A paraffin-wax-based system filled with sub-micrometer alumina particles is developed for use as impregnation of superconducting magnets operating at cryogenic temperatures. The addition of alumina fillers significantly enhances the thermal and cryo-mechanical performance of the wax matrix.Compared with pure wax, the filled system exhibits significant increases in compressive strength, elastic modulus and fracture toughness from room temperature down to its cryogenic service temperature. The filled wax retains a low melt viscosity, ensuring effective impregnation of coils, while the improved match in the thermal expansion coefficient with other magnet components reduces the accumulation of local thermal stresses after cooldown.2D representative volume element (RVE) simulations containing rigid particles embedded in the wax matrix were used to elucidate the mechanisms of damage initiation and stress evolution during thermal contraction and subsequent mechanical loading. The simulation results show good agreement with microscopic fracture observations and provide valuable insights for the design of mechanically robust and thermally compatible next-generation wax-based impregnation systems for superconducting magnets.

The Magnet Development (MagDev) laboratory at the Paul Scherrer Institute (PSI) has designed and successfully manufactured the first subscale stress-managed common coil magnet. The magnet was tested at CERN and reached 98% of its short sample current at 4.5 K. Following the high-field magnet roadmap of the Swiss Accelerator Research and Technology initiative (CHART), a new magnet was assembled after replacing two of the four Nb3Sn coils and manufacturing and integrating four copper-based coils, which are part of the Energy Shift with Coupling (ESC) quench protection method. The ESC system uses normal-conducting auxiliary coils that are strongly magnetically coupled with the magnet's Nb3Sn coils for protection. When a quench is detected, a current is discharged through the auxiliary coils, leading to a rapid transfer of the magnet's energy from the Nb3Sn coils to the copper-based coils. This process results in transient losses and quick transition to the normal state of the Nb3Sn conductor, which facilitates quick energy extraction. This work presents the manufacturing of the copper-based coils, magnet assembly, and test results of the subscale SMCC2.

In recent years, the magnet section at the Paul Scherrer Institute (PSI) has considerably strengthened its expertise in the design, fabrication, and qualification of advanced magnet technologies for particle accelerators. This progress, driven by flagship initiatives such as the Swiss Light Source upgrade (SLS 2.0) and the Swiss Accelerator Research and Technology (CHART) program, has led to the establishment of key competencies in magnet design, dedicated infrastructure, and high-precision magnetic qualification. A prominent example is the SLS 2.0 upgrade, which implements a unique combination of magnet technologies: NdFeB-based permanent magnets, compact combined-function copper electromagnets, and, in a later phase, NbTi superconducting dipoles with a longitudinal field gradient. All magnets are designed, assembled, and magnetically qualified in-house to meet the stringent field-quality and alignment requirements of the new storage ring. In parallel, low-temperature (Nb-Ti, Nb3-Sn) and high-temperature (REBCO) superconducting technologies are being developed and tested in prototype magnets, including those for the PSI Positron Production experiment and for future collider projects such as FCC-ee and FCC-hh, within the framework of CHART. This paper presents an overview of PSI's recent advancements in magnet technology and discusses prospects. These developments serve both PSI's internal research programs and collaborative projects with European and international partners, paving the way for a new generation of efficient and environmentally responsible accelerator magnets.

REBCO coated conductor tapes are a promising technology for developing high-field accelerator magnets since their increased current carrying capacity and operational temperature allows achieving higher-fields and current levels with higher thermal margin. Superconducting materials still present challenges associated with their non-negligible losses in transient conditions, hence, finite element analyses become essential to design feasible superconducting systems. The H formulation is known in literature for its accuracy, while the T-A formulation offers computational efficiency. Nonetheless, both methods remain computationally demanding, especially when the superconducting tapes are modelled considering the extreme aspect ratios of different materials in the layered tapes. Homogenized models have been proposed to reduce computational requirements, however, modelling all layers as a single domain can impose the current to flow through all conducting layers rather than only the REBCO layer, even when its resistivity is very low. This study presents a comparative analysis using the H and the T-A formulations for a partially homogenized model, where the superconducting layer is modelled independently from the remaining conducting layers, and a fully homogenized model. The models' accuracy for transport loss estimation in transient conditions is discussed and compared with experimental loss measurements for a REBCO tape powered with AC currents.

