Study of the Impact of Fringe Fields of the Large Aperture Triplets on the Linear Optics of the HL-LHC

High-luminosity hadron colliders such as the High Luminosity LHC (HL-LHC) project place demanding requirements on existing and new magnet technology. The very low β* achieved by the Achromatic Telescopic Squeeze (ATS) optics scheme for the HL-LHC in particular, requires large apertures in the high gradient Nb$_{3}$Sn final focusing inner triplet triplet. Such magnets have extended fringe fields which perturb the optics. This paper presents studies into the linear optics of the LHC using a range of fringe field models, including realistic fringe fields from prototype magnets, and presents calculations of the resulting beta-beating. Furthermore a similar study is presented on the nominal LHC optics, which uses final focus quadrupoles of higher gradient but significantly smaller aperture.