Superconducting magnets for particle accelerators are particularly challenging to design because they involve a large number of coupled physical phenomena and the management of complex datasets. Artificial Intelligence (AI), including machine learning and advanced optimisation techniques, offers promising approaches to address these challenges and accelerate the design process. This paper presents a new AI-based optimisation and data management platform, and highlights several ongoing applications of AI methods carried out at CEA Paris-Saclay, including multiphysics optimisation using active learning, topology optimisation, holistic modelling of an Electron Cyclotron Resonance (ERC) ion source, and anomaly detection in quench events.

US Magnet Development Program is leading an effort to design and manufacture a 20 T accelerator dipole magnet. Various designs are under development featuring cos-theta, block- coil, or common-coil geometries. To achieve the target field while maintaining cost-effectiveness the magnet cross-section includes high-temperature superconductor (HTS) inner coils and Nb3Sn outer coils, which are all powered in series. The quench protection of this class of high-field accelerator magnets is extremely challenging due to the high energy density, high current density, slow quench propagation, in particular in the HTS coils, and highly inhomogeneous thermal properties of HTS and Nb3Sn coils. The magnet quench discharge is simulated with the STEAM-LEDET program as coupled electro-magnetic and thermal transients. The peak temperature and voltage to ground in the magnet coils during the transient are presented. The performance of a CLIQ-based quench protection system applied to 1 m long model magnets in terms of peak temperature and voltage to ground is investigated. Furthermore, the scalability of the proposed solution to full-scale, 15 m long magnets is discussed.

ASTERICS is an ECR (Electron Cyclotron Resonance) ion source designed by CEA, GANIL and LPSC for the NEWGAIN project in France. The design of the Nb-Ti superconducting magnet is inspired from two magnets built for 28 GHz ion sources (VENUS and FRIB ion sources) and is composed of a sextupole inside three solenoids to confine the plasma. The main improvement in terms of magnetic design comes from an increase of the plasma chamber radius from 71.85 mm to 91 mm aiming at increasing the metallic beam yield at both 18 and 28 GHz. This change in magnetic design leads to an increase of Lorentz forces, impacting the design of the mechanical structure. Like the FRIB ion source, the architecture uses an aluminum shell-based support structure with bladders and keys to compress the sextupole azimuthally, and endplates for its axial compression. The bladders and keys allow a disassembly of the sextupole coils, and an adjustment of the coils pre-stress. The solenoids are wound under tension around an aluminum mandrel acting as a shell for the sextupole pre-load. Interfaces between solenoids and mandrel are designed to allow detachment and low friction sliding during excitation. The scale-up of the support structure, to address the dimension increase, is presented here. The 2D and 3D mechanical models developed to perform the mechanical analysis and the results obtained are detailed along with the preliminary assembly process.

In the framework of the NEWGAIN project (NEW GAnil INjector), a new injector is under development to supply the SPIRAL2 LINAC at GANIL with heavy ion of a mass to charge-state ratio up to A/q = 7. In order to produce this heavy ion beam, a superconducting 28 GHz ECR Ion Source called ASTERICS is under development and its superconducting magnet used for plasma confinement is designed at CEA in collaboration with LPSC and GANIL. The magnetic design of the ion source is based on the well-proved sextupole-in-solenoids configuration used in different laboratories worldwide. The superconducting coils will be in Nb-Ti placed in a He bath cooled by 6 in-situ cryocoolers. A magnetic and protection optimization has been done to meet the NEWGAIN requirements which calls for a bigger plasma chamber than the existing superconducting ECR ion sources while maintaining the same temperature margin in the coils. This paper focuses on the magnetic analysis, the protection studies and the choice of the superconducting conductor for the sextupole and the solenoids. To validate the coil fabrication steps and the assumptions made in the magnetic design, some winding trials have been done. Both simulations and mock-up results are presented here.

The next generation of high-field magnets for accelerators relies on Nb3Sn conductors, mostly Rutherford-type cables. Superconducting cables are anisotropic composites structures that can comprise strands, impregnation and insulation wrapping materials. Moreover, Rutherford cables are characterized by a multi-scale architecture going from the micron-size sub-elements to meter-size coils. Due to the mechanical sensitivity of the Nb3Sn material, the sub-element behavior drives the performance of the magnet. To predict and improve the performance and behavior of the magnets, numerical modeling is now crucial. The multi-physic and multi-axial loadings, the complex multi-scale structure and the intrinsic properties of the Nb3Sn material require three-dimensional models to be able to understand and represent the different phenomena. A tool that is able to generate 3D Finite Element (FE) model of a Rutherford cable has been developed at CEA over the last years in the framework of the CoCaSCOPE approach. It allows generating a meshed FE model from the main cable parameters (size, number of strands, etc.) and usable with multi-physic simulation software. This paper presents the different steps to construct the geometry of the cable, and the main features of the mesh. Techniques to model different configurations are presented, considering the stainless-steel core and/or a keystoned shape. Today, the CoCaSCOPE mesh generator (CoCaSCOPE-MG) is open to the scientific community. The authors propose to generate any type of Rutherford cable on demand.

Superconducting magnets are crucial components in various scientific, industrial, and medical applications, offering unparalleled high magnetic fields and energy efficiency. However, the transition from the superconducting to the normal state, known as a quench, can pose significant challenges due to the sudden local release of stored energy and damage to the magnet system. Quench protection strategies have emerged as essential mechanisms to mitigate the adverse effects of quenches. One of the commonly used methods in accelerator magnets is to use strip heaters on coil surfaces. The heater element length and configuration influence the performance of the quench protection. The study of the quench protection by heaters requires the coupled modelling of the Joule heating, normal zone propagation, and transferring heat from the heaters to the cable. In this paper, we present a new 2D finite element simulation model to model the increase of the cable resistance under different heater lengths in Nb3Sn accelerator magnets. The model allows analyzing heaters with several different lengths of heating stations along the cable. This strategy can be used to maximize the cable resistance increase at high operation current while still providing the needed normal zone propagation at lower currents. We demonstrate the model use with a high-field racetrack dipole model.

The Research Racetrack Dipole Demonst rator (R2D2) is a Nb 3 Sn graded magnet developed in the framework of the CEA-CERN collaboration with the goal to assess key technologies for future high field accelerator magnets. This demonstrator magnet features two 1.7 m long racetrack coils, designed in the graded configuration needed for compact and efficient high field magnets. Each coil is made of two different Nb3Sn cables wound around each other and submitted together to the high temperature heat treatment needed for Nb3Sn compound formation. The experience on Nb 3 Sn coils has taught us that the management of the deformations undergone by the Nb 3 Sn cable during its formation must be a priority in the definition and the dimensioning of the tools and the manufacturing processes of the coils. This paper reports the results of the test campaigns carried out at CEA Saclay to study the behavior of R2D2 cables during heat treatment. The first campaign consisted of reduced-coils made of a few turns of each cable, with representative lengths. For each coil, the winding is performed with gaps in the components, and the gaps are measured before and after the heat treatment to quantify the coil length variations. A second campaign consisted in measuring the thickness variations of cable stacks in various configurations. The results allowed validating the choices made for the final R2D2 coils and heat treatment tooling to manage the longitudinal contraction and the transverse expansion.

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.

The Research Racetrack Dipole Demonstrator (R2D2) is being studied as a demonstrating magnet for future FCC magnets. The R2D2 is meant to prove the feasibility of grading in block-coil Nb $_{3}$ Sn dipoles and explore quench behaