Optics errors from the interaction points of the LHC, where β* is most strongly squeezed, can significantly impact machine performance and protection. In anticipation of the HL-LHC, correction strategies extending up to dodecapole order are being targeted. Direct measurement of high-order resonance driving terms (RDTs) remains challenging, however. Applying crossing angle orbit bumps in the experimental insertions induces feed-down from higher-order errors, increasing the magnitude of lower-order RDTs. Leveraging this effect, a novel correction scheme based on RDT feed-down was implemented for the first time in 2025. Skew-octupole errors were successfully corrected, which enabled optics measurements at the collisions working point, down to an unprecedented level of β*=18cm. Measurements of feed-down from dodecapole errors, to decapole RDTs were also achieved, opening a practical pathway to efficient corrections of very high-order optics errors.

Small momentum offsets in the LHC can generate significant optics distortions, particularly at low $\beta$*. The beam energy carries a relative uncertainty of approximately $10^{-3}$, which is insufficient for precise optics control. To better understand the impact of energy on the optics, two beam-based techniques have been explored. The first applies a global linear response matrix between BPM phase advances and $\Delta p/p$; while effective in simulation, this method is sensitive and does not reproduce the response observed in the machine. We introduce a new approach based on the principle of Deep Lie Map Networks (DLMN), which fits turn-by-turn BPM trajectories to a differentiable tracking model. Using the single-pass forward differentiation capability of MAD-NG, derivatives of the orbit with respect to $\Delta p/p$ are computed directly within the symplectic tracking engine. The results reveal arc-by-arc variations consistent with dipole-induced orbit distortions, providing insight into orbit behaviour around the ring. The measured response also agrees with that observed in the machine, demonstrating that the DLMN offers a promising new method for analysing the effect of energy on the optics of the LHC.

Local chromaticity can be defined as the local variation of the total betatron phase advance with momentum deviation $\delta$, and it can be interpreted as a measurement of the chromaticity generated over a limited segment of the lattice, rather than for the entire ring. It can be a useful tool to understand various insights of the beam operation, in particular how the phase is locally modulated by $\delta$ and how the overall chromaticity builds up along the lattice. The local chromaticity was first evaluated in the Large Hadron Collider (LHC) during the Run 3 commissioning in 2025, when a large RF frequency scan was performed up to $\pm \, $350 Hz, revealing a very large discrepancy with respect to the LHC optics model. This paper presents the methods and the results of the analysis.

The High Luminosity (HL–LHC) project aims to increase the integrated luminosity of CERN’s Large Hadron Collider (LHC) up to 3 ab−1, and 4 ab−1, as Nominal and Ultimate goals, respectively, over the full lifetime of the facility. The large boost in bunch population and beam brightness, compared to the currently achieved beam parameters in the LHC and stemming from the LHC injector upgrade project deployed during the previous long shutdown 2, poses several beam dynamics challenges that must be addressed, including, for example, electron cloud, impedance-related stability, and beam lifetime. In addition, the increasing availability of measurements for the magnets to be installed in the ATLAS and CMS interaction regions also allows for a more precise determination and optimisation of the dynamic aperture. Recently, modifications of the HL–LHC operations baseline, including ion runs throughout the lifetime of the project, led to a tighter margin on the integrated luminosity goals. Therefore, we present here an update of the baseline scenario of HL–LHC, together with alternative proposals that could mitigate potential shortcomings.

The Future electron positron Circular Collider, FCC-ee, is a proposed next-generation facility designed to deliver very high luminosities across a broad beam-energy range, from the Z pole at 45.6 GeV up to 182.5 GeV. Achieving the target performance in the presence of realistic lattice imperfections represents a significant challenge. To address this, a comprehensive commissioning strategy is being developed, featuring dedicated optics configurations, robust beam-based alignment procedures, and advanced optics-correction techniques supported by refined beam-based measurements. In parallel, specifications for the main magnet families, corrector circuits, and required instrumentation are being explored to ensure compatibility with the expected tuning procedures. This contribution summarizes the current status of these developments and outlines the key steps and milestones envisioned on the path toward the reference design.

During summer 2025, the CERN Large Hadron Collider operated for the first time with oxygen and neon ion beams. Three different machine configurations---with collisions of p‑O, O‑O, and Ne‑Ne and with varying beam energies and optics---had to be commissioned and exploited for physics operation during the eight days allocated. This short run was challenging because of its very tight schedule, the novel modes of operation, and new beam‑physics effects such as transmutation of oxygen and neon nuclei into other nuclei with the same magnetic rigidity. In spite of these challenges the run was very successful with the luminosity targets set by the LHC experiments fully met and, in most cases, even exceeded by large factors. In addition, time was allocated for machine studies, resulting in the first LHC data on crystal channeling with O and Ne ions. In this article we give a general overview of the LHC machine configuration, operational challenges, and experience during the run, as well as the achieved performance and the key contributors to the successful outcome. The results demonstrate the LHC’s flexibility for mixed‑species operation and give valuable input for future ion

In 2026, the Large Hadron Collider will conclude its final operational run, before being upgraded to the High-Luminosity Large Hadron Collider during the following long-shutdown. Originally conceived with a nominal beta* of 0.55m in both planes, over successive years, its optics design has been steadily pushed beyond those initial goals, with round optics down to 0.25m/0.25m (2018), and flat optics down to 0.6m/0.18m (2025) used in operation. In 2025, dedicated beam-studies were performed to test the viability of controlling beta* waist errors at such low-beta*, and to explore the viability of squeezing and commissioning the optics even further. Possible operational scenarios for 0.5m/0.15m and 0.4m/0.12m were tested, and optics measurements down to a potential minimum beta* of 0.07m achieved. The outcome of these tests will be presented.

