Daniel Novelli

Among the most innovative and promising next generation particle accelerators, a muon collider is at a time a viable compromise between the increase of available energy at the interaction point and the sustainability of the related infrastructure. The International Muon Collider Collaboration is pursuing the design of a complete accelerator complex, up to the detectors to be installed on the two interaction points foreseen on the collider. Here we present a preliminary design of a solenoid magnet for one of the proposed detectors, MUSIC, aiming at a compromise between the requests for the detector tracker and the beam-induced background rejection. The goal is to achieve up to 5 T at the interaction point, good field uniformity (of the order of 10%) on a volume comparable with the warm bore of the solenoid (4.6 metres in diameter and 4.6 metres long), non trivial integration with the sub detectors and with the final focusing magnets of the collider, which are foreseen at less than 8 metres from the magnet centre. Starting from a CMS-like design, we plan to fulfil the requirements with a central solenoid coupled with additional coils embedded in the hadronic calorimeter and the end caps of the return yoke.

Following the publication of [1], the authors identified an error in the author list. Diego Perini has therefore been removed from the author list with agreement of all authors.

Over the past few years, interest in a Muon Collider as a potential post-LHC machine has grown significantly. By colliding muons, it is possible to achieve both precision and high energy, overcoming the limitations of synchrotron radiation in conventional lepton colliders. However, the very short muon lifetime at rest requires high beam intensity and fast acceleration rates limiting the collider ring dimensions. These limitations lead to several challenges in the design of superconducting magnets, which must generate high magnetic fields in large apertures to provide shielding from the radiation due to muon decay. This work explores the design of combined function magnets, which are essential to address the neutrino flux issue in straight sections by bending the particles during focusing/defocusing stages. The superconducting material selected for these magnets is REBCO, a High Temperature Superconductor (HTS), with operating temperatures ranging from 4.5 K to 20 K. Various configurations of combined function magnets are studied and simulated using a Python code interfaced with the Finite Element Method (FEM) software ANSYS, employing the sector coil approximation. The goal is to identify feasible designs that can accommodate substantial internal shielding while continuing to provide the high fields and gradients demanded by the lattice optics. To validate the manufacturability of such concepts, a preliminary winding test has been performed using Nb$_{3}$Sn in a Canted-Cosine-Theta (CCT) geometry. While REBCO represents the most promising HTS conductor for future high-field applications, Nb$_{3}$Sn remains one of the most mature options for large accelerator magnets, providing a valuable feasibility benchmark.

An International Muon Collider Collaboration (IMCC) has been formed following the recommendation of the Updated European Strategy for Particle Physics (ESPPU) to study the feasibility of a 10 TeV muon collider within a compact 10 km ring. This machine combines the precision of lepton colliders with the energy reach and discovery potential of hadron colliders, overcoming synchrotron radiation limitations affecting electron-positron machines. However, the short muon lifetime (2.2 μs at rest) presents several challenges in the development of magnets, RF systems, targets, shielding, and cooling. Super conducting magnets of the collider ring are influenced by the need for tungsten shields inside the bore apertures to protect superconducting coils from radiation caused by muon decay, as well as the elimination of straight sections in the accelerator to mitigate harmful neutrino-induced radiation. This work extends the Aperture-Field (A–B) plot methodology, previously applied to dipoles and quadrupoles, to sextupole magnets, delineating feasible designs based on aperture, sextupolar gradient strength, mechanical stress, quench protection, and cost. Using a Python ANSYS tool, optimized configurations were simulated under the sector coil approximation, focusing on REBCO coils operating at 4.5 K, 10 K, and 20 K, providing Aperture– Sextupole Gradient (A–G2) plots for the sextupoles standalone and Dipole Field Sextupole Gradient (B–G2) plots for the sextupoles combined with dipoles. These results provide a quantitative framework to evaluate the achievable field strengths and geometric constraints of sextupole-based solutions in the demanding environment of a high-energy muon collider.

