TABLE I: PARAMETERS OF MODEL FOR ONE-QUARTER OF LEP[2]

The luminosity lifetimes of e+e- colliders are often dominated by the halo produced by the beam-beam interaction. We have developed a simulation technique to model this halo using the flux across boundaries in amplitude space to decrease the CPU time by a factor of one-hundred or more over "brute force " tracking. It allows simulation of density distributions and halos corresponding to realistic lifetimes[1]. Reference 1 shows the agreement with brute force tracking in a number of cases and the importance of beam-beam resonances in determining the density distribution at large amplitudes. This research is now directed towards comparisons with operating colliders and studies of the combined effects of lattice and beam-beam nonlinearities. LEP offers an ideal opportunity for both, and in this paper we are presenting the first results of LEP simulations. We have simulated a collider corresponding to one-quarter of LEP with the parameters in Table I. We estimate that the simulation technique reduced the CPU time by a factor of 2500 for LEP