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The Super Tau-Charm Facility (STCF), a next-generation high-luminosity frontier collider, adopts a large crossing angle with the Crab-Waist scheme to enhanced collision luminosity. The center-of-mass energy range of STCF is 2-7 GeV, and the designed collision luminosity will exceed $0.5 \times 10^{-35} \, \text{cm}^{-2} \text{s}^{-1}$. The STCF’s collider rings are two high-current, low-emittance electron and positron storage rings operating over a wide energy range. However, synchrotron radiation damping from lattice alone is inadequate to achieve the desired short damping time, low horizontal emittance, and relatively high beam energy spread. To address this, the damping wigglers are incorporated into the rings to enhance damping effects.
This study finds that the longitudinal magnetic field distribution $B_{y}(s)$ in practical damping wigglers often deviates from the ideal sinusoidal curve. Particularly for damping wigglers with large period lengths, the field profile near the peak approaches a flat-top shape, which differs significantly from a sinusoidal curve. To better represent such field distributions, a trapezoidal field model was developed with the definition of a rectangularity parameter $k$. Based on this model, analytical formulas for synchrotron radiation integrals and beam parameters under the trapezoidal field approximation have been derived, enabling further parameter optimization of the damping wigglers in the STCF collider rings.
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