Addition of a beam-beam element to MAD LEP simulation results

This paper reports that the study of the interaction between a single particle and a counter-rotating bunch of any particles is useful to determine which are the important single particle effects in the beam-beam interaction. To this end a beam-beam element has been implemented in the optics simulation program MAD. This element is a thin lens which reproduces the effect of a two dimension Gaussian beam. This implementation makes it possible to investigate the transverse coupling between the beam-beam potential and the machine non linearities. A first application to the LEP nominal conditions shows that no dramatic effect is expected