The Incoherent Long Range Beam - Beam Interaction in CESR

CESR has reached the world's highest luminosity[1] using mutibunch operation. The key to this operation is a horizontal `pretzel' separation of the beams in the arcs and a crossing angle at the IP. The pretzel separation is needed since the counter rotating bunches share the same beam pipe and there is thus a long range beam{beam interaction (LRBBI) between the beams. The e ects of the LRBBI can be divided into coherent and incoherent parts. The coherent part involves motion of the bunches as a whole. In CESR the coherent LRBBI is strong enough to cause operational problems in terms of tune shifts and orbit displacements[2] but it does not lead directly to instabilities. The incoherent LRBBI, on the other hand, involves individual particles of one beam (henceforth called the \probe" beam) interacting with the other \strong" beam. Particles of the probe beam are destabilized when their horizontal oscillation amplitude is large enough to pass near, and feel the full e ect of, the strong beam. Because of the possible lifetime problems, it is the incoherent LRBBI that sets the limit for the minimum practical pretzel separation between beams and it is the incoherent LRBBI that is the subject of this paper. Future plans call for increases in current as well as the number of bunches. Since more current will mean a stronger beam-beam kick and more bunches will mean more parasitic crossing points, it is important to understand how the LRBBI destabilizes particles. Temnykh, Welch and Rice[3] have studied the LRBBI experimentally and have put forward phenomenological models to predict the minimum separation achievable for a 50 minute beam lifetime. The criteria from these models have been incorporated into the CESR optic design