Accurately modeling the transient behavior of non-insulated (NI) ReBCO superconducting coils is crucial for fully assessing their potential for high-field magnet applications. 3D Finite Element (FE) models are among the most promising approaches for capturing the thermal-electrodynamics of these coils. However, most popular mathematical formulations of Maxwell's equations for superconductors, such as the well-known H-$\phi$ formulation, are currently too computationally expensive to simulate large-scale systems like accelerator magnets. To address this challenge, we present a novel mathematical formulation that couples a 3D FE magnetic model with a 1D FE + 2D Finite Difference (FD) electric model, implemented in COMSOL Multiphysics. The formulation has been used to develop a model that simulates the electrodynamics of large ReBCO NI pancake coils. Although still under development, the model has been validated against other models across various test cases, and preliminary results demonstrate its ability to efficiently capture critical phenomena such as persistent current effects while significantly reducing the computational time. In this paper, we describe the electrodynamic model and present selected results benchmarked against more established approaches (e.g., the H-$\phi$ formulation). Work is currently ongoing to integrate thermal behavior into the model.

The final stage of the cooling channel of a muon collider contains several cooling cells, each requiring a very high-field solenoid. Such a so-called 'final cooling' solenoid is key in strongly reducing the emittance of the beam during pre-acceleration and subsequent injection of the beam into the collider ring. In the muon collider design, about 12 to 14 final cooling solenoids of different lengths are foreseen. The conceptual design of the final cooling solenoid that is currently pursued has a homogeneous ( similar to 1%) magnetic field of > 40 T over a length of approximately 0.5 m and features a stack of 52 No-Insulation (NI) High-Temperature Superconductor (HTS) pancake coils. Its ramp scheme has been investigated and a ramp profile has been derived for a constant dissipation of 200 W during the majority of the ramp, while keeping the overall magnet characteristic time at 2700 s. Protection calculations have been performed and show that these solenoids require active quench protection at nominal field to limit the Lorentz forces and thus tape tensile and magnet radial stress during a quench. This contribution provides an overview of the current state of the thermo-electromagnetic design, operational aspects, and several simulated quench and protection scenarios for our design of a final cooling solenoid for a muon collider.

REBCO, the leading candidate conductor for ultra high field magnets, is typically produced in the form of thin tapes, consisting of multiple layers of diverse materials with very different natures and properties. Knowledge of the mechanical properties of these different layers is crucial for magnet design. In this paper, we propose a methodology to measure the elasticity, plasticity and fracture toughness of conductor layer materials, at the scale of its constituents, based on nanoindentation, micropillar compression and micropillar splitting techniques. Measurements with these techniques are carried out at room temperature on a commercial conductor, and the results obtained are compared to the values found in the literature and to those specified by the manufacturers.

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.

In the framework of the design studies of a Muon Collider (MuC), the design of Ultra-High-Field (UHF) magnets is a crucial part, particularly for the MuC's final cooling stage. To address this, CERN has recently introduced a conceptual design for a 40 T solenoid characterized by very compact pancake coils. Due to the high magnetic field and operating current density (approximately 600 A/mm(2)), the Lorentz forces acting on the winding are extremely large. Consequently, the mechanical design, along with quench protection, represents a significant challenge in the development of this magnet. An additional mechanical complexity is constituted by the strong anisotropy and low strength of ReBCO tapes. This article focuses on the proposed mechanical design of the 40 T solenoid. The primary objective of this design is to keep the stresses induced in the coils by Lorentz forces below materials admissible limits. Initially, the paper presents a conceptual design based on analytical calculations relying on the application of a radial pre-compression (approximately 200 MPa) to the pancake coils by shrink-fitting, prior to energization. Subsequently, a finite element analysis is performed, introducing various nonlinearities (material, geometric, plasticity) to optimize the magnet's design. The study also investigates a hybrid solution, in which the initial coil loading is obtained by a combination of shrink fitting and mechanical compression by a clamped conical connection based on shrink discs. The highly anisotropic mechanical properties of the tape, which are not extensively documented in current literature, were investigated by a series of dedicated tests relying on specially designed tooling. This design and experimental testing complement the simulation efforts by allowing to derive and implement in the models more accurate material properties. In conclusion, the proposed magnet design exemplifies a synergistic integration of experimental work and simulation efforts, advancing the development of UHF magnets for the Muon Collider.

