Study of superconducting magnets for a Muon Collider

Future high-energy particle colliders will require superconducting magnet systems capable of generating high magnetic fields, enabling accelerator designs that are more compact and energy efficient, while maintaining mechanical stability and operational reliability under extreme conditions. Among the proposed concepts, the Muon Collider represents a particularly promising option for extending the energy frontier in a sustainable way, combining high center-of-mass energy with reduced synchrotron radiation losses. In accordance with the guidelines set forth in the Updated European Strategy for Particle Physics, the International Muon Collider Collaboration (IMCC) has been established to assess the feasibility of a muon collider facility operating at a center-of-mass energy of 10 TeV. The primary challenges arise from the short muon lifetime at rest, limited to 2.2 μs, which imposes severe constraints on the design and operation of the machine. Meeting these demanding conditions requires the use of advanced technologies in magnets, RF systems, targets, shielding, and cooling. To minimize the formation of collimated neutrino beams generated by muon decay and to reduce the radiation background around the facility, the straight sections of the collider ring must be kept as short as possible. This objective can be achieved by integrating beam optics quadrupoles with bending dipoles that combine a high magnetic field (>10 T) and gradient (>100 T/m) within a large aperture (∼140 mm). These stringent constraints call for cutting-edge solutions in material selection, mechanical design, quench protection, shielding, and cryogenic systems. This work explores the performance limits of potential candidate materials for dipole, quadrupole and sextupole magnets, specifically Low-Temperature Superconductors (LTS) such as NbTi and Nb3Sn, and High-Temperature Superconductors (HTS) such as REBCO, in terms of maximum achievable field, mechanical stress, and stored energy. An original methodology has been developed to investigate the accessible parameter space using both analytical models and finite-element simulations performed in ANSYS, automated through a Python interface. This approach allows a systematic exploration of magnet geometries, identifying feasible configurations for dipoles, quadrupoles, and sextupoles. Finally, the study has been extended to combined-function magnets, capable of simultaneously generating dipole and quadrupole, or dipole and sextupole, field components within the same aperture. This configuration allows the beam to be bent during focusing, defocusing, and chromaticity correction stages, thereby reducing straight sections and significantly mitigating the issue of neutrino flux at ground level.