Optics Transition Between Injection and Collision Optics for the HL-LHC Upgrade Project

Plans for the luminosity upgrade of the LHC collider at CERN (HL-LHC) are based on implementation of magnets with larger apertures in the interaction regions, together with the ATS [1] technique to reach very low values of the beta function at the collision points. Aperture restrictions mean that the collision optics can only be applied after ramping to high energy. The transition from injection to collision optics will be carried out in two stages, and will involve varying the strengths of the quadrupoles within the straight sections. Solutions for the optics transition have to meet a variety of challenging constraints, including constraints on the phase advances and Twiss parameters throughout the straights involved in the transition, specified minimum and maximum strengths of the quadrupoles, etc. Moreover, to minimise the time taken for the transition and to simplify the overall process, the variation of the quadrupole strengths should be as smooth as possible, especially for the strongest quadrupoles. Avoiding changes of slope as much as possible will also minimize hysteresis effects in the super-conducting matching quadrupoles involved in the process. This paper presents one possible solution for the optics transition, calculated for the HLLHCv1.0 [2] version of the optics and layout of the HLLHC.