Collective beam-beam effects in hadron colliders

Coherent beam-beam tune shift of unsymmetrical beam-beam interactions with large beam-beam parameter

Coherent beam-beam tune shift of unsymmetrical beam-beam interactions was studied experimentally and numerically in HERA, where the lepton beam has such a large beam-beam parameter (up to xi(y) = 0.272 ) that the single-particle motion is locally unstable at the origin (closed orbit). Unlike the symmetrical case of beam-beam interactions, the ratio of the coherent beam-beam tune shift and the beam-beam parameter in this unsymmetrical case of beam-beam interactions was found to decrease monotonically with an increase of the beam-beam parameter. The results of self-consistent beam-beam simulation, the linearized Vlasov equation, and the rigid-beam model were compared with the experimental measurement. It was found that the coherent beam-beam tune shifts measured in the experiment and calculated in the simulation agree remarkably well but they are much smaller than those calculated by the linearized Vlasov equation with the single-mode approximation or the rigid-beam model. The study indicated that the single-mode approximation in the linearization of the Vlasov equation is not valid in the case of unsymmetrical beam-beam interactions. The rigid-beam model is valid only with a small beam-beam parameter in the case of unsymmetrical beam-beam interactions.

Importance of beam-beam tune spread to collective beam-beam instability in hadron colliders

In hadron colliders, electron-beam compensation of beam-beam tune spread has been explored for a reduction of beam-beam effects. In this paper, effects of the tune-spread compensation on beam-beam instabilities were studied with a self-consistent beam-beam simulation in model lattices of Tevatron and Large Hodron Collider. It was found that the reduction of the tune spread with the electron-beam compensation could induce a coherent beam-beam instability. The merit of the compensation with different degrees of tune-spread reduction was evaluated based on beam-size growth. When two beams have a same betatron tune, the compensation could do more harm than good to the beams when only beam-beam effects are considered. If a tune split between two beams is large enough, the compensation with a small reduction of the tune spread could benefit beams as Landau damping suppresses the coherent beam-beam instability. The result indicates that nonlinear (nonintegrable) beam-beam effects could dominate beam dynamics and a reduction of beam-beam tune spread by introducing additional beam-beam interactions and reducing Landau damping may not improve the stability of beams.

Multipole compensation of long-range beam-beam interactions with minimization of nonlinearities in Poincaré maps of a storage-ring collider

In cases of multibunch operation in storage-ring colliders, serious long-range beam-beam effects could be due to many parasitic collisions that are localized inside interaction regions or/and distributed around the ring. To reduce the long-range beam-beam effects, the compensation of long-range beam-beam interaction with magnetic multipole correctors based on minimizations of nonlinearities in one-turn or sectional maps of a collider has been proposed. With Large Hadron Collider as a test model, the effectiveness of the multipole compensation of long-range beam-beam interactions was studied in terms of improvement of dynamic aperture and reduction of emittance growth. The emittance growth was studied with a self-consistent beam-beam simulation. The study showed that both the local and global compensation of long-range beam-beam interactions with magnetic multipole correctors are very effective in increasing the dynamic aperture and improving the linearity of the phase-space region relevant to the beams.