Perturbation expansion for particle distributions in hadron storage rings

Collective beam-beam effects in hadron colliders

Collective beam-beam effects in hadron colliders were studied with a strong-strong beam-beam simulation on the CERN Large Hadron Collider, including multipole field errors in the lattice and beam-beam interactions at two high-luminosity interaction points. It was found that the beam-beam interaction could result in two distinct dynamics for hadron beams: a slow beam-size growth and an unstable beam-centroid oscillation. The instability of the beam-centroid oscillation has typical characteristics of the chaotic transport, i. e., the amplitude increase of the oscillation consists of slow escape from the remnants of invariant manifolds and fast diffusion in fully developed chaotic regions. The simulation results indicate that there is a threshold of the beam-beam parameter below which no unstable beam-centroid motion was observed. The escape rate of the unstable beam-centroid motion, on the other hand, increases with the nonlinear field errors in the lattice. As the slow beam-size growth is strongly enhanced by the beam-centroid oscillation, an elimination of the centroid motion with feedback can effectively suppress the beam-size growth. No steady state of coherent beam-beam oscillation was observed.