Modeling of nonlinear effects due to head-on beam-beam interactions

The beam-beam interaction is one of the most severe limitations on the performance of circular colliders,as it is an unavoidable strong nonlinear effect. As one aspires for greater luminosity in future colliders, onewill simultaneously achieve stronger beam-beam interactions. We study the limitations caused by strongincoherent head-on beam-beam interactions, using a new code (CABIN) that calculates on a graphicsprocessing unit (GPU), allowing for a detailed description of the long-term particle trajectories in 6D phasespace. The evolution of the beam emittance and beam intensity has been monitored to study the impactquantitatively, while frequency map analysis has been performed to understand the impact qualitatively.Results fromCABINhave shown good quantitative agreement with dedicated experiments in the LargeHadron Collider (LHC). For large beam-beam tune shifts, alternatives to the LHC tunes have been found toimprove the beam quality. Schemes devised to cancel beam-beam driven resonances, by use of specificintermediate phase advances between the interaction points, work very well with zero crossing angle, andthe accuracy required is achievable. Due to lack of symmetry, these schemes have an almost negligibleimpact with a significant crossing angle. The hourglass effect has been found to reduce the detrimentaleffects caused by the chromaticity and vice versa. The optimal level of the hourglass effect has beenachieved whenβ¼1.5σs. The ultimate parameters of the Future Circular Hadron Collider (FCC-hh) seemwithin reach, in absence of residual odd resonances.