Coherence properties of the high-energy fourth-generation X-ray synchrotron sources

An analysis of the coherence properties of the fourth-generation high-energy storage rings with emittance values of 10 pm rad is performed. It is presently expected that a storage ring with these low emittance values will reach diffraction limit at hard X-rays. Simulations of coherence properties were performed with the XRT software and an analytical approach for different photon energies from 500 eV to 50 keV. It was demonstrated that a minimum photon emittance (diffraction limit) reached at such storage rings is λ/2π. Using mode decomposition it is shown that, for the parameters of the storage ring considered in this work, the diffraction limit will be reached for soft X-ray energies of 500 eV. About ten modes will contribute to the radiation field at 12 keV photon energy and even more modes give a contribution at higher photon energies. Energy spread effects of the electron beam in a low-emittance storage ring were analysed in detail. Simulations were performed at different relative energy spread values from zero to 2 × 10^-3. A decrease of the degree of coherence with an increase of the relative energy spread value was observed. This analysis shows that, to reach the diffraction limit for high photon energies, electron beam emittance should go down to 1 pm rad and below.