The Future Circular Collider (FCC) integrated programme begins with the FCC-ee, an electron-positron collider, followed by the FCC-hh, a proton–proton collider installed in the same 91 km circumference tunnel near CERN. Spanning 15 years from the mid-to-late 2040s through the early 2060s, the FCC-ee will operate at centre-of-mass energies between approximately 90 and 365 GeV, consistently delivering the highest possible luminosities to four experiments in a sustainable and energy-efficient manner. A key element of its design is top-up injection from a full-energy booster housed in the same 91 km tunnel, along with the world’s most intense positron source and 20 GeV injector linacs. The FCC-ee injector complex, comprising a high intensity positron source, a damping ring, and a linac accelerating electrons and positrons up to 20 GeV, is expected to start operation several years earlier than the booster and the collider. The primary objective of the FCC-ee is its rich High Energy Physics programme based on electron-positron collisions at various centre-of-mass energies (Benedikt et al. in Eur Phys J C 85:1468 https://doi.org/10.1140/epjc/s10052-025-15077-x , 2025). In addition, thanks to its large circumference, high beam energy, abundant positron production, and low-emittance beams, the FCC-ee also offers unique opportunities for various fields of physics and science. These include the potential production of true muonium, the creation of a Bose-Einstein condensate of positronium, Compton imaging with high-energy photons, the generation of spatially coherent photon beams, possibly down to 0.1 Åwavelengths—achieving several orders of magnitude higher average and peak brightness than any existing or planned light source—radioactive isotope production, and an electron- or photon-beam-driven neutron source. We present these and other science exploitations of the FCC-ee accelerator complex.

Abstract Volume 1 of the FCC Feasibility Report presents an overview of the physics case, experimental programme, and detector concepts for the Future Circular Collider (FCC). This volume outlines how FCC would address some of the most profound open questions in particle physics, from precision studies of the Higgs and EW bosons and of the top quark, to the exploration of physics beyond the Standard Model. The report reviews the experimental opportunities offered by the staged implementation of FCC, beginning with an electron-positron collider (FCC-ee), operating at several centre-of-mass energies, followed by a hadron collider (FCC-hh). Benchmark examples are given of the expected physics performance, in terms of precision and sensitivity to new phenomena, of each collider stage. Detector requirements and conceptual designs for FCC-ee experiments are discussed, as are the specific demands that the physics programme imposes on the accelerator in the domains of the calibration of the collision energy, and the interface region between the accelerator and the detector. The report also highlights advances in detector, software and computing technologies, as well as the theoretical tools/reconstruction techniques that will enable the precision measurements and discovery potential of the FCC experimental programme. The content and structure of this report are guided by the scope and priorities defined in the mandate of the FCC Feasibility Study. It is therefore not intended to serve as an exhaustive review of the full physics potential of FCC. Several topics, already covered in earlier reports such as the FCC CDR, are not reiterated here or are addressed only briefly, in alignment with the study’s focus. This volume reflects the outcome of a global collaborative effort involving hundreds of scientists and institutions, aided by a dedicated community-building coordination, and provides a targeted assessment of the scientific opportunities and experimental foundations of the FCC programme.

For Laser WakeField Accelerators with dedicated applications, the role of the transport line is essential, as its mission is to drive the accelerated beam from the plasma exit to the application, where all the requirements on beam quality should be met. This article investigates a two-quadrupole transport line with typical beam parameters at its entrance and exit. Consequences on its capacities and limits are discussed, considering the emittance growth that can be significant.

Previous studies for the electron-positron version of the Future Circular Collider (FCC-ee) have highlighted the need to define tolerances on magnet imperfections and develop correction strategies. This is crucial for ensuring the performance of one of the main elements in the acceleration chain: the High Energy Booster (HEB) ring. The efficiency and overall performance of these correction strategies, as well as the magnet field quality and misalignment tolerances, directly influence the specifications of correction magnets. This, in turn, affects key parameters such as beta functions, dispersion, transverse coupling, and emittance. Horizontal and vertical orbit corrections utilize horizontal and vertical kickers, respectively. Skew quadrupoles address vertical dispersion, introduced by normal dipole roll, and transverse coupling. Normal quadrupoles corrects the horizontal and vertical phase advances. This study simulates the distribution of these four corrector types to minimize equilibrium emittance at the extraction energy of 45.6 GeV. The computed strengths of these correctors and the associated misalignments are presented.