The Paul Scherrer Institute (PSI) is developing an integrated system for cooling and protection of high-field superconducting magnets. Increasing the overall current density of superconducting cables reduces the conductor volume required for high fields but also decreases magnet protectability. To mitigate this, a strategy combining auxiliary coils and electrical discharge has been proposed to generate fast transients in the superconducting coils and enhance protection. For effective coupling, the auxiliary conductor must be located close to the magnet coils; however, in multi-layer configurations, this can reduce magnetic efficiency. Another key challenge in high-field magnets is cryogenic efficiency—both in steady-state cooling and in handling transient losses. To avoid the high costs of helium-bath systems in large magnets, PSI is investigating a conduction-cooling approach using forced-flow pipes embedded between coil layers. Yet, this integration can also impact magnetic performance. To address both protection and cooling challenges simultaneously, PSI proposes a dual-function concept using a hollow electrical conductor that serves as both the protection circuit and the cooling channel. The auxiliary coils are wound from this hollow conductor, which offers suitable electrical properties and enhanced thermal performance through forced-flow cooling. This work applies the proposed strategy to the subscale stress-managed asymmetric common-coil magnet under development at PSI. The study includes multi-physics transient analyses to assess system performance and validate the concept as a compact and efficient approach for superconducting accelerator magnets

We present a systematic method to tune the turn-to turn contact resistance R-ct in high-temperature superconducting (HTS) solenoids by applying a polyvinyl butyral (PVB) thermoplastic coating filled with silver-coated copper flakes (SCCF). The filler type and its volume fraction determines the accessible resistance range in the final coil. R-ct strongly affects the charging dynamics and quench resilience of non-insulated (NI) HTS magnets, hence it is important to be able to control this parameter in a reliable and reproducible way. The coating is applied prior to winding in a continuous dip coating process and results in a dry polymeric film on the tape. After winding, the coating layers are fused above 60 degrees C and the final Rct is adjusted through the temperature and the duration of the heat-treatment. This method gives access to a wide range of R-ct. Values from about 50 to 10(6) & micro;Omega & centerdot; cm(2) can be obtained with the right choice of filler type, concentration and heat treatment conditions. An 80-turn demonstrator solenoid fabricated using this approach and tested at 77 K achieved the targeted R-ct of around 70 & micro;Omega & centerdot; cm(2). A finite-element model, calibrated with the measured field-decay time, was used to extract the average turn-to-turn resistance and validate the tuning method.

The decreasing cost and expanding production of REBCO tapes make them promising candidates for accelerator magnets operating at high current density and high magnetic field. Within the CHART program supporting accelerator-magnet development, we perform electromagnetic and thermal analyses of the first REBCO subscale (RS1) magnet developed in the MagDev Lab at PSI, designed to enable direct experimental comparison between HTS and LTS technologies. The RS1 magnet adopts the same configuration as a previously tested LTS SMCC common-coil magnet, in which the Nb3Sn cable is replaced by a straight, soldered REBCO tape-stack cable with comparable geometric parameters. The magnet comprises four racetrack winding layers, with two layers located on each side of the aperture.We present models of resistive and AC-loss induced heating in the REBCO stack under operating conditions relevant to superconducting magnets: liquid helium (4.5 K), gaseous helium (20 K), and liquid nitrogen (77 K). Magnetic-field harmonics and transient behavior in the REBCO cables are computed using an H–A formulation in FEM. The analysis further includes predictions for REBCO magnet protection using a dump resistor as well as alternative protection strategies. Numerical results are compared with experimental data from the two-layer configuration and the full magnet tested in liquid nitrogen, and predictions are provided for liquid- and gaseous-helium tests upcoming at CERN in 2026. These results support the development of accelerator magnets at higher magnetic fields where REBCO conductors offer significant potential.

