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.

中文翻译：

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大跨越角和有限束长的螃蟹跨越方案的同步甜菜碱共振

螃蟹穿越方案是必不可少的碰撞方案，可为未来具有较大穿越角度的对撞机实现高亮度。但是，当一个或两个碰撞光束的束长与蟹腔电压的波长相当时，捕蟹涌动的非线性相关性可能会对碰撞光束的光束动力学构成挑战，并影响光束质量和光度寿命。在本文中，使用解析和数值方法，给出了蟹跨方案中非线性动力学的结果。结果表明，在大角度交叉的螃蟹穿越方案中，可能会激发更高阶的同步等速共振，从而导致光束质量下降和光度下降。研究还揭示了抑制同步β共振的可能对策，