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

Abstract

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.

71 pages, 20 figures - Version accepted for publication in Nuclear Inst. and Methods in Physics Research, A

References in corpus (3)

• Statistical Optics approach to the design of beamlines for Synchrotron Radiation
• Spatial Coherence of Synchrotron Radiation
• Understanding transverse coherence properties of X-ray beams in third generation Synchrotron Radiation sources

Cited by in corpus (11)

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• Coherence properties of the high-energy fourth-generation X-ray synchrotron sources
• Synchrotron radiation representation in phase space
• Coherent modes of X-ray beams emitted by undulators in new storage rings
• A hierarchical approach for modelling X-ray beamlines. Application to a coherent beamline
• Effects of energy spread on Brightness and Coherence of undulator sources
• A fast and light tool for partially-coherent beamline simulations in fourth generation storage rings based on coherent mode decomposition
• Hard X-ray optics simulation using the coherent mode decomposition of Gaussian Schell model
• Propagation of partially coherent radiation using Wigner functions
• Speckled cross-spectral densities and their associated correlation singularities for a modern source of partially coherent x rays
• Coherent superposition of orthogonal modes