Within the framework of the International Muon Collider Collaboration (IMCC), a feasibility study is underway for a 10 km collider ring aiming to achieve 10 TeV of center-of-mass energy. The short muon lifetime (2.2 $\mathrm{\mu }$s at rest) imposes stringent requirements on the magnets, which must be compact, high-field, and large aperture to both maximize luminosity and host the internal shielding for the muon decay products. These challenges point to the use of REBCO High-Temperature Superconductors (HTS) and motivate the development of innovative design strategies addressing electromagnetic performance, quench protection, AC losses and mechanical integrity. This work presents an updated 2D analysis of dipoles in a block-coil configuration for the muon collider ring, featuring an innovative stacked-cable orientation with a novel end-winding concept. An improved electromagnetic design with a bore field of 16 T in a 140 mm aperture diameter is introduced, accompanied by an analytical estimation of hysteretic losses, which now accounts also for transport current effects. In addition, an advancement of the preliminary mechanical design is provided through Finite Element Method (FEM) using ANSYS software, employing a stress-management strategy to mitigate the high Lorentz forces.

The Muon Collider represents an exciting proposal for a post-LHC accelerator, capable of exploring higher-energy regions with greater power consumption efficiency compared to hadronic alternatives, while avoiding synchrotron radiation limitations inherent in electron colliders. This contribution will focus on the magnets for the Muon Collider storage ring. These magnets pose an unprecedented technological challenge: high magnetic fields are required to ensure the compactness of the ring, maximizing the number of muon beam passes through the interaction region and thereby increasing luminosity. Additionally, large apertures are essential to accommodate an adequate shielding system that keeps the thermal and nuclear loads induced by the beam within acceptable limits. Furthermore, minimizing straight sections is critical to avoid the radioactive hazard posed by collimated neutrino beams, necessitating the use of combined-function magnets (dipole + quadrupole and dipole + sextupole). The interaction region also presents extreme conditions that demand the development of magnets beyond the current state of the art. In this contribution, we will discuss the progress in the feasibility study of magnets for both the arc and the interaction region of the Muon Collider storage ring. Performance limits will be analyzed for dipoles and quadrupoles, taking into consideration constraints on mechanical stresses, margin on the load line, ease of the protection system and cost for ReBCO-based magnets. Finally, the most up-to-date conceptual designs of the arc dipole will be presented, comparing the strengths and challenges of the cos-theta and block coil layouts in terms of achieving of electromagnetic requirements, mechanical structure feasibility, and windability.

Within the framework of the International Muon Collider Collaboration (IMCC), researchers are involved in a feasibility study to develop high-temperature superconducting (HTS) magnets for a 10 km collider ring, designed to reach a 10 TeV Center-of-Mass (CoM) energy.Due to the short lifetime of muons of only 2.2 $\mathrm{\mu }$s, the machine must minimize their acceleration time, allowing them to collide before the decay. To optimize the machine cost and maximize the collider luminosity, the superconducting dipoles of the collider ring must be compact and generate high steady-state magnetic fields. In addition, they must feature large apertures for the insertion of a shielding structure needed to preserve the superconducting coils from muon decay products. These demanding specifications pose significant technological challenges for the design of the dipole magnets, both in terms of physics and engineering. In this contribution, we give an overview of the conceptual 2D electromagnetic design of the main collider dipoles, followed by a preliminary mechanical analysis for a first estimation of stresses due to the Lorentz forces. Since the coil design is based on REBCO tapes - whose magnetization effects must be taken into account - an analytical code was written in MATLAB to evaluate the magnet performances considering non-uniform current distribution according to the Brandt model.A validation study of the code by comparing its results with finite element method (FEM) simulations is also presented. In this comparison, the computational time of the analytical and numerical approaches will also be pointed out to better appreciate the importance of the work done in developing the new tool.