Experimental observations indicate that a significant fraction of the stored beam energy in the CERN Large Hadron Collider (LHC) is contained in the transverse beam halo. Combined with the anticipated increase in beam brightness in the High-Luminosity LHC (HL-LHC) and new expected fast failure scenarios resulting in a loss of large-amplitude particles, an overpopulated beam halo poses risk to the safe operation of the machine. Following removal from the HL-LHC baseline of the Hollow Electron Lens, which was studied as the preferred method for active halo control, alternative halo-cleaning methods need to be investigated. A novel method being explored is the use of an AC multipole operated in resonance with the betatron tune to create a stable island in phase space in which halo particles are adiabatically trapped and transported to the collimators in a controlled manner. This paper presents the results of the first successful proof-of-principle measurement of both controlled beam-halo population and cleaning using an AC dipole at the LHC.

Following the SPS crab cavity tests in 2025, dedicated machine studies were carried out to investigate optics perturbations introduced by the cavity module and their relation to resonance driving terms. Particular emphasis was placed on identifying possible sextupolar components and assessing their impact on the betatron tune. Measurements using controlled orbit bumps were performed to isolate the cavity’s contribution and to benchmark model predictions. The results provide valuable input for the interpretation of beam dynamics observations during the tests and for the refinement of the SPS optics model in view of future crab cavity operation.

Small momentum offsets in the LHC can generate significant optics distortions, particularly at low $\beta$*. The beam energy carries a relative uncertainty of approximately $10^{-3}$, which is insufficient for precise optics control. To better understand the impact of energy on the optics, two beam-based techniques have been explored. The first applies a global linear response matrix between BPM phase advances and $\Delta p/p$; while effective in simulation, this method is sensitive and does not reproduce the response observed in the machine. We introduce a new approach based on the principle of Deep Lie Map Networks (DLMN), which fits turn-by-turn BPM trajectories to a differentiable tracking model. Using the single-pass forward differentiation capability of MAD-NG, derivatives of the orbit with respect to $\Delta p/p$ are computed directly within the symplectic tracking engine. The results reveal arc-by-arc variations consistent with dipole-induced orbit distortions, providing insight into orbit behaviour around the ring. The measured response also agrees with that observed in the machine, demonstrating that the DLMN offers a promising new method for analysing the effect of energy on the optics of the LHC.

Local chromaticity can be defined as the local variation of the total betatron phase advance with momentum deviation $\delta$, and it can be interpreted as a measurement of the chromaticity generated over a limited segment of the lattice, rather than for the entire ring. It can be a useful tool to understand various insights of the beam operation, in particular how the phase is locally modulated by $\delta$ and how the overall chromaticity builds up along the lattice. The local chromaticity was first evaluated in the Large Hadron Collider (LHC) during the Run 3 commissioning in 2025, when a large RF frequency scan was performed up to $\pm \, $350 Hz, revealing a very large discrepancy with respect to the LHC optics model. This paper presents the methods and the results of the analysis.

Segment-by-Segment (SbS) analysis is employed in accelerators for the determination of lattice errors and corrections, by identifying deviations between optics functions propagated through a modelled lattice segment and measured values. For the Large Hadron Collider (LHC), this method is routinely used during optics commissioning for the compensation of strong local errors in the experimental insertions and arcs. Beyond the determination of corrections however, the SbS approach is also of interest to propagate optics functions measured at the BPMs, to key instrumentation in other locations in the ring, for example to improve emittance measurements by providing more accurate estimates of the optics functions at relevant devices. The SbS tools used in the LHC have been further developed to support the propagation of measurement to lattice target locations distinct from the BPMs, leading to new possible applications. In this paper the analysis methods and results from recent LHC commissioning are presented.

The $3Q_y$ resonance is of particular concern at LHC injection given its potential to degrade the lifetime and the machine dynamic aperture. During measurements of the chromatic linear optics for the 2025 LHC commissioning, a large variation of the $3Q_y$ resonance strength at different momentum deviations $\delta$ was noticed. Further studies have been performed in order to assess the contribution to this variation from higher order multipoles, in particular from octupole and decapole fields. Benchmarking has been performed to the LHC magnetic model pointing to a large discrepancy in the skew-octupole sources present at injection. Methods and results of this analysis are presented in this work.

Optics measurements are usually performed with low-intensity, non-colliding pilot beams in the interest of machine safety. However, Long-Range Beam-Beam (LRBB) interactions can drive substantial optics perturbations. In 2024, a weak-strong measurement scheme was developed that probes the weak beam while leaving the strong beam unaffected, and machine tests validated this method. In 2025, a reported luminosity discrepancy between ATLAS and CMS motivated further study of the LRBB-induced beta-beat in the new 18 cm flat-optics configuration. A large beta-beat was observed, reaching typical LHC machine-protection limits. Correction strategies using magnets in the experimental insertions were demonstrated successfully, and, for the first time, non-linear corrections addressing sextupolar and octupolar resonance driving terms were also successfully demonstrated.

Optics errors from the interaction points of the LHC, where β* is most strongly squeezed, can significantly impact machine performance and protection. In anticipation of the HL-LHC, correction strategies extending up to dodecapole order are being targeted. Direct measurement of high-order resonance driving terms (RDTs) remains challenging, however. Applying crossing angle orbit bumps in the experimental insertions induces feed-down from higher-order errors, increasing the magnitude of lower-order RDTs. Leveraging this effect, a novel correction scheme based on RDT feed-down was implemented for the first time in 2025. Skew-octupole errors were successfully corrected, which enabled optics measurements at the collisions working point, down to an unprecedented level of β*=18cm. Measurements of feed-down from dodecapole errors, to decapole RDTs were also achieved, opening a practical pathway to efficient corrections of very high-order optics errors.