A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.

The High Luminosity Large Hadron Collider (HL-LHC) is the new flagship project of CERN. First endorsed in 2013 and approved in 2016, HL-LHC is an upgrade of the accelerator aiming to increase by a factor of ten the statistics of the LHC collisions at the horizon of 2035–2040. HL-LHC relies on cutting edge technologies: among them, large aperture superconducting magnets will replace the present hardware to allow a smaller beam size in two interaction points (IPs). The project involves the construction of about 150 magnets of six different types: the quadrupole triplet, two main dipoles and three orbit correctors. The triplet, manufactured at CERN and in the USA, will consist of 30 magnets based on Nb₃Sn technology, with an operational peak field of 11.4 T. These will be the first quadrupole Nb₃Sn magnets installed in a particle accelerator. The other five types of magnets, all relying on Nb–Ti technology, present non-trivial challenges in the design and construction; they will be manufactured as part of in-kind contribution under the responsibility of institutes in Japan, China, Spain, and Italy. The project is now in the phase of transition between qualification through short models and prototypes and the beginning of the series construction. In this paper we review the magnet requirements, the reasons for selecting the design, the technological challenges with respect to previous projects, and we summarize the steps that have been taken to validate the baseline.

ReBCO high temperature superconducting (HTS) coated conductor tapes are a promising candidate for pushing the magnetic fields in accelerator magnets well beyond 20 T. They are capable of very high current densities in intense applied magnetic field, have a very high thermal stability, can withstand high transverse pressures and allow operation in 20-30 K helium gas flow, potentially reducing operating cost significantly. During the EuCARD2 program, significant developments have been made in terms of coil design, manufacturing, and testing. Now that EuCARD2 has come to an end, CERN and collaborators are initiating a new program to continue the development of HTS accelerator magnets. This paper presents our initial thoughts on the conceptual design of a 20 T+ accelerator magnet, using the results and technologies from EuCARD2 combined with some new ideas. The paper discusses the options available for the cross-sectional layout, the use of a hybrid configurations, including Aligned Block, the design of the coil-ends and dual aperture configurations. Also, discussed is the quench protection of the magnets. Due to the high thermal stability of the conductor and high energy densities, it will be required to explore an entirely a new approach.

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.

In view of the preparation for a post-LHC collider, in 2010 the high-energy physics (HEP) community started to discuss various options, including the use of HTS for very high-field dipoles. Therefore, a small program was begun in Europe that aimed at exploring the possibility of using HTS for accelerator-quality magnets. Based on various EU-funded programs, though at modest levels, it has enabled the European community of accelerator magnet research to start getting experience in HTS and address a few issues. The program was based on the use of REBa₂Cu₃O_7−x (REBCO) tapes to form 10 kA Roebel cables to wind small dipoles of 30–40 mm aperture in the 5 T range. The dipoles are designed to be later inserted in a background dipole field (in Nb₃Sn), to reach eventually a field level in the 16–20 T range, beyond the reach of Low Temperature Superconductors (LTS). The program is currently underway: more than 1 km of high-performance tape (J_e > 500 A/mm² at 20 T, 4.2 K) has been manufactured and characterized, various 30 m long Roebel cables have been assembled and validated up to 13 kA, a few dipoles have been wound and tested, reaching 4.5 T in stand-alone (while a dipole made from flat race track coils exceeded 5 T using stacked tape cable), and tests in background field are being organized.