Study Progress of the Coupling Resonance of the Crab Crossing Scheme in Electron-Ion Collider

Crab crossing scheme is essential collision scheme to achieve high luminosity for the future electron-ion collider (EIC). The bunch length effect of the ion beam cannot be ignored even when cooling is present compared with the wavelength of the crab cavity, therefore, the nonlinear dependence of the crabbing kick may present a challenge to the beam dynamics of the ion beam, hence an impact to the luminosity lifetime. In this paper, we present the result of numerical beam dynamics studies of the crab crossing scheme. The result indicates that there is a special coupling resonance in the nonlinear relation of the crab crossing scheme of the EIC, which dominates the luminosity degradation. And we will discuss the possible remedies for such resonance.