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  Bahrdt, J.: Shaping Photon Beams with Undulators and Wigglers. In: Jaeschke, E.J.; Khan, S.; Schneider, J.R.; Hastings, J.B. [Eds.] : Synchrotron light sources and free-electron lasers: Accelerator physics, instrumentation and science applications, volume 1-3 / second editionCham: Springer, 2020. - ISBN 978-3-030-23200-9, p. 851-933

Abstract:
Periodic magnetic structures, i.e., undulators and wigglers, have been used for nearly 40 years as sources of brilliant synchrotron radiation. Today, sophisticated undulator designs provide many degrees of freedom such as photon beam energy, variable polarization, and orbital angular momentum. Specific designs efficiently suppress higher orders or reduce the on-axis power density. All tuning parameters are required to be freely accessible by the users. Still, the majority of undulators are based on permanent magnets with a clear trend to short-period in-vacuum and cryogenically cooled systems. The development of superconducting undulators is rapidly progressing, and high-quality devices are operated at two multiuser facilities. Similar designs are used for storage rings and free-electron lasers, though, the field quality requirements are different. Today, the optimization of a specific experiment follows a global approach. This includes not only the undulator design itself but also local lattice modifications to cope with ambitious designs, elaborate tracking schemes to estimate the impact on the dynamic aperture, and last but not least radiation propagation tools which transport a realistic photon beam phase space to the sample. This chapter summarizes the theory of undulator radiation and reviews the technological realization of undulators and wigglers. Operational issues are discussed, as well.