First measurement and correction of nonlinear errors in the experimental insertions of the CERN Large Hadron Collider

Abstract

Nonlinear magnetic errors in low-β insertions can contribute significantly to detuning with amplitude, linear and nonlinear chromaticity, and lead to degradation of dynamic aperture and beam lifetime. As such, the correction of nonlinear errors in the experimental insertions of colliders can be of critical significance for successful operation. This is expected to be of particular relevance to the LHC's second run and its high luminosity upgrade, as well as to future colliders such as the Future Circular Collider. Current correction strategies envisioned for these colliders assume it will be possible to calculate optimized local corrections through the insertions, using a magnetic model of the errors. This paper shows however, that reliance purely upon magnetic measurements of the nonlinear errors of insertion elements is insufficient to guarantee a good correction quality in the relevant low-β Ã regime. It is possible to perform beam-based examination of nonlinear magnetic errors via the feed-down to readily observed beam properties upon application of closed orbit bumps, and methods based upon feed-down to tune have been utilized at RHIC, SIS18, and SPS. This paper demonstrates the extension of such methodology to include direct observation of feed-down to linear coupling in the LHC. It is further shown that such beam-based studies can be used to complement magnetic measurements performed during LHC construction, in order to validate and refine the magnetic model of the collider. Results from first attempts of the measurement and correction of nonlinear errors in the LHC experimental insertions are presented. Several discrepancies of beam-based studies with respect to the LHC magnetic model are reported.

New approach to LHC optics commissioning for the nonlinear era

“…On their own these measurements cannot be used to determine corrections, as it is impossible to distinguish sources in IP1 and IP5. When comparing measurements of feed-down to tune as a function of crossing angle in IP1 however, it was found that the quadratic tune shift (ΔQ ∝ y 2 , dependent on IR-octupole errors) consistently showed a good agreement with predictions of the magnetic model [49]. An example is shown in Fig.…”

“…During LHC design it was assumed that nonlinear corrections in the IRs would be inferred directly from magnetic measurements performed during construction [47,48]. Comparison of beam-based measurements to models incorporating the magnetic measurements however, revealed significant discrepancies for several multipoles [49] which precluded straightforward application of the design strategy. Consequently greater emphasis has been placed on methods for beam-based study of the nonlinear errors in the experimental insertions at 6.5 TeV.…”

“…In particular, an AC-dipole (which can repeatedly and adiabatically excite driven oscillations of the same beam [50]) is an important tool for optics study at top energy in a slowcycling machine such as the LHC. Understanding the influence of such driven oscillations on action-dependent tune shifts [24] and dynamic aperture [51,52] has enabled a beam-based approach to nonlinear optics correction at 6.5 TeV, as did refinements to methods based on feeddown to tune and linear coupling during orbit scans in the IRs [49,53].…”

Innovative method to measure the extent of the stable phase-space region of proton synchrotrons

“…In the LHC, the combined effect of magnets' misalignments and measured triplets' field quality is such that it is not possible to provide reliable information to compute the correctors' optimal strength. Beam-based measurements are therefore mandatory, yet extremely difficult and time-consuming to perform [45]. Moreover, the physical observables probed in these experiments are only indirectly linked with DA, the ultimate figure-of-merit.…”

First experimental demonstration of forced dynamic aperture measurements with LHC ac dipoles

“…ac dipoles were proposed in the LHC as a complementary tool to measure optics functions alongside the more conventional kickers (MKQ and MKA [8,9]). However over the years, the importance of the LHC ac dipoles [10,11] has grown and they have now become critical in correcting linear [12][13][14] and nonlinear [15][16][17] optics parameters. To such an extent that they are the single most important measurement method for the linear and nonlinear correction strategies in the LHC and for the High Luminosity LHC [18].…”