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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 beamdoi:10.2172/784786 fatcat:g2lhaee26ve6rblcmz6iczhcpi