Beam-beam effect for the LHC Phase I Luminosity Upgrade

The Phase I Luminosity Upgrade of the LHC will be based on a new Nb-Ti inner triplet for the high luminosity region ATLAS and CMS. The new proposed layout aims at pushing B down to 30 cm replacing the current LHC inner triplets, with longer ones operating at lower gradient (123 T/m) and therefore offering enough aperture for the beam to reduce B to its prescribed value. As a consequence of this new longer interaction region, the number of parasitic encounters will increase from 16 to 21 in front of the separation dipole D1, with an impact on the dynamic aperture of the machine. In this paper the effect of the beam-beam interaction is evaluated for the Phase I layout and optics, at injection and in collision, evaluating the possible impact of a few additional parasitic collisions inside and beyond the D1 separation dipole till the two beams do no longer occupy the same vacuum chamber. Whenever needed, a comparison with the nominal LHC will be given. In addition a possible backup collision optics will be discussed for the Phase I upgrade, offering a much wider crossing angle at an intermediate B* of 40 cm in order to reach a target dynamic aperture of 7.5.