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Crab crossing scheme is an essential collision scheme to achieve highluminosity for the future colliders with large crossing angles. However, whenbunch length of one or both colliding beams is comparable with the wavelengthof the crab cavity voltage, the nonlinear dependence of the crabbing kick maypresent a challenge to the beam dynamics of the colliding beams and impact thebeam quality as well as the luminosity lifetime. In this paper, the results ofnonlinear dynamics in the crab crossing scheme are presented, using bothanalytical and numerical studies. The result indicates that higher-ordersynchro-betatron resonances may be excited in the crab crossing scheme withlarge crossing angle, which causes the beam quality deterioration andluminosity degradation. The studies also reveal possible countermeasures tosuppress the synchro-beta resonance, hence mitigate the degradation of beamquality and luminosity.

Synchro-betatron Resonance of Crab Crossing Scheme with Large Crossing Angle and Finite Bunch Length