Synchrobetatron resonance of crab crossing scheme with large crossing angle and finite bunch length

Crab crossing scheme is an essential collision scheme to achieve high luminosity for the future colliders with large crossing angles. However, when bunch length of one or both colliding beams is comparable with the wavelength of the crab cavity voltage, the nonlinear dependence of the crabbing kick may present a challenge to the beam dynamics of the colliding beams and impact the beam quality and the luminosity lifetime. In this paper, the results of nonlinear dynamics in the crab crossing scheme are presented, using both analytical and numerical approaches. The result indicates that higher-order synchrobetatron resonances may be excited in the crab crossing scheme with large crossing angle, which causes the beam quality deterioration and luminosity degradation. The studies also reveal possible countermeasures to suppress the synchrobeta resonance, hence mitigate the degradation of beam quality and luminosity.