The international particle physics community, among various options for developing future high-energy particle colliders and exploring fundamental interactions, considers Muon Colliders (MC) as a significant opportunity to achieve high discovery potential and integrated luminosity compatible with a compact and cost-effective accelerator machine. An international muon collider collaboration (IMCC) has recently been established, following the recommendations of the European Strategy for Particle Physics (ESPP), to develop a conceptual design for a Muon Collider with a 10 TeV center-of-mass energy. From the analysis of the collider's various magnetic components, large stored energies for the capture and cooling solenoids, very high magnetic fields up to 40 T for the final cooling solenoids, and large bore (up to 140 mm) and high-field combined function magnets for the accelerator and collider rings are required. High-temperature superconductors (HTS) enable the technology to address these challenges and achieve the required collider performances. Given the peculiar accelerator stages of the muon collider, most superconducting magnets are required to operate in steady-state mode, with normal-conducting dipoles handling rapid acceleration and fast field variations, allowing the use of HTS-coated conductors to enhance magnet performance compared to low-temperature superconductors (LTS) technology. This aspect is also fundamental in advancing the energy efficiency and sustainability goals of next-generation accelerator facilities for high-energy physics. By enabling magnet operation at temperatures above liquid helium, HTS offer the potential to significantly reduce the energy consumption of entire accelerator complexes. This energy-saving capability must be increasingly prioritized in magnet design strategies with different impacts on the collider performance, cost, and feasibility. In this paper, we elaborate on the above aspects, discussing the technological challenges for the 10 TeV muon collider configuration and how HTS will make them viable and efficient to pave the way to new compact and high-performance particle collider machines capable of overcoming the current energy frontier.

The Falcon Dipole is a project led by the Italian Institute of Nuclear Physics (INFN), which aims tofabricate a 12 T short model of a Nb$_{3}$Sn cos-theta accelerator dipole as part of the High Field Magnet (HFM) R&D program at CERN [1]. The status of the project is at the fabrication step of the first dummy coil in the industry and, in this paper, the results of the first campaign of winding tests conducted in the industry are presented. The winding process for the Falcon Dipole is challenging because the size of the Rutherford Cable used for the coils is comparable to the bore radius. This results in high bending and torsion stresses, making the cable structure unstable. To address these challenges, the previous 3D model has been modified to improve the winding feasibility. The setup has been prepared to monitor technical parameters that will help in modeling the coil geometry and identifying sources of critical issues. In this paper, the outcomes of the winding campaign are reported and the proposed changes to the coil end design to address the issues that arose are discussed.

Future particle accelerators require high-field dipole and quadrupole magnets to guide the particles inside the collider ring. Magnets based on High-Temperature Superconductors (HTS) allow operation with higher magnetic field and higher operation temperature compared with the Low-Temperature Superconductor (LTS) based options. One of the issues presently limiting the HTS technology seems to be their protection in case of an unwanted resistive transition, i.e., a quench. New magnet technologies based on non-insulated or partially insulated (metal-insulated) winding technologies ease the problem compared with traditionally insulated magnets. In these magnets, the current can by-bass the quenched segment and the peak temperature remains lower. However, in high current density and high energy density operation, also the insulation-free options will have limitations, and the quench temperatures should be analyzed. In this contribution we present a method for analytical estimation of the protection limits in insulated, non-insulated and metal-insulated magnets. The equations can be used in early stages of magnet design to assess the feasibility and performance requirements of the eventual protection systems. The work stems from the International Muon Collider Collaboration and the results shown here review the protection limits in the dipoles and quadrupoles considered in its collider ring design. We discuss how parameters such as the coil size, metal insulation thickness and the amount of stabilizer copper in the tape impact the protectability of the magnet. This analysis considers only an adiabatic estimation of the peak temperature. Other potentially critical aspects such as voltages and mechanical stresses must be considered with more detailed models as the magnet designs mature.