Beam-beam with a Few Long Range Encounters at Long Distance*

The high nominal luminosity of the LHC requires a large number of bunches spaced by about 25 ns. To prevent more than one head-on collision in each interaction region, a total crossing angle of 0.285 mrad is necessary, and the bunches experience around 30 long range (LR) interactions per IP with at mean separation of 9.5 σ. For the LHC luminosity upgrade, there are two possible scenarios: the early separation scheme and low Piwinski angle (LPA) scheme. In the early separation scheme, a few long range interactions need to be tolerated, this paper the discuss the possibility of having a few LR encounters at a minimum separation smaller than the 9 σ, and present observations from other hadron machines with a smaller beam separation.