Beam-beam limit in e+e- circular colliders.

Beam-beam effects limit the luminosity of circular colliders. Once the bunch population exceeds a threshold, the luminosity increases at a slower rate. This phenomenon is called the beam-beam limit. Onset of the beam-beam limit has been analyzed with various simulation methods based on the weak-strong and strong-strong models. We have observed that an incoherent phenomenon is mainly concerned in the beam-beam limit. The simulation have shown that equilibrium distributions of the two colliding beams are distorted from Gaussians when the luminosity is limited. The beam-beam limit is estimated to be xi approximately 0.1 for a B factory with damping time of several thousand turns.