Studies of Transverse Mode Coupling Instability with the Consideration of Longitudinal Impedance

Systematic studies of the influences of the longitudinal impedance on the TMCI threshold were carried out in the manuscript. We concluded that the imaginary part of the longitudinal impedance, which caused the reduction of the incoherent synchrotron tune, was the main reason for the reduction in the TMCI threshold. And the real part of the longitudinal impedance helped to raise the TMCI threshold. The data of the key figures have been uploaded.