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

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.