In the quest to explore the fundamental properties of particles at the energy frontier, the International Muon Collider Collaboration (IMCC) has made significant progress in the conceptual design study of a Muon Collider (MC). Central to this effort is the development of the various MC's magnet systems, particularly the Ultra-High-Field (UHF) solenoids needed for the MC final cooling stage. For this purpose, CERN recently presented a conceptual design of a 40 T solenoid characterized by very compact coils. This fully superconducting magnet, featuring a 50 mm free bore and requiring 1% field homogeneity over 0.5 m length, is designed to operate at 4.2 K using ReBCO tapes. The solenoid comprises several tens of Non/Metal-Insulated (N/M-I) single pancakes. The pancakes are axially stacked one over the other and supported radially by a stiff mechanical structure that also applies a 200 MPa radial precompression to counter the Lorentz force-induced stresses. Except for a few pancakes at the magnet extremities, all the pancakes are identical and have a winding outer radius of 90 mm. In this paper we present an overview of the various ongoing activities at CERN to realize this ambitious project. Key highlights include the procurement and characterization of conductors, the development of specialized tools for manufacturing the pancakes and for testing the feasibility of applying significant radial precompression to them. Additionally, we discuss the progress in developing mechanical and thermal electro-dynamic models for the 40 T solenoid, strategies for its protection in various quench scenarios, and advancements in solenoid manufacturing technologies.

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.

High-temperature superconductor (HTS) coated conductors (CC) are often wound into pancake coils with electrical insulation in-between the turns. The copper terminals are used for current injection and conduction cooling. An inherent variation of the critical current along the CC length results from its manufacturing process. This variation causes non-uniform heat generation, particularly when the coil is operated at a high fraction of the nominal critical current or when large critical current defects are present. The temperature distribution resulting from the balance between cooling and heating, in combination with the magnetic field and critical current distributions, determines whether a thermal runaway occurs. Accurately predicting the level of critical current defects that can be tolerated during conduction-cooled operation is difficult and requires a three-dimensional (3D) coupled electromagnetic and thermal simulation. This paper presents the results of simulations that are performed with the open-source Finite Element Quench Simulator (FiQuS) tool developed at CERN as part of the STEAM framework. The 3D coupled magnetodynamic-thermal simulations are based on the H- phi formulation and use thin shell approximations, a CC homogenization and conduction-cooling. The critical current can be varied along the CC length. The effect of a single defect specified as a reduction of the critical current along the CC length is investigated in terms of the coil's ability to reach and maintain the operating conditions. The critical current and length of the defect that results in a thermal runaway are analyzed in terms of defect location in the coil. These defect locations are compared in terms of the voltage signal available for quench detection and the implications are discussed.

High-temperature superconductor (HTS) coated conductors (CC) are often wound into pancake coils with electrical insulation in-between the turns. The copper terminals are used for current injection and conduction cooling. An inherent variation of the critical current along the CC length results from its manufacturing process. This variation causes non-uniform heat generation, particularly when the coil is operated at a high fraction of the nominal critical current or when large critical current defects are present. The temperature distribution resulting from the balance between cooling and heating, in combination with the magnetic field and critical current distributions, determines whether a thermal runaway occurs. Accurately predicting the level of critical current defects that can be tolerated during conduction-cooled operation is difficult and requires a 3D coupled electromagnetic and thermal simulation. This paper presents the results of simulations that are performed with the open-source Finite Element Quench Simulator (FiQuS) tool developed at CERN as part of the STEAM framework. The 3D coupled magnetodynamic-thermal simulations are based on the H-phi formulation and use thin shell approximations, a CC homogenization and conduction-cooling. The critical current (Ic) is varied along the CC length. The effect of a single defect specified as a reduction of Ic along the CC length is investigated in terms of the coil's ability to reach and maintain the operating conditions. The Ic and length of the defect that results in a thermal runaway are analyzed in terms of defect location. In addition, a classical 1D scenario with a quench heater is studied. Both the local defect and the heater cases are compared in terms of the voltage signal available for quench detection. These cases result in very different requirements for quench detection, and their implications are discussed.