In the context of the high-field magnet program, the Swiss Accelerator Research and Technology initiative is dedicated to researching and developing robust, high-field accelerator magnets for the future circular collider. As part of this initiative, the PSI team successfully designed, prototyped, and tested the first subscale stress-managed Nb3Sn common coil dipole magnet with enhanced training behavior. Following this accomplishment, a proposal was made for a stress-managed asymmetric common coil design for improved field quality, compatible with the requirements of accelerator magnets. This work follows the conceptual methodology proposed by PSI and details the electromagnetic and thermal design of a subscale asymmetric common coil magnet, equipped with a ferromagnetic yoke. The influence of the iron yoke on the magnet's field quality is analyzed and optimized according to the specified nominal current. A cooling strategy is proposed that involves cooling the windings using pipes carrying a fluid under forced flow, with the pipes in contact with the conductor. An alternative option, where the yoke is cooled to a higher temperature using a second fluid, is also considered. The magnet protection is analyzed considering an energy extraction system.

Abstract We present a predictive multiscale modeling workflow for Nb₃Sn Rutherford cables that bridges strand and cable scales to support the design of accelerator magnets in the 14 T range. This experimentally validated framework enables prediction of critical current reduction under load of Nb₃Sn Rutherford cables. The workflow is parameterized in strand and cable architecture, allowing it to be applied across cable designs; as done here on two 21-strand cables of different design (CD1 and SMACC-HF), differing most notably in strand diameter and Cu/non-Cu ratio. The workflow integrates a cabling model capturing strand transposition and compaction-induced deformation, a Python tool for generating FEM-ready 2D cross-sections, homogenization of the Nb₃Sn interfilamentary region with inter-strand contact modeling, and a linkage connecting simulated strain to critical current reduction. The workflow was mechanically validated against 10-stack Rutherford cable measurements at 77 K, with the simulated macroscopic stress–strain slope matching the measurement to within 6% in virgin loading and 0.1% in reloading. The predicted critical current reduction was validated against the Compression BOX experiment. Across the 10–250 MPa transverse-pressure range covered by the experiments, the predicted cable critical current agrees with the measurement to a mean absolute error of ≤3.2% for CD1, where Ic was taken from an independent strand measurement and ≤0.9% for SMACC-HF, where the initial Ic is taken from the virgin cable measurement. Both measurement and simulation show a correlation between a lower Cu/non-Cu ratio and retaining a higher fraction of the virgin critical current under transverse pressure.

Stress-management of Nb3Sn coils offers a promising approach for high-field magnets by reducing conductor stress. The combination of stress-management and the common-coils magnet type simplifies manufacturing processes, such as utilizing the coil former in reaction and impregnation tooling. The common-coils architecture provides an attractive solution for 2- in-1 dipole magnets, with its racetrack geometry facilitating manufacturing and potentially allowing the react-and-wind (R&W) technique for cost-effective large-scale production. A key contribution of this work is overcoming the need for pole coils to achieve field quality by introducing an asymmetric design using only common-coils. The PSI 2-in-1 dipole magnet, featuring eight stress-managed Nb3Sn layers, employs bladder-and-keys technology for pre-loading at room temperature, eliminating the need for an aluminum shell or pads. The magnet includes two cable grades spliced in the low-field region, along with other features discussed in this paper. This work presents the conceptual design, including 3D magnetic design, mechanical analysis, and protection results.

