Impact of coherent wiggler radiation impedance in Tau-Charm factories

Coherent synchrotron radiation (CSR) has long been recognized as a significant source of longitudinal impedance driving microwave instability in electron storage rings. In the pursuit of higher luminosity, next-generation circular $e^+e^-$ colliders operating in the few-GeV energy range, such as B-factories and Tau-Charm factories, are being designed with low-emittance beams and high beam currents. Damping wigglers are commonly introduced to reduce damping times and control beam emittance. In this study, we systematically investigate the impact of coherent wiggler radiation (CWR), a specific form of CSR generated within wigglers, on beam stability in Tau-Charm factories. We revisit the threshold conditions for CWR-induced microwave instability and evaluate its effects under realistic lattice configurations of collider rings. Furthermore, we examine theoretical models of longitudinal CWR impedance and identify improved formulations that better capture its influence. As an illustrative example, the developed CWR impedance models are applied to simulate beam stability in the Super Tau-Charm Facility currently under design in China.