Optics Design and Lattice Optimisation for the HL-LHC

The luminosity upgrade project of the LHC collider at CERN is based on a strong focusing scheme to reach lowest values of the β function at the collision points. Depending on the magnet technology (Nb$_{3}$Sn or Nb-Ti) that will be available, a number of beam optics has been developed to define the specifications for the new superconducting magnets. In the context of the optics matching new issues have been addressed and new concepts have been used that play a major role in dealing with the extremely high beta functions. Quadrupole strength flexibility and chromatic corrections have been studied, the influence of the quadrupole fringe fields has been taken into account and the lattice in the matching section had been optimised including the needs of the crab cavities that will be installed. The transition between injection and low β optics has to guarantee smooth gradient changes over a wide range of β* values and the tolerances on misalignments and power converter ripple has been re-evaluated. Finally the successful combination of the quadrupole strengths in the high luminosity matching sections with those in the neighbouring sectors - a key concept of the ATS - plays an essential role to reach smallest β* values. This paper presents the results obtained within the Hi-Lumi collaboration Task 2.2 [1] and summarises the main parameters of the project.