Beam-beam effects in the high-pile-up tests of the LHC

Investigating the beam-beam limit in the LHC is of great importance, since identifying its source is crucial for the luminosity optimization scenario. Several experiments were carried out to search for this limit and check whether it is dominated by the head-on (HO) or the long-range (LR) interactions. In this paper only the HO collision effects will be considered, tracking the evolution of the maximum tune shift achieved during the dedicated machine developments and the special high pile-up fills.