Abstract
Undulator radiation is partially coherent in the transverse plane, with the degree of coherence depending on the ratio of the electron beam phase space area (emittance) to the characteristic radiation wavelength $\ensuremath{\lambda}$. On the other hand, numerical codes used to predict x-ray beam line performance can typically only propagate coherent fields from the source to the image plane. We investigate methods for representing partially coherent undulator radiation using a suitably chosen set of coherent fields that can be used in standard wave propagation codes, and discuss such ``coherent mode expansions'' for arbitrary degrees of coherence. In the limit when the electron beam emittance along at least one direction is much larger than $\ensuremath{\lambda}$ the coherent modes are orthogonal and therefore compact; when the emittance approaches $\ensuremath{\lambda}$ in both planes we discuss an economical method of defining the relevant coherent fields that samples the electron beam phase space using low-discrepancy sequences.
Highlights
Modern storage rings produce partially coherent x rays for experimental use, and new facilities under both construction and design hold the promise for increasing the coherent flux by 1–2 orders of magnitude
In tandem with these developments, a host of experimental x-ray techniques have been developed over the last few decades that take advantage of partially coherent radiation, including x-ray photon correlation spectroscopy and scattering [5,6], coherent x-ray diffractive imaging [7,8,9], x-ray scanning microscopy [10], and x-ray nanoprobe spectroscopy [11]
III B we investigate the limit where one emittance is large while the other is arbitrary; this case applies at modern third generation storage rings over a wide range of parameters
Summary
Modern storage rings produce partially coherent x rays for experimental use, and new facilities under both construction and design hold the promise for increasing the coherent flux by 1–2 orders of magnitude (see, e.g., [1,2,3,4]). The ability to make detailed predictions of the x-ray properties has become an important component in both the design and interpretation of these experiments This in turn requires accurately simulating the radiation from the source to the detector, including realistic models of all beam line optical elements, and of the sample itself. (or emittance) in both horizontal and vertical planes is much larger that λ=4π
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