Energy Deposition Patterns in the LHC Inner Triplet and Their Impact on the Phase II Luminosity Upgrade

Recent studies show that the energy deposition for the LHC Phase I luminosity upgrade, aiming at a peak luminosity 2.5×10**34 cm**-2s**-1, can be handled by appropriate shielding. The Phase II upgrade aims at a further increase of peak luminosity by a factor 4, possibly using Nb$_{3}$Sn quadrupoles. This paper describes how the main features of the triplet layout, such as quadrupole lengths, gaps between magnets, and aperture, affect the energy deposition in the insertion. We demonstrate how the energy deposition patterns depend on the triplet lay-out. An additional variable which is taken into account is the choice of conductor, i.e. solutions with Nb-Ti and Nb$_{3}$Sn are compared. Nb$_{3}$Sn technology gives possibilities for increasing the magnet apertures and space for new shielding solutions. Our studies give an indication on the possibility of managing energy deposition for the Phase II upgrade.