Theoretical studies of beam-beam effects in the Tevatron at collision energy

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 betatron and synchro-betatron resonance widths. We report on these calculations and dynamic aperture calculations with longterm tracking. These theoretical results are compared with observations at collision energy and used to predict performance at design values of beam intensities and emittances.