We h a ve developed an e cacious algorithm for simulation of the beam-beam interaction in synchrotron colliders based on the nonlinear f method, where f is the much smaller deviation of the beam distribution from the slowly evolving main distribution f 0 . In the presence of damping and quantum uctuations of synchrotron radiation it has been shown that the slowly evolving part of the distribution function satis es a Fokker-Planck equation. Its solution has been obtained in terms of a beam

more »

... pe function and an amplitude of the distribution, which satisfy a coupled system of ordinary di erential equations. A numerical algorithm suited for direct code implementation of the evolving distributions for both f and f 0 has been developed. Explicit expressions for the dynamical weights of macro-particles for fas well as an expression for the slowly changing f 0 have been obtained.