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.

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.

Next generation ion therapy magnets both for gantry and for accelerator (synchrotron) are under investigation in a recently launched European collaboration that, in the frame of the European H2020 HITRI plus and I.FAST programmes, has obtained some funding for work packages on superconducting magnets. Design and technology of superconducting magnets will be developed for ion therapy synchrotron and -especially- gantry, taking as reference beams of 430 MeV/nucleon ions (C-ions) with 10 ¹⁰ ions/pulse. The magnets are about 60–90 mm diameter, 4 to 5 T peak field with a field change of about 0.3 T/s and good field quality. The paper will illustrate the organization of the collaboration and the technical program. Various superconductor options (LTS, MgB ₂ or HTS) and different magnet shapes, like classical CosTheta or innovative Canted CosTheta (CCT), with curved multifunction (dipole and quadrupole), are under evaluation, CCT being the baseline. These studies should provide design inputs for a new superconducting gantry design for existing facilities and, on a longer time scale, for a brand-new hadron therapy centre to be placed in the South East Europe (SEEIIST project).

Canted Cosine Theta layout for accelerator magnets is a very attractive since such magnets can be manufactured and assembled without big tooling, and with a relatively modest number of parts and tools. In the frame of European Horizon2020 funds, two collaborations, HITRI plus and I.FAST, are developing a CCT design, of 80 mm free bore, 4 T central dipole field, and 0.4 T/s ramp-rate. This magnet is expected to be the bending element of a gantry, to control the beam delivery in therapy with ions (hadrontherapy). The paper illustrates first a comparison between CCT and more classical cosine theta layout, followed by the comparison between Nb-Ti, Nb ₃ Sn, MgB ₂ , and HTS tapes coils. Relevant requirement for the magnets of this study is to be operated at low current, to limit the heat generation, in sight of a liquid-free cooling system. The results of the comparison is then applied to the design of two magnet demonstrators. Both adopt a low-losses Nb-Ti rope, consistently with the need for keeping the heat generation as low as possible. The first is a straight combined function dipole-quadrupole, while the second is a curved CCT dipole. The paper concludes with the first manufacturing tests for the CCT formers, for which aluminium -bronze, stainless steel and charged PEEK polymer are being explored as basic material.

The Superconducting Ion Gantry (SIG) project is the contribution from INFN (the Italian National Institute for Nuclear Physics) to the international SIGRUM project with the aim of exploring new technological solutions for the critical elements of a 430 MeV/u carbon ion gantry. The project includes the design and construction of a cos $\theta$ 4 T superconducting dipole demonstrator magnet whose main scope is to prove the feasibility of winding and assembling an accelerator magnet type with a relatively small radius of curvature (1.65 m). In addition to the complexity due to the curvature, the target field ramp rate is 0.4 T/s and the cooling system must not adopt liquid helium. This paper discusses the design activities carried out in the last year on the electromagnetic and thermal domains and reports on the present concepts and infrastructure for the first winding trials.