In response to the 2020 Update of the European Strategy for Particle Physics , the Future Circular Collider (FCC) Feasibility Study was launched as an international collaboration hosted by CERN. This report describes the FCC integrated programme , which consists of two stages: an electron-positron collider (FCC-ee) in the first phase, serving as a high-luminosity Higgs, top, and electroweak factory; followed by a proton-proton collider (FCC-hh) at the energy frontier in the second phase. The FCC-ee is designed to operate at four key centre-of-mass energies: the Z pole, the WW pair production threshold, the ZH production peak, and the top/anti-top production threshold—each delivering the highest possible luminosities to four experiments. Over 15 years of operation, FCC-ee will produce more than 6 trillion Z bosons, 200 million WW pairs, nearly 3 million Higgs bosons, and 2 million top anti-top pairs. Precise energy calibration at the Z pole and WW threshold will be achieved through frequent resonant depolarisation of pilot bunches. The sequence of operation modes between the Z, WW, and ZH substages remains flexible. The FCC-hh will operate at a centre-of-mass energy of approximately 85 TeV—nearly an order of magnitude higher than the LHC—and is designed to deliver 5 to 10 times the integrated luminosity of the upcoming High-Luminosity LHC. Its mass reach for direct discovery extends to several tens of TeV. In addition to proton-proton collisions, the FCC-hh is capable of supporting ion-ion, ion-proton, and lepton-hadron collision modes. This second volume of the Feasibility Study Report presents the complete design of the FCC-ee collider, its operation and staging strategy, the full-energy booster and injector complex, required accelerator technologies, safety concepts, and technical infrastructure. It also includes the design of the FCC-hh hadron collider, development of high-field magnets, hadron injector options, and key technical systems for FCC-hh.

Volume 3 of the FCC Feasibility Report presents studies related to civil engineering, the development of a project implementation scenario, and environmental and sustainability aspects. The report details the iterative improvements made to the civil engineering concepts since 2018, taking into account subsurface conditions, accelerator and experiment requirements, and territorial considerations. It outlines a technically feasible and economically viable civil engineering configuration that serves as the baseline for detailed subsurface investigations, construction design, cost estimation, and project implementation planning. Additionally, the report highlights ongoing subsurface investigations in key areas to support the development of an improved 3D subsurface model of the region. The report describes development of the project scenario based on the 'avoid-reduce-compensate' iterative optimisation approach. The reference scenario balances optimal physics performance with territorial compatibility, implementation risks, and costs. Environmental field investigations covering almost 600 hectares of terrain - including numerous urban, economic, social, and technical aspects - confirmed the project's technical feasibility and contributed to the preparation of essential input documents for the formal project authorisation phase. The summary also highlights the initiation of public dialogue as part of the authorisation process. The results of a comprehensive socio-economic impact assessment, which included significant environmental effects, are presented. Even under the most conservative and stringent conditions, a positive benefit-cost ratio for the FCC-ee is obtained. Finally, the report provides a concise summary of the studies conducted to document the current state of the environment.

Volume 1 of the FCC Feasibility Report presents an overview of the physics case, experimental programme, and detector concepts for the Future Circular Collider (FCC). This volume outlines how FCC would address some of the most profound open questions in particle physics, from precision studies of the Higgs and EW bosons and of the top quark, to the exploration of physics beyond the Standard Model. The report reviews the experimental opportunities offered by the staged implementation of FCC, beginning with an electron-positron collider (FCC-ee), operating at several centre-of-mass energies, followed by a hadron collider (FCC-hh). Benchmark examples are given of the expected physics performance, in terms of precision and sensitivity to new phenomena, of each collider stage. Detector requirements and conceptual designs for FCC-ee experiments are discussed, as are the specific demands that the physics programme imposes on the accelerator in the domains of the calibration of the collision energy, and the interface region between the accelerator and the detector. The report also highlights advances in detector, software and computing technologies, as well as the theoretical tools /reconstruction techniques that will enable the precision measurements and discovery potential of the FCC experimental programme. This volume reflects the outcome of a global collaborative effort involving hundreds of scientists and institutions, aided by a dedicated community-building coordination, and provides a targeted assessment of the scientific opportunities and experimental foundations of the FCC programme.

