Combined phenomenon of transverse impedance and beam-beam interaction with large Piwinski angle

Abstract

The crab-waist scheme becomes the baseline for future circular e^{+}e^{-} colliders, where a large Piwinski angle is a must. It has been first found that a strong coherent head-tail instability in the vertical direction may be induced by the interplay of beam-beam interaction and ring impedance below the conventional transverse mode-coupling instability threshold. The collision would be stable only considering pure beam-beam interaction. That is to say, the new instability is a combined effect of beam-beam interaction and ring impedance. The instability can limit the performance of future colliders based on the crab-waist scheme. Mode analysis has been done to help understand the physics. Mitigation schemes are also presented and verified by analysis and simulation.