Andy Sven Langner

Non-Linear Errors in the Experimental Insertions of the LHC

Correction of nonlinear magnetic errors in low-β insertions can be of critical significance for the operation of a collider. This is expected to be of particular relevance to LHC Run II and the HL-LHC upgrade, as well as to future colliders such as the FCC. Current correction strategies for these accelerators have assumed it will be possible to calculate optimized local corrections through the insertions using a magnetic model of the errors. To test this assumption the nonlinear errors in the LHC experimental insertions have been examined via feed-down and amplitude detuning. It will be shown that while in some cases the magnetic measurements provide a sufficient description of the errors, in others large discrepancies exist which will require beambased correction techniques. INTRODUCTION As the LHC progresses to more challenging β∗ regimes nonlinear errors in the low-β insertion regions (IRs) will play an increasing role in limiting the performance of the accelerator. In particular a ∼ 5σ reduction in dynamic aperture is expected in the HL-LHC due to these errors [1]. For this reason dedicated nonlinear correctors are provided in the common-beam regions left and right of the experimental insertions. A schematic of the corrector layout is shown in Fig. 1. Figure 1: Corrector layout in LHC experimental IRs [2]. Two correction strategies have been considered for the LHC and HL-LHC. The first method compensates magnetic errors in IR elements via local minimization of selected resonance driving terms [2]. The second method is based upon a direct compensation of the transverse map coefficients left and right of the interaction point (IP) [3]. For these strategies to be valid however, an accurate magnetic model of the insertions is required. Magnetic measurements performed on the LHC magnets during construction provide a foundation for such a model, but must be verified and refined through beam-based measurements to ensure the validity of the IR correction scheme. Strategies for nonlinear correction based upon feed-down to tune have previously been employed around the whole ring in SIS18 and CERN-SPS [4, 5], and in the RHIC experimental insertions [6]. In the RHIC method linear coupling was held constant during the feed-down scan, with correction attempted through minimization of observed tune shifts. At the LHC study of nonlinear multipoles in the IRs has been performed through feed-down to both tune and linear coupling. The focus of the studies in the LHC was also upon testing the magnetic model, rather than any beam-based minimization of the observable symptoms of the nonlinear errors. Table 1 summarizes the feed-down of normal and skew nonlinear multipoles, due to horizontal or vertical displacement from the magnetic axis, generating shifts in tune (ΔQ) and linear coupling (Δ|C−|). In Run I such studies were performed in the LHC by varying crossing angle bumps in the IRs, which are intended for prevention of collisions at parasitic crossing points either side of the IP (studies were performed with non-colliding probe bunches). More details of Run I studies may be found in [7, 8]. In 2015 feed-down scans were also performed [9], however new theoretical developments [10] also allowed use of an AC-dipole for measurement of amplitude detuning at top energy, providing an additional measure of normal octupole errors. MODEL VS MEASUREMENT Results from beam-based studies were compared to predictions of MAD-X simulations incorporating the best available knowledge of the magnetic errors in the IRs. This allowed for the validation of several components of the LHC magnetic model. Figure 2 shows an excellent agreement between modelled and measured variation of linear coupling with vertical crossing angle in the ALICE IR (IR2), dominated by the b3 component of the separation dipoles.