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Fast computation of Wigner functions of undulator radiation in a multiple-beam-waist configuration
Phys. Rev. Accel. Beams 29, 113402 – Published 10 November, 2026
DOI: https://doi.org/10.1103/4hnq-5t8d
Abstract
In the formulation of synchrotron radiation (SR), the Wigner function represents the photon flux density in the four-dimensional phase space, and thus defines the brilliance and coherence. Although we have to rely on a numerical method to evaluate the Wigner function for a realistic electron beam, a convolution approach is available under the assumption that each electron travels along a straight line apart from a sinusoidal motion driven by an undulator magnetic field. As a result, the computation of Wigner functions for typical SR sources is usually completed within an acceptable time. It should be noted, however, that the above assumption is violated in a multiple-beam-waist (MBW) configuration, in which the lattice function is designed to have more than one beam waist position where the vertical betatron function is optimized to accommodate a narrow-gap undulator. In such a case, we have to carry out a Monte Carlo simulation, which requires a huge amount of time to get a reliable result. To overcome this difficulty, we introduce a theoretical-numerical method aimed at reducing the cost of computing Wigner functions in the MBW configuration. We show that the computation time can be saved by 2–4 orders of magnitude by means of the proposed method.
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