The damage mechanisms and limits of superconducting accelerator magnets due to the impact of high-intensity particle beams have been subject to extensive studies in the past years at CERN. Recently an experiment with dedicated sample coils made from Nb-Ti and Nb3Sn strands was performed at CERN's HiRadMat facility. This paper describes the design and construction of the sample coils as well as the results of their qualification before the beam impact. In addition, the experimental setup will be discussed. Finally, measurements during the beam experiment like the beam-based alignment, the observations during the impact of 440GeV protons on the sample coils and the achieved hot-spots and temperature gradients will be presented.

The international particle physics community considers a Muon Collider (MC) as a possible option for the successor of the Large Hadron Collider (LHC) at CERN. An international collaboration has recently been set up to produce a conceptual design study of a Muon Collider. One of the main challenges is the need for an ultra-high magnetic field solenoid for the final cooling of the muons. This magnet must have a bore aperture of about 5 cm and a 1% magnetic field homogeneity over 0.5 m of length. CERN is exploring the possibility of developing such a magnet by only using a stack of Rare-earth Barium Copper Oxide (ReBCO) tapes as a conductor. The study's main idea is to produce a modular compact magnet constituted by an assembly of identical pancakes electrically connected in series. Quench protection and stress management are the biggest design challenges. To cope with them, we are investigating the option of Non/Metal-Insulated (N/M-I) pancakes, each made of a single coil (i.e., discarding concentric, nested coils), inserted in a stiff outer ring that provides a sufficient precompression to the coil (similar to 200 MPa). To protect the magnet after a quench and to ramp up the field sufficiently fast, the N/M-I coil interlayer electrical resistance must be optimized and controlled. In this paper, we present a preliminary design of this concept. If successful, this type of design will contribute to developing high-field solenoids for particle accelerators and promote the use of ReBCO tapes in compact windings needed for different applications, such as electrical machines and fusion reactors based on magnetic confinement.

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.

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.

Advanced Series on Directions in High Energy PhysicsThe High Luminosity Large Hadron Collider, pp. 371-389 (2024) Open AccessChapter 16: 11T Dipole and New Connection Cryostats for CollimatorsBernardo Bordini, Luca Bottura, Arnaud Devred, Lucio Fiscarelli, Mikko Karppinen, Gijs de Rijk, Lucio Rossi, Frédéric Savary, Daniel Schörling, and Gerard WilleringBernardo BordiniCERN, Geneva 23, CH-1211, Switzerland, Luca BotturaCERN, Geneva 23, CH-1211, Switzerland, Arnaud DevredCERN, Geneva 23, CH-1211, Switzerland, Lucio FiscarelliCERN, Geneva 23, CH-1211, Switzerland, Mikko KarppinenCERN, Geneva 23, CH-1211, Switzerland, Gijs de RijkCERN, Geneva 23, CH-1211, Switzerland, Lucio RossiCERN, Geneva 23, CH-1211, Switzerland, Frédéric SavaryCERN, Geneva 23, CH-1211, Switzerland, Daniel SchörlingCERN, Geneva 23, CH-1211, Switzerland, and Gerard WilleringCERN, Geneva 23, CH-1211, Switzerlandhttps://doi.org/10.1142/9789811278952_0016Cited by:0 (Source: Crossref) PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: This chapter describes the design of, and parameters for, the 11 T dipole [11] developed at FNAL and the European Organization for Nuclear Research (CERN) for the High Luminosity Large Hadron Collider (HL-LHC) project. FiguresReferencesRelatedDetails Recommended The High Luminosity Large Hadron ColliderMetrics History Information© Oliver S Brüning and Lucio RossiThis is an open access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License.PDF download

The International Muon Collider Collaboration (IMCC) [1] was established in 2020 following the recommendations of the European Strategy for Particle Physics (ESPP) and the implementation of the European Strategy for Particle Physics-Accelerator R D Roadmap by the Laboratory Directors Group [2], hereinafter referred to as the the European LDG roadmap. The Muon Collider Study (MuC) covers the accelerator complex, detectors and physics for a future muon collider. In 2023, European Commission support was obtained for a design study of a muon collider (MuCol) [3]. This project started on 1st March 2023, with work-packages aligned with the overall muon collider studies. In preparation of and during the 2021-22 U.S. Snowmass process, the muon collider project parameters, technical studies and physics performance studies were performed and presented in great detail. Recently, the P5 panel [4] in the U.S. recommended a muon collider R D, proposed to join the IMCC and envisages that the U.S. should prepare to host a muon collider, calling this their "muon shot". In the past, the U.S. Muon Accelerator Programme (MAP) [5] has been instrumental in studies of concepts and technologies for a muon collider.

