Beam-beam effects at the Fermilab Tevatron: Theory

The Tevatron in Run II is operating with three trains of 12 bunches each. Long-range beam-beam interactions have been significant sources of beam loss and lifetime limitations of antiprotons. The dynamics due to the long-range beam-beam interactions depends on several beam parameters such as tunes, coupling, chromaticities, beam separations, intensities, and emittances. We have developed analytical tools to calculate, for example, amplitude dependent tune shifts and chromaticities, beam-beam induced coupling, and resonance driving terms. We report on these calculations and estimates of dynamic aperture and diffusion coefficients with long-term tracking. These theoretical results are compared with observations and used to predict performance at design values of beam parameters