Abstract
The beam-beam limit at hadron colliders manifests itself in the form of degraded luminosity lifetime and/or reduced beam lifetime. In particular, for increasing beam intensity, the nonlinear beam-beam force causes incoherent emittance growth, while the (linear) coupling force between the two colliding beams can result in coherent beam-beam instabilities. These phenomena may be enhanced (or suppressed) by lattice errors, external noise, and other perturbations. We investigate the luminosity degradation caused both by incoherent emittance growth and by coherent beam-beam instability. The resulting beam-beam limit for an ideal machine and the of question how it is affected by some of the aforementioned errors are discussed in theory and simulation.
Highlights
The beam-beam limit is conventionally characterized in terms of the permissible tune shift due to the beam-beam interaction, i.e., by a value for the maximum beam-beam tune shift
The beam-beam limit may be defined as the value of the tune shift above which the luminosity degradation due to the emittance growth is significant
Since the start of Large Hadron Collider (LHC) beam operation, several beam experiments related to the beam-beam limit have been performed in the LHC
Summary
The beam-beam limit is conventionally characterized in terms of the permissible tune shift due to the beam-beam interaction, i.e., by a value for the maximum beam-beam tune shift. Based on the experience at the Spp S collider [2], the Large Hadron Collider (LHC) was designed with a nominal beam-beam parameter of ξ 1⁄4 0.0034 for each of three interaction points Many simulations using both strongstrong and weak-strong models were performed to predict the beam-beam limit in the LHC, e.g., Ref. Since the start of LHC beam operation, several beam experiments related to the beam-beam limit have been performed in the LHC These demonstrated that beambeam tune shifts far larger than the design value could be reached without an appreciable degradation of the luminosity lifetime [4,5], which appears fully consistent with the past simulations. The Appendixes A and B present numerical coefficients for the Hamiltonian amplitude-detuning and resonance-driving terms for a single beam-beam collision with horizontal crossing at the LHC, and analytical expressions for the emittance growth due to random offset noise in collision-based on a weak-strong model, respectively
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