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

An analysis of the coherence properties of the fourth-generation high-energystorage rings with emittance values of 10 pm rad is performed. It is presentlyexpected that a storage ring with these low emittance values will reachdiffraction limit at hard X-rays. Simulations of coherence properties wereperformed with the XRT software and an analytical approach for differentphoton energies from 500 eV to 50 keV. It was demonstrated that a minimumphoton emittance (diffraction limit) reached at such storage rings is \pi/2. Usingmode decomposition it is shown that, for the parameters of the storage ringconsidered in this work, the diffraction limit will be reached for soft X-rayenergies of 500 eV. About ten modes will contribute to the radiation field at12 keV photon energy and even more modes give a contribution at higherphoton energies. Energy spread effects of the electron beam in a low-emittancestorage ring were analysed in detail. Simulations were performed at differentrelative energy spread values from zero to 2 10^{-3}. A decrease of the degree ofcoherence 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