We describe the magnet challenges for a Muon Collider, an exciting option considered for the future of particle physics at the energy frontier. Starting from the comprehensive work performed by the US Muon Accelerator Program, we have reviewed the performance specifications dictated by beam physics and the operating conditions to satisfy the accelerator needs. Among the many magnets that make up a muon collider, we have identified four systems that represent well the envelope of challenges: the target and capture solenoid, the final cooling solenoid, the accelerator dipoles and the collider dipoles. These systems provide focus for the development of novel concepts, largely based on HTS for reasons of performance, cost and sustainability. After giving a consolidated overview of the needs for the magnet systems, we describe here the basic technology options considered, and the plan for design and development activities.

Superconducting magnets experience significant thermo-mechanical loads throughout their life cycle. These are introduced by the electro-magnetic forces during powering, but also by the prestress applied in many magnet designs. Further to this, the large thermal excursion that components of different materials experience can generate significant internal forces. The loads are also experienced by the superconducting coils, whose critical current can decrease as a consequence of the applied strain. It is then crucial to predict the overall mechanical behavior and conservatively design a magnet, avoiding failure of the mechanical components and of the superconducting coils. Finite Element Analysis (FEA) is generally used to perform these tasks, but its results rely heavily on the material properties and models used. This is in particular true for the coil composite, which is simplified to allow reasonable model sizes in full magnet models. In this paper, we present the state-of-art knowledge of the mechanical properties of the materials mostly used in superconducting magnet construction. We review elastic and plastic properties at room and cryogenic temperature, thermal contraction, and summarize the state-of-art failure criteria for these materials. Finally, the paper summarizes the present understanding of the mechanical behavior and limits of Nb 3 Sn coils. For the first time, an orthotropic failure criteria is proposed.

Superconducting magnet coils are subject to large thermo-mechanical loads applied during magnet assembly, cooldown and operation. These loads can cause the reduction of their critical current due to mechanical strains or local filament failures. Measurements on longitudinally stretched strands and Rutherford cables under transverse pressure have allowed exploration of material limits in two directions. However, no systematic study of the effect of multi-axial loading conditions has been done. Finite Element (FE) models show that, indeed, the actual limits of the material are strongly dependent on the nature of the applied load and that the strength under multi-axial loading can be significantly higher with respect to uniaxial loading conditions. In this paper, we try, for the first time, to measure the effect of multi-direction loading conditions on Nb 3 Sn Rutherford cables. The experiments are performed on impregnated cable stacks under transverse, lateral, and longitudinal constraints. The integrity of the cables is verified by destructive metallography inspection, evaluating the damage as a function of the applied loading condition.

Future particle colliders in search for new physics at the energy frontier require the development of accelerator magnets capable of producing fields well beyond those attainable with Nb-Ti. As the next generation of high-field accelerator magnets is presently planned to be based on Nb 3 Sn, it becomes crucial to establish precisely the mechanical limits at which this brittle and strain sensitive superconductor can operate safely. This paper reports on the stress dependence and the permanent reduction of the critical current under transverse compressive loads up to 240 MPa in state-of-the-art restacked-rod-process (RRP ® ) and powder-in-tube Nb 3 Sn wires. Single-wire experiments were performed at 4.2 K in magnetic fields ranging between 16 T and 19 T on resin-impregnated samples to imitate the operating conditions of a wire in the Rutherford cable of an accelerator magnet. Depending on the wire technology, we measured irreversible stress limit values—defined as the transverse stress value, leading to a permanent reduction in the critical current of 5%, assessed by convention at 19 T—ranging between 110 MPa and 175 MPa. This permanent reduction of the critical current after mechanical unload can occur for two reasons, which can be concomitant: the plastic deformation of the Cu matrix that produces residual stresses on the Nb 3 Sn lattice and the formation of cracks. We developed a method to identify the dominant degradation mechanism in our experiments that allowed us to predict the fraction of critical current lost due to residual stresses. Interestingly, we found that in the RRP ® wires the measured reduction of I c after unload from stresses as high as 240 MPa can be fully ascribed to residual stresses. An independent confirmation of this conclusion coming from a study combining x-ray tomography and deep learning Convolutional Neural Networks is also reported.