Longitudinal beam-beam effects in circular colliders

The longitudinal beam-beam interaction, which can lead to incoherent heating, synchrobetatron coupling, and coherent longitudinal instabilities in circular colliders, is examined. This analysis discusses two types of energy kicks, those due to the transverse particle motion coupling to the electric portion of the transverse kick, and those derived from the inductive electric field induced near the interaction, which is obtained from the transverse kick through use of a generalization of the Panofsky-Wenzel Theorem. Implications for low energy e/sup +/e/sup -/ colliders (/spl phi/ and B factories) with beams crossing head-on, and at finite angles, with and without crab crossing, are discussed.<>