Non linear field correction effects on the dynamic aperture of the FCC-hh

The Future Circular Collider (FCC) design study aims to develop the designs of possible circular colliders in the post LHC era. In particular the FCC-hh will aim to produce proton-proton collisions at a center of mass energy of 100 TeV [1]. Given the large beta functions and integrated length of the quadrupoles of the final focus triplet the effect of systematic and random non linear errors in the magnets are expected to have a severe impact on the stability of the beam. Following the experience on the HL-LHC this work explores the implementation of non-linear correctors to minimize the resonance driving terms arising from the errors of the triplet. Dynamic aperture studies are then performed to study the impact of this correction. INTRODUCTION The FCC-hh lattice features two high luminosity insertions and two special purpose experiments, just like the LHC. An illustration of the layout of the FCC-hh is given in Fig. 1. The two high luminosity insertions are located in the interaction regions A and G (IRA and IRG). Figure 1: Layout of the FCC-hh ring [2]. Several options have been proposed for the design of the low β interaction regions [3]. This study will present in the case with the distance between the interaction point and the first quadrupole (L) of 45 m and a β of 30 cm [3]. The two high luminosity insertions require strong magnets to focus the beam into the interaction point. The model of these magnets and its error table has been based on the quadrupole magnet technology of the High Luminosity-LHC ∗ This work was supported by the HORIZON 2020 project EuroCirCol, grant agreement 654305. † emilia.cruzalaniz@physics.ox. ac.uk (HL-LHC) [4] but the design is adjusted to scale it to the new energies. Previous studies have been performed to study the dynamic aperture (DA) at injection with errors on the arcs [5], as well as studies performed at collision energy with no errors on the arc dipoles (minimum DA= 30-85 σ) and with errors on the inner triplet but crossing angles off (minimum DA= 20 σ) [6]. However, studies with errors on the inner triplet and crossing angles on proved to be challenging [6] due to the fact that the resulting orbit made it more sensitive to errors. This works aims to address this issue by the use of different orbit correction techniques and the implementation of non linear correctors to compensate for non linear triplet errors. DYNAMIC APERTURE STUDIES DA studies were performed using SixTrack [7] on a thinlens version of the FCC-hh lattice with β = 30 cm over 105 turns with crossing angles on, 30 particles pairs per amplitude step of 2 σ, 5 angles and a momentum offset of 2.7e-4. The energy is 50 TeV and the normalised emittance is =2. 2μm. Concerning the magnetic imperfections of the triplet 60 different realisations (seeds) have been used. These errors are given in the following form [8]: bn = bnS + ξU 1.5 bnU + ξRbnR, (1) with bnS , bnU and bnR referring to the main, uncertainty and random components, and both ξU and ξR are Gaussian distribution random variables cut at 1.5 a 3 σ respectively; ξU changes from seed to seed but remains the same for all magnets of the same class while ξR changes also from magnet to magnet. The magnetic field in the magnets is then given as: