Beam-Beam Interaction with Longitudinal Impedance and Its Application in TMCI Study

Simulations have showed a novel coherent head-tail instability induced by beam-beam interaction with a large Piwinski angle. The localized cross-wake force has been introduced to explain the instability. The longitudinal impedance would cause coherent and incoherent synchrotron tune shift and distort the particle¿s trajectories in longitudinal phase space. Further beam-beam simulation revealed that the longitudinal impedance has strong impacts on the beam stability, squeezing the horizontal stable tune area seriously. The instability has become an important issue during the designs of CEPC and FCC-ee. In this paper, we develop a transverse mode coupling analysis method that could be used to study beam-beam instability with and without longitudinal impedance. This method can also be applied in synchrotron light sources to study transverse mode coupling instability (TMCI) with longitudinal impedance and harmonic cavity. Some preliminary results at Shenzhen Innovation Light Source (SILF) are also shown.