Transverse mode-coupling instability with longitudinal impedance

Transverse mode-coupling instability(TMCI) is a dangerous transverse single-bunch instability that can lead to severe particle loss. The mechanism of TMCI can be explained by the coupling of transverse coherent oscillation modes owing to the transverse short-range wakefield(i.e., the transverse broadband impedance). Recent studies on future circular colliders, e.g.,FCC-ee, showed that the threshold of TMCI decreased significantly when both longitudinal and transverse impedances were included. We performed computations for the circular electron–positron collider(CEPC) and observed a similar phenomenon. Systematic studies on the influence of longitudinal impedance on the TMCI threshold were conducted. We concluded that the imaginary part of the longitudinal impedance, which caused a reduction in the incoherent synchrotron tune, was the primary reason for the reduction in the TMCI threshold. Additionally, the real part of the longitudinal impedance assists in increasing the TMCI threshold.