A 13 T Nb3Sn common-coil accelerator-type magnet is being developed at the Paul Scherrer Institute (PSI). The magnet cross-section features an innovative design with asymmetric elements and effective stress-management. Thanks to the asymmetric design narrow pole racetrack coils are not required in proximity of the magnet apertures to improve the field quality. Its magnetic design achieves adequate margin with respect to the short-sample limit while utilizing two available cables. This choice accelerates the completion of the 0.8 m long demonstrator magnet, but limits the flexibility of the conductor grading and makes the magnet quench protection more challenging. In this contribution, the strategy to limit the hot-spot temperature and peak voltage to ground reached in the magnet conductor after a quench is discussed. The electro-magnetic and thermal transients occurring during a quench discharge are simulated with the STEAM-LEDET program. Quench detection based on differential-voltage monitoring is proposed, and the expected quench detection times are evaluated in the case of quenches occurring in different coil locations. Furthermore, the performances of various quench protection systems, including energy-extraction based either on a resistor or a varistor, a CLIQ (Coupling-Loss Induced Quench) system, or combinations of these are assessed. It is shown that while energy-extraction is a viable option to protect the magnet, acceptable performance can be achieved with CLIQ while achieving a significantly lower peak voltage to ground. The lowest hot-spot temperature is obtained by combining energy extraction and CLIQ.

This paper presents the design of a non-insulated (NI) high-temperature superconductor (HTS) 15 T solenoid with a 72 mm warm bore, intended for use in the PSI Positron Production (P^3) experiment. The P^3 experiment, scheduled to start in Q3 2026, aims to demonstrate a high-yield positron source that is relevant in the context of FCC-ee. The coils will be solder-impregnated using techniques developed with a small-bore HTS NI coil stack. This magnet produced a magnetic field of 18 T at 12 K and 2 kA, in a cryogen-free, conduction-cooled setup. Similarly, the P^3 magnet will be conduction-cooled by two cryocoolers. This larger-bore magnet is designed to operate at 15 K with a nominal operating current of 1.2 kA. To ensure the protection of the NI magnet, quench prevention is the preferred strategy. Several potential failure modes are analyzed, including thermal runaway in the event of failures in the current leads, power supply, or cryocoolers. By enhancing the cold mass' heat capacity through the addition of a large lead mass, the stored magnetic energy can be safely dissipated in the cold mass through the electrical path formed by the superconductor and the solder. Mechanical analysis indicates that the hoop, radial and axial stresses are kept below allowable limits.

Muons offer a unique opportunity to build a compact high-energy electroweak collider at the 10 TeV scale. A Muon Collider enables direct access to the underlying simplicity of the Standard Model and unparalleled reach beyond it. It will be a paradigm-shifting tool for particle physics representing the first collider to combine the high-energy reach of a proton collider and the high precision of an electron-positron collider, yielding a physics potential significantly greater than the sum of its individual parts. A high-energy muon collider is the natural next step in the exploration of fundamental physics after the HL-LHC and a natural complement to a future low-energy Higgs factory. Such a facility would significantly broaden the scope of particle colliders, engaging the many frontiers of the high energy community. The last European Strategy for Particle Physics Update and later the Particle Physics Project Prioritisation Panel in the US requested a study of the muon collider, which is being carried on by the International Muon Collider Collaboration. In this comprehensive document we present the physics case, the state of the work on accelerator design and technology, and propose an R&D project that can make the muon collider a reality.

The magnet development (MagDev) laboratory at the Paul Scherrer Institute (PSI) has designed the subscale stressmanaged common-coils (subSMCC1) 2-in-1 dipole magnet as part of the CHART (Swiss Accelerator Research and Technology) contribution to the CERN HFM (High-Field Magnet) programme. This R&D vehicle is part of the CHART/MagDev high-field roadmap. The nature of the subscale magnet allows it to be manufactured and tested quickly, so lessons learned from it will be applied to the high-field stressmanaged common-coils demonstrator that is currently under development. The magnet has a straight section of 150 mm, two clear bore apertures of 22 mm, and an inter-beam spacing of 120 mm. In the first version, the magnet structure consists mainly of inner and outer pads surrounding the straight sections of the coil, and inner and outer pads at the coil ends, with no iron yoke or shell. Axial pre-load is provided by six rods connected to the end pads. All structural components, including the split-former pieces, are made from the same stainless-steel alloy. The first magnet, with four stress-managed Nb3Sn common-coils, was manufactured and tested. This contribution presents the detailed manufacturing process as well as test results, training behavior and mechanical measurements

