Simulation of beam-beam effects in a circular e⁺e^- collider

We have carried out a strong-strong simulation to study the beam-beam effect in a circular electron-positron collider. In the simulation, both the positron and electron beams are represented by macroparticles, and the interaction between the two beams is obtained by solving the Poisson equation for the charge distribution of the macroparticles. Using the simulation, we investigate the beam-beam limit and the coherent beam-beam tune shift, two characteristic phenomena of the beam-beam effect. We also study collision with a finite crossing angle, and verify its feasibility for the KEKB factory. Our results for KEKB yield an estimated luminosity of 8.5×10³³ cm^-2 s^-1, only slightly lower than the design value of 1×10³⁴ cm^-2 s^-1.