Optics design of the Super Tau-Charm Facility collider rings

The Super Tau-Charm Facility (STCF), China's next-generation electron-positron collider, targets an unprecedented luminosity exceeding 5x10^34 cm^-2 s^-1 at a center-of-mass energy of 4 GeV. The implementation of a submillimeter vertical beta function at interaction point (< 1 mm) and crab-waist collision scheme in this low-energy regime introduces critical challenges through severe nonlinear effects that constrain dynamic aperture and degrade Touschek lifetime. To address these constraints, we propose a novel quasi-two-fold symmetric lattice design integrating several synergistic features: Linear optics optimization minimizing the H-invariant around the ring to maximize local momentum acceptance (LMA); Up to third-order of local chromaticity correction in the interaction region combined with second-order achromatic arc optics, enhancing off-momentum beam dynamics; Configured FODO arc structure with interleaved sextupole groups satisfying -I transformation, suppressing third-order geometric aberrations while optimizing Montague function distributions; Advanced final focus system integrating chromatic sextupoles, crab sextupoles, and strategically positioned octupoles to counteract final quadrupole fringe fields. Furthermore, we develop a multi-objective genetic algorithm using the in-house toolkit PAMKIT to simultaneously optimize 46 sextupole families, maximizing both dynamic aperture and momentum bandwidth. Optics performance is evaluated under error conditions with appropriate corrections, ensuring robust beam dynamics.