Lawrence Berkeley National Laboratory

Crab crossing scheme is essential collision scheme to achieve high luminosity for the future electron-ion collider (EIC). Since the ion beam is long when cooling is not present, the nonlinear dependence of the crabbing kick may present a challenge to the beam dynamics of the ion beam, hence a impact to the luminosity lifetime. In this paper, we present the initial result of the weak-strong and strong-strong beam-beam tracking with the crab crossing scheme. The result provides beam dynamics guidance in choosing the proper frequency the crab cavity for the future EIC.