Fundamental beam-beam limit from head-on interaction in the Large Hadron Collider

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.

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

“…The intermediate phase advance is set to μ 1 ¼ μ=2. This is similar to the configuration considered in [13], and the results presented as functions of ΔQ Tot ðϕ PIW Þ in Fig. 22(a) are in good agreement.…”

“…splitting the phase advance equally between the two separate parts of the lattice. This phase advance was found from a symmetry perspective [10], and confirmed numerically through trial to give the best performance [13]. The suggested intermediate phase advances in Eqs.…”

“…A full parametric study of relevant parameters has been conducted. The discovered trends will be explained by the underlying mechanisms through frequency analysis [14], and compared to relevant previous studies [10,13,15]. A realistic limit on the beam-beam interaction will be presented, relevant for the FCC-hh study.…”

“…The weak-strong approach assumes that the bunch generating the electromagnetic fields stays unaltered [11]. In previous studies, it has been applied to study singleparticle stability, and the impact of the strength of the beambeam interaction [12,13]. While already advanced, several mechanisms and mitigation schemes were not detailed, mainly due to the heavy computing load compared to the available resources.…”

Beam blow up due to beamstrahlung in circular e$$^+$$e$$^-$$ colliders

“…Secondly, we may also require that the excitation of synchrobetatron (SB) resonances due to the residual IP dispersion be small compared with the synchrobetatron coupling induced by the horizontal crossing angle, e.g. [36], or…”