The effects of the beam‐beam interaction on particle dynamics in a synchrotron collider are investigated. The main highlight of this work is the investigation of collective effects of the beam‐beam interaction in a self‐consistent approach that naturally incorporates the correct single particle dynamics. The most important target of this simulation is to understand and predict the long‐time (108–109rotations) behavior of the beam luminosity and lifetime.For this task a series of computer codes in one spatial dimension have been developed in increasing order of sophistication. They are: the single particle dynamics tracking code, the strong‐strong particle‐in‐cell (PIC) code, and the particle code based on the &dgr;falgorithm. The latter two include the single particle dynamics of the first. The third approach is used to understand beam lifetime by improving the numerical noise problem in the second.Scans in tune &ngr;0and tune shift &Dgr;&ngr;0show regions of stability and instability that correspond to the regions predicted by a linear theory. Strong resonance beam blowup is observed just above &ngr;0=1/2 and &ngr;0=1/4, where the rate of beam blowup drops with the order of the resonance.In both the strong‐strong code and &dgr;fcode using the reference parameters of the Superconducting Super Collider (SSC), oscillations in the tune shift &Dgr;&ngr; are observed. The odd moments of the beam increase in oscillation amplitude with rotation number, while the amplitudes of the even moments either decrease or remain constant. The ‘‘flip‐flop’’ effect is observed in the strong‐strong code simulations and is found to be sensitive to the initial conditions.In studying slow particle diffusion in the phase space of the beams away from resonances, the tracking code shows no diffusion of particles from the beam‐beam interaction after 105rotations. The strong‐strong code is found too noisy to study particle diffusion from the beam‐beam interaction. The much quieter &dgr;fcode shows all particles diffusive after 105rotations, in contrast to single particle tracking results. The diffusion coefficients are several orders of magnitude higher than the tracking code, and they increase exponentially with the action. However, this amount of diffusion (D∼10−10−10−11in the normalized unit) is still permissible for the SSC design parameters. This diffusion is caused by the collision induced variation of the second moment of the beam ⟨x2⟩. © 1995American Institute of Physics