possibilities for IXS. Extended information about our work can be found in**.