Analysis of the Non-Linear Fringe Effects of Large Aperture Triplets for the HL-LHC Project

The HL-LHC project relies on large aperture quadrupoles which are compatible with the very large beam sizes in the inner triplets resulting from the strong reduction of beta*. As a result the beam is much more sensitive to non-linear perturbations in this region, such as those induced by the fringe fields of the low-beta quadrupoles. The spatial extension of these fringe fields increases as well more or less linearly with the coil aperture, which is an additional motivation to analyse this aspect in detail in the framework of the High Luminosity LHC design study. This paper will quantify this effect by direct analytical estimates using first order Hamiltonian perturbation theory, applied to quadrupole and dipole fringe fields. Both detuning with amplitude and chromatic effects will be considered. A numerical estimate for the proposed triplet quadrupoles will be presented, and the implementation of special symplectic integrators in SixTrack for tracking simulations outlined