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,

Opportunities for Two-Color Experiments in the Soft X-ray Regime at the European XFEL

X-ray pump/X-ray probe applications are made possible at X-ray Free Electron Laser (XFEL) facilities by generating two X-ray pulses with different wavelengths and controllable temporal delay. In order to enable this capability at the European XFEL, an upgrade project to equip the soft X-ray SASE3 beamline with a magnetic chicane is underway. In the present paper we describe the status of the project, its scientific focus and expected performance, including start-to-end simulations of the photon beam transport up to the sample, as well as recent experimental results demonstrating two-color lasing at photon energies of 805 eV + 835 eV and 910 eV + 950 eV. Additionally, we discuss methods to analyze the spectral properties and the intensity of the generated radiation to provide on-line diagnostics for future user experiments