This document is comprised of a collection of consolidated parameters for the key parts of the muon collider. These consolidated parameters follow on from the October 2024 Preliminary Parameters Report. Attention has been given to a high-level consistent set of baseline parameters throughout all systems of the complex, following a 10 TeV center-of-mass design. Additional details of the designs contributing to this baseline design are featured in the appendix. Likewise, explorative variations from this baseline set can be found in the appendix. The data is collected from a collaborative spreadsheet and transferred to overleaf.

Following a recommendation of the 2020 update of the European Strategy for Particle Physics Update (ESPPU) to intensify the accelerator R\&D, the European Accelerator R&D Roadmap with five topical research panels was implemented in 2022. Two of the panels, high field magnets, and high gradient RF structures and systems are technology oriented and their R&D efforts will support several collider concepts. Three panels are developing advanced concepts for a future energy frontier collider facility. These concepts involve specific advancements over classical circular or linear collider concepts, but are associated with higher technical complexity. These include high gradient plasma and laser accelerators, bright muon beams and muon colliders and energy recovery linac (ERL).

The European Strategy for Particle Physics (ESPP) reflects the vision and presents concrete plans of the European particle physics community for advancing human knowledge in fundamental physics. The ESPP is updated every five-to-six years through a community-driven process. It commences with the submission of specific proposals and other input from the community at large, outlining projects envisioned for the near-, mid-, and long-term future. All submitted contributions are evaluated by the Physics Preparatory Group (PPG), and a preliminary analysis is presented at a Symposium meant to foster a broad community discussion on the scientific value and feasibility of the various ideas proposed. The outcomes of the analysis and the deliberations at the Symposium are synthesized in the current Briefing Book, which provides an important input in the deliberations of the Strategy recommendations by the European Strategy Group (ESG).

The major advantage of reduced magnetic vector potential formulations (RMVPs) is that complicated coil structures do not need to be resolved by a computational mesh. Instead, they are modeled by thin wires, whose source field is included into the simulation model along Biot-Savart's law. Such an approach has already been successfully employed in ROXIE for the simulation of superconducting Large Hadron Collider magnets at CERN. This work presents an updated RMVP approach, which significantly outperforms the original method. The updated formulation is postulated, implemented, verified, compared to the original formulation, and applied for the simulation of a quadrupole magnet. The promising results of this work encourage further investigation towards an updated simulation framework for next-generation accelerator magnets.

We worked out an approach for obtaining “clean” magnets by introducing oxygen during the reaction heat treatment (RHT) of a single glass fiber insulated Nb 3 Sn Rutherford cable in a channel. A reduction of the RRR by 16% was measured while the glass fiber insulation and support structure was visually clean after the RHT. We developed a filled wax system, consisting of fully refined paraffin wax, carnauba wax and alumina particles, which is compatible with the common glass fiber insulation on Rutherford cables. The filled wax showed a flexural modulus of 19 GPa at −100 °C and a thermal shrinkage of −1.2% from RT to 77 K. We used a commercial glass ceramic coating on stainless steel as primary insulation in single cable in a channel applications or as secondary electrical insulation from the former. The coating survives the RHT and operation temperatures and keeps its electrical insulation properties.

This document is comprised of a collection of updated preliminary parameters for the key parts of the muon collider. The updated preliminary parameters follow on from the October 2023 Tentative Parameters Report. Particular attention has been given to regions of the facility that are believed to hold greater technical uncertainty in their design and that have a strong impact on the cost and power consumption of the facility. The data is collected from a collaborative spreadsheet and transferred to overleaf.