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.

Operating at 45.6 GeV with high beam current, low emittances, and long damping times, the FCC-ee low-energy collider configuration is particularly sensitive to collective effects and impedance-induced beam instabilities. Controlling these effects requires a continuously refined impedance model to guide design choices and to establish reliable instability thresholds. Recent studies identify the collimation system as a dominant contributor to the total machine impedance, with geometric effects playing a key role in beam stability. Within this framework, a flexible, modular, and comprehensive impedance model enables targeted optimization and systematic stability assessments. The total impedance model includes the beam pipe, collimators, RF cavities, bellows, tapers, and beam position monitors. This work presents the latest FCC-ee impedance model with a full evaluation of collimator impedance, addressing current limitations related to the challenging simulation regime. It provides an in-depth analysis of the contribution of collimators to beam stability, comparing different optics configurations, novel materials, and advanced design solutions, as well as highlighting ongoing progress in impedance modelling, intensity threshold evaluation, and instability mitigation.

Accurate beam coupling impedance modeling is essential for predicting collective effects and ensuring stable high-intensity operation in the LHC and its High-Luminosity upgrade. Operational experience has shown that even small mechanical details can have a significant impact on the impedance of accelerator components, potentially leading to performance degradation or hardware failure. In addition, impedance sources are not static: beam-induced heating and the resulting mechanical stresses can drive gradual geometric changes, such as loss of electrical contact or deformation of shielding elements, thus modifying the impedance during operation. In this work, we present recent advancements in high-fidelity impedance modeling and demonstrate their relevance through representative case studies in the LHC. These examples show how improved modeling, combined with beam-based diagnostics, provides critical input for operational strategies and supports informed design and optimization of components in view of the challenging HL-LHC requirements.

A comprehensive impedance model is required to ensure beam stability and optimize performance in the FCC-ee main rings. The model integrates contributions from a wide range of components, accounting for both resistive-wall and geometric effects. In this paper, we discuss the main challenges introduced by the peculiar FCC-ee parameter regime. A first difficulty arises from the combination of large beam-pipe dimensions and very short bunch lengths, which drives wakefield simulations into an extremely demanding computational regime, where very fine spatial resolution is necessary to accurately capture the beam–environment interaction. In addition, the beam-pipe cut-off lies within the frequency range excited by the FCC-ee beam. As a consequence, several higher-order modes may propagate over long distances, leading to non-local impedance effects and possible crosstalk between different accelerator elements. This means that the impedance environment cannot be treated as purely local, but requires a distributed description and an assessment of how propagating power is transported and potentially absorbed within the machine.

One of the main drivers of integrated luminosity production in the High-Luminosity LHC (HL-LHC) era is the bunch intensity, expected to reach $2.3\times10^{11}$~protons per bunch at injection compared to the maximum $1.8\times10^{11}$ achieved in Run~3 operation. Such high intensities bring significant challenges, in particular localized beam induced heating due to impedance and the associated risk of equipment damage. In that respect, any issue discovered only in Run~4, the first run of the HL-LHC era, could lead to significant downtime or intensity limitations until appropriate mitigation measures are put in place. It is therefore essential to identify such potential limitations to achieve the target intensity before the end of the presently ongoing Run~3. This paper summarizes the preparation steps and strategy foreseen for dedicated high-intensity tests at the end of the 2026 LHC operation, as a last step before Long Shutdown~3 (LS3). The tests aim at reaching and sustaining HL-LHC beam parameters with various HL-LHC beam types, in order to probe impedance-related limits and assess equipment non-conformities, as well as potential design issues and unknown limitations in view of reliable HL-LHC operation. Preparation for the high-intensity tests started with dedicated machine development studies in 2025, making significant progress towards HL-LHC beams and identifying critical devices. Key observations and plans for 2026 are presented.

In preparation for High Luminosity (HL) LHC operation from 2030, a dedicated injector reliability run was undertaken in 2025 in the LHC injectors to evaluate the beam stability and reproducibility following the upgrade of the LHC injectors. The objective of this campaign was to demonstrate the capability of Linac4, PSB, PS, and SPS to deliver beams for the HL-LHC in a stable and reproducible manner with minimal downtime and specialist intervention, while defining clear performance metrics, verifying the performance of the available automatic beam optimisers, and identifying any issues arising during routine high-intensity operation. Extensive preparation was required across the injectors, including the deployment of new monitoring tools and coordinated operational procedures. This contribution presents an overview of the reliability run objectives and schedule, the required preparation work carried out in the LHC injectors, and the results obtained in each accelerator. The lessons learned and operational improvements identified provide valuable input for future high-intensity operation and help validate the readiness of the LHC injector complex for the HL-LHC era.