Experiments on the beam--beam effect in e+e- storage rings

The maximum luminosity in a positron electron storage ring is fundamentally limited by the beam--beam effect. This is the perturbing effect of the electromagnetic field of one beam on the trajectory of every single particle of the other beam. The electromagnetic field of a charged particle beam is highly nonlinear. At a large distance from the beam center the field falls off like the inverse of the distance. Right in the center of the beam where we have a more or less uniform density distribution over a limited region the field rises linear with the distance from the center. So the field rises from the center of the beam, saturates at some distance and going further out falls off again as 1/r. The amplitude of the field depends on the charge density as well as the aspect ratio of the beam. If the electromagnetic field of one beam gets too large, particles of the other beam get lost which leads to a reduced beam lifetime. This effect has been observed in all electron--positron or electron--electron storage rings built so far and is considered the fundamental limit of the performance of electron--positron storage rings. Over the years many measurements have been performed at various laboratories to find the maximum permissible perturbation and the parametric dependence of that perturbation. In this paper, new measurements performed at SPEAR are presented and compared with measurements from ACO, ADONE, and VEEP-2M. Results from other storage rings have been ignored because they either show lower permissible perturbations or because of insufficient published data