The High Luminosity LHC (HL-LHC) project aims to increase the integrated luminosity of CERN’s Large Hadron Collider (LHC) over its exploitation era up to the end of 2041 by an order of magnitude compared to the initial LHC design value. This requires doubling the bunch intensity along with several other important changes to the LHC configuration. Dedicated beam experiments in the LHC and its injectors have already demonstrated the feasibility of reaching many of the HL-LHC project design parameters, and simulations show that some parameters could be pushed to further increase the integrated luminosity or used as mitigation measures against potential shortcomings. This paper presents a review of the latest experimental results and the possible reach of the final HL-LHC parameters.

During 2022 and 2023 LHC optics commissioning, it was observed that at low-beta* small changes in the beam-energy could generate substantial perturbations of the linear beam optics, requiring re-commissioning of local corrections in the experimental insertions. This issue may become even more significant at the very low beta* anticipated for operation in the High Luminosity LHC (HL-LHC). Furthermore, energy drifts, for example due to the terrestrial tides, have generally been ignored during LHC optics commissioning, with no regular corrections applied during the duration of a specific measurement campaign. This paper examines the anticipated sensitivity of HL-LHC optics corrections to energy errors at end of the beta* squeeze.

Beam-based studies at the LHC injection energy showed that compensation of the strongly driven sextupolar resonance, Qx+2Qy, improved both the dynamic aperture and lifetime of the beam, even when far from the working point and on the far side of the 3Qy resonance. Thus, a reduction of other strong normal sextupolar resonance sources was of interest. In 2024, the first measurements of resonance driving terms with long-range beam-beam (LRBB) interactions were performed. These showed that LRBB was driving the same Qx+2Qy resonance strongly when colliding, in agreement with model predictions. A correction was found for the strongest normal sextupole resonances using the existing sextupole corrector magnets in the LHC, obeying the constraints on the chromatic coupling and the maximum magnet powering. Beam-based tests to validate the response of this correction with non-colliding beams have been performed along with the testing of the LRBB resonance correction during LHC commissioning.

During operation for luminosity production, the LHC runs with very strong Landau octupoles to ensure the collective stability of the beams. A disadvantage of this is that these octupoles can drive resonances which can be detrimental to beam lifetime. Recently, a special optics configuration has been utilised to reduce the impact of the main octupoles on lifetime. This design relies on correctly modelling the resonance driving term (RDT) response to changes in these magnetic circuits. This paper presents beam-based studies comparing the RDT response to simulations where large discrepancies were found. To try and understand the source of this, several approaches were taken. Various methods including individual circuit measurements, studies of other circuits, and tests at different energy were employed but it remained challenging to localise the source of the discrepancy around the ring. This paper presents an attempt to apply and extend a segment-by-segment method, that has been very effective at identifying local linear optics errors, to non-linear errors through analysis of RDTs.

Compensation of the 3Qy resonance at injection energy in the LHC is of significant interest, given its potential to degrade the lifetime of high-intensity beams. In the absence of dedicated corrector circuits for the 3Qy compensation of each beam at low energy, an alternative approach is needed. Using skew-sextupoles in the four common experimental insertions it has been possible to develop a scheme to independently control the 3Qy resonance of the two LHC beams. Beam-based measurements and corrections of the 3Qy resonance at injection were performed, with beneficial impacts on lifetime and emittance growth observed.

The LHC is approaching the end of its third operational run, with machine protection and performance having demanded an excellent control of the single-particle dynamics. Additionally, the requirement to rapidly commission multiple diverse sets of optics configurations within each year and from year-to-year, placed clear demands on the measurement and correction methods employed. Tight tolerances on the linear optics have been consistently achieved, with the drive to ever-more pushed optics for the High Luminosity LHC era continuing to introduce new challenges. Routine control of linear coupling has been an operational necessity, while significant progress has also been made extending the understanding and control of the optics into the nonlinear regime. This paper presents the key methods used, the results obtained, and discusses the challenges to control of the beam-optics in the LHC.

Optics studies in the LHC are generally performed on low-intensity, non-colliding beams. Understanding the optics perturbation from beam-beam effects however, is of significant interest. This was particularly true for the LHC in 2024, where the 3Qy resonance driven by the long-range beam-beam (LRBB) contributed to breaking of the collimator hierarchy, limiting beta* reach and luminosity. By performing optics measurements on a low-intensity bunch in collision with a nominal train, it has been possible for the first time to directly measure the optics perturbation from LRBB in the LHC. Benchmarking of the beta-beat and resonance driving terms against simulation shows good agreement. Based on these models, it was possible to find corrections for the LRBB driven 3Qy resonance using the skew-sextupole correctors present in the LHC.

With a change in the LHC machine optics foreseen for 2025 and the possible reduction of beta-star, optics commissioning will become even more of a challenge for the CERN Optics Measurement and Correction (OMC) team. In particular, the increased sensitivity of the optics to non-linear imperfections, requiring a plethora of accurate measurements, is expected to be a time consuming task. In preparation, continuous effort has been undertaken to develop new correction strategies and convert them into ready-to-use algorithms, allowing the automation of repetitive tasks while keeping the python-base software tools up-to-date. In this paper the status of these tools is summarized with highlights and improvements underlined. These tools are now widely used beyond the LHC in the entire CERN accelerator complex, as well as in Super-KEKB and for Future Circular Collider studies, and could be of great interest to correct and improve the optics in other machines.

To mitigate the risk of radiation damage induced failure while operating the LHC beyond its initial integrated luminosity target, changes to the triplet polarity and crossing angles have been applied in the two main experimental interaction regions of the LHC. This allows for a more distributed radiation deposition in the insertion region magnets, which should allow their survival until they are replaced as part of the High Luminosity LHC upgrade from 2026-2030. These changes in the optics during 2024 and 2025 came with important challenges regarding machine commissioning and optics correction. In this paper, we discuss our experience of linear optics correction for the various triplet polarity configurations and review the implications for nonlinear optics corrections.

The LHC is approaching the end of its third operational run, with machine protection and performance having demanded an excellent control of the single-particle dynamics. Additionally, the requirement to rapidly commission multiple diverse sets of optics configurations within each year, and from year-to-year, placed clear demands on the measurement and correction methods employed. Tight tolerances on the linear optics have been consistently achieved, with the drive to ever-more pushed optics for the High Luminosity LHC era continuing to introduce new challenges. Routine control of linear coupling has been an operational necessity, while significant progress has also been made extending the understanding and control of the optics into the nonlinear regime. This paper presents the key methods used, the results obtained, and discusses the challenges to control of the beam-optics in the LHC.