Beam-beam interaction study in an electron-ion collider adopting the local crab crossing scheme

Crab cavities are key components used by most colliders to enhance luminosity. The local crab crossing scheme is adopted in the EicC (Electron-Ion Collider in China) project. Ideally, the beams would achieve head-on collisions at the interaction point subjected to transverse deflecting forces that linearly depend on the longitudinal position. However, in practical machine design and operation, unavoidable but realistic factors can ruin this perfect situation, including synchrobetatron resonance excited by the finite bunch length effect, imperfections in optics design, and errors in the crab cavity system. These may have significant effects on the colliding beam dynamics. This paper reviews the baseline design of the EicC project from the perspective of checking the rationality, exploring the adjustability, and investigating the tolerance of the design parameters. The self-consistent strong-strong simulation technique is employed. The simulation results suggest that increasing the proton crab cavity frequency up to 400 MHz has no impact on the luminosity lifetime since the proton beam-beam parameter is small. The option of providing more transverse space for forward detectors by doubling the crossing angle is feasible at this newly selected crab frequency. The optics imperfections are acceptable or manageable for both proton and electron beams. The cavity voltage errors need to be carefully controlled in both rings to ensure a better beam lifetime. In addition, the proton emittance growth caused by crab cavity noise is severe, and the tolerance is well beyond state-of-art levels. Electron beams, on the other hand, are not overly affected thanks to synchrotron radiation.