Nonlinear beam-beam resonances

Head-on collisions of bunched beams are considered, assuming the two colliding beams have opposite charges. A few experimental observations are described. The single resonance analysis is developed that is applicable to the strong-weak case of the beam-beam interaction. In this case, the strong beam is unperturbed by the beam-beam interaction; motions of the weak beam particles are then analyzed in the presence of the nonlinear electromagnetic force produced by the strong beam at the collision points. The coherent motions of the two coupled strong beams are shown to exhibit distinct nonlinear resonance behavior. 16 refs., 22 figs. (LEW)