Beam-Beam Simulation for LEP

A multi-particle two-beam (strong-strong) simulation program has been written for investigation of the beam-beam effect in ´LEP´. The motion of the superparticles is treated in six-dimensional phase space and the effects of quantum excitation and radiation damping are included. The effects of perturbations to the superperiodicity (errors) are also included. Non-zero dispersion at the RF cavities allows computation of single beam synchro-betatron resonances. These resonances may also be driven by the beam-beam interaction either by non-zero dispersion at the interaction point or by the longitudinal motion of the interaction ´point´ between a particle and the centre of the ´other´ beam due to the synchrotron motion of the particle. After each revolution the parameters influencing the beam-beam force (e.g. the beam dimensions and the beam current) are reevaluated in order to simulate a real situation. For the beam-beam force an elliptical beam with Gaussian charge distribution has been assumed. The computation of this force is speeded up by using tabulated values of the complex error function and a fast interpolation procedure. The ´beam-beam limit´ is shown to be a function of many machine parameters but is always significantly below the assumed maximum value of 0.06.