In response to the 2020 Update of the European Strategy for Particle Physics, the Future Circular Collider (FCC) Feasibility Study was launched as an international collaboration hosted by CERN. This report describes the FCC integrated programme, which consists of two stages: an electron-positron collider (FCC-ee) in the first phase, serving as a high-luminosity Higgs, top, and electroweak factory; followed by a proton-proton collider (FCC-hh) at the energy frontier in the second phase. FCC-ee is designed to operate at four key centre-of-mass energies: the Z pole, the WW production threshold, the ZH production peak, and the top/anti-top production threshold - delivering the highest possible luminosities to four experiments. Over 15 years of operation, FCC-ee will produce more than 6 trillion Z bosons, 200 million WW pairs, nearly 3 million Higgs bosons, and 2 million top anti-top pairs. Precise energy calibration at the Z pole and WW threshold will be achieved through frequent resonant depolarisation of pilot bunches. The sequence of operation modes remains flexible. FCC-hh will operate at a centre-of-mass energy of approximately 85 TeV - nearly an order of magnitude higher than the LHC - and is designed to deliver 5 to 10 times the integrated luminosity of the HL-LHC. Its mass reach for direct discovery extends to several tens of TeV. In addition to proton-proton collisions, FCC-hh is capable of supporting ion-ion, ion-proton, and lepton-hadron collision modes. This second volume of the Feasibility Study Report presents the complete design of the FCC-ee collider, its operation and staging strategy, the full-energy booster and injector complex, required accelerator technologies, safety concepts, and technical infrastructure. It also includes the design of the FCC-hh hadron collider, development of high-field magnets, hadron injector options, and key technical systems for FCC-hh.

One of the major upcoming challenges in particle physics is achieving precise measurements of the Z, W, and H bosons, as well as the top quark. To meet these targets, the next e + e - collider complex, FCC-ee, will need to achieve unprecedented luminosities. The FCC-IS European Study is investigating the feasibility of these challenges, with a cornerstone of the study being the design and optimization of the high-energy booster (HEB). This paper provides an update on the status of the HEB of FCC-ee in light of recent developments in the injector and collider survey, as well as an overview of ongoing work on longitudinal stability and design robustness in relation to field, alignment, and diagnostics errors. Constraints and effects related to the design frequency of the accelerating cavities, as well as collective effects, are also highlighted. Lastly, the paper presents an investigation into an alternative arcs cell design.

During 2022, a dedicated study was undertaken at CERN, together with the FCC Feasibility Study collaborators, to propose a robust configuration for the FCC-ee arc half-cell. The proposed layout considers integration aspects of the elements in the arc cross section, both for the booster and the collider, as well as aspects related to powering, cooling and ventilation, supporting and alignment, optics, instrumentation, handling and installation. The interfaces between the arc elements and the straight sections have also been analysed. This paper summarizes the main conclusions of the assessment and reports the preliminary engineering analyses performed to design the supporting system of the booster and of the collider. A proposal for a possible mock-up of the arc half-cell, to be built at CERN in the next years, is also presented.

After the discovery of the Higgs boson at the LHC, particle physics community is exploring and proposing next accelerators, to address the remaining open questions on the underlying mechanisms and constituents of the present universe. One of the studied possibilities is FCC (Future Circular Collider), a 100 km long collider at CERN. The feasibility study of this future proposed accelerator implies the definition of tolerances on magnets imperfections and of the strategies of correction in order to guarantee the target performances of the High Energy Booster ring. The efficiency of the correction scheme, used to control the orbit, directly bounds the corrector needs and magnet tolerances. Analytic formulae give a first estimation of the average rms value of the required linear correctors' strengths and of the allowed magnets misalignments and field quality along the entire ring. The distribution of the correctors along the ring is simulated in order to verify the quality of the residual orbit after the proposed correction strategy and compared with the analytical predictions. First specifications of the orbit correctors strength and tolerances for the alignment of the main elements of the ring are presented. The limits of the studied correction scheme and method are also discussed.

In 2022, the FCC Feasibility Study management mandated a working group to analyse the best configuration of the FCC-ee tunnel in the arc regions, in view of the construction of a mock-up of the arc half -cell. One of the main and most challenging goals of the study, named FCC-ee Arc Half -Cell Mock-up Project, was to perform a preliminary investigation on the principles of supporting the Short -Straight Sections and dipoles of the half -cells, both for the booster and for the collider machines. This is an important input needed for the choice of the best configuration of the relative placement of the booster with respect to the collider. The structural stiffness, mass and stability of the supporting structures must be optimized to minimize the vibrations transmitted/transferred to the magnetic system of the accelerators by elements such as pumps, water cooling system, beam thermomechanical stresses, powering elements, etc. To perform the study, tools such as CAD software, FEM and analytical techniques were employed. This paper summarizes the preliminary design concepts and the results of the simulations performed.

The International Muon Collider Collaboration (IMCC) [1] was established in 2020 following the recommendations of the European Strategy for Particle Physics (ESPP) and the implementation of the European Strategy for Particle Physics-Accelerator R D Roadmap by the Laboratory Directors Group [2], hereinafter referred to as the the European LDG roadmap. The Muon Collider Study (MuC) covers the accelerator complex, detectors and physics for a future muon collider. In 2023, European Commission support was obtained for a design study of a muon collider (MuCol) [3]. This project started on 1st March 2023, with work-packages aligned with the overall muon collider studies. In preparation of and during the 2021-22 U.S. Snowmass process, the muon collider project parameters, technical studies and physics performance studies were performed and presented in great detail. Recently, the P5 panel [4] in the U.S. recommended a muon collider R D, proposed to join the IMCC and envisages that the U.S. should prepare to host a muon collider, calling this their "muon shot". In the past, the U.S. Muon Accelerator Programme (MAP) [5] has been instrumental in studies of concepts and technologies for a muon collider.

The SARAF Phase II cryogenic linear accelerator (linac) is currently under construction and will be commissioned through collaborative efforts between SNRC and CEA. The linac will accelerate a 5 mA pulsed/continuous wave (CW) proton and deuteron beam, reaching energies of up to 35 MeV and 40 MeV, respectively. The linac injector consists of Phase I components, including an ECR ion source, a Low-Energy Beam Transport (LEBT) line, and a 4-rod Radio Frequency Quadruple (RFQ). Additionally, a new Medium Energy Beam Transport (MEBT) line has been installed and integrated into the injector infrastructure. The MEBT includes three rebuncher resonators, magneto-optical elements, and beam diagnostics. The MEBT beam diagnostics, as well as the Phase I D-plate installed downstream, were used for beam characterization. The downstream-installed Temporary Beam Line (TBL) and a prototype of the Gallium Indium Liquid Target (GALIT) were used for commissioning, operating at high beam duty cycles, including CW mode. The report describes the proton beam commissioning process of the injector prior to the delivery of the cryomodules, scheduled for the second half of 2023.

The 2020 update of the European Strategy for Particle Physics emphasised the importance of an intensified and well-coordinated programme of accelerator R&D, supporting the design and delivery of future particle accelerators in a timely, affordable and sustainable way. This report sets out a roadmap for European accelerator R&D for the next five to ten years, covering five topical areas identified in the Strategy update. The R&D objectives include: improvement of the performance and cost-performance of magnet and radio-frequency acceleration systems; investigations of the potential of laser / plasma acceleration and energy-recovery linac techniques; and development of new concepts for muon beams and muon colliders. The goal of the roadmap is to document the collective view of the field on the next steps for the R&D programme, and to provide the evidence base to support subsequent decisions on prioritisation, resourcing and implementation.

The Future Circular Collider (FCC) study was launched as a world-wide international collaboration hosted by CERN. Its goal is to push the field to the next energy frontier beyond LHC, increasing by an order of magnitude the mass of particles that could be directly produced, and decreasing by an order of magnitude the subatomic distances to be studied. The FCC study covers two accelerators, namely, an energy-frontier hadron collider (FCC-hh) and a highest luminosity, high-energy lepton collider (FCC-ee). Both rings are hosted in the same 100 km tunnel infrastructure, replicating the CERN strategy for LEP and LHC, i.e. developing a lepton and a hadron ring sharing the same tunnel. This paper is devoted to the FCC-hh and summarizes the key features of the FCC-hh accelerator design, performance reach, and underlying technologies. The material presented in this paper builds on the conceptual design report published in 2019, and extends it, including also the progress made and the results achieved since then.

Figure 20.1 was not correct in the published article. The original article has been corrected. The published apologizes for the inconvenience.