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Modern synchrotron light sources are sometimes characterized with high-brightness synchrotron radiation from insertion gadgets. Inevitably, insertion devices introduce nonlinear distortion to the beam motion. Symplectic tracking is crucial to review the affect, especially for the low- and medium-power storage rings. This paper makes use of a Robinson wiggler as an example to illustrate an universally relevant analytical representation of the magnetic discipline and to summarizes 4 completely different symplectic tracking methods. With the purpose of excessive-brightness synchrotron radiation, the storage rings of trendy synchrotron gentle sources largely undertake sturdy-focusing lattices, which result in massive negative pure chromaticities and need robust sextupoles to right the chromaticity to suppress the top-tail instability. Therefore nonlinear distortion is launched to beam motion by robust sextupole fields. Furthermore, insertion devices, fringe fields and imperfections of magnets are further sources of nonlinearity. The nonlinear distortion from the magnets determines lengthy-term beam stability and has sturdy affect on operational efficiency.
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