Optimization of Triplet Quadrupoles Field Quality for the LHC High Luminosity Lattice at Collision Energy

Beta functions at two interaction points (IP) in the high luminosity LHC upgrade lattice (HL-LHC) at collision energy will be significantly reduced compared to the nominal LHC lattice. This will result in much higher beta functions in the inner triplet (IT) quadrupoles adjacent to these IPs. The consequences are a larger beam size in these quadrupoles, higher IT chromaticity, and stronger effects of the IT field errors on dynamic aperture (DA). The IT chromaticity will be compensated using the Achromatic Telescopic Squeezing scheme [1]. The increased IT beam size will be accommodated by installing large aperture Nb$_{3}$Sn superconducting quadrupoles with 150 mm coil diameter. The stronger effects of the IT field errors can be remedied by optimizing the IT field error specifications. The latter must satisfy two conditions: provide an acceptable DA and be compatible with realistically achievable field quality. Optimization of the IT field errors was performed for the LHC upgrade layout version SLHCV3.01 with IT gradient of 123 T/m and IP beta functions of 15 cm. Dynamic aperture calculations were performed using SixTrack. Details of the optimization are presented along with recommendation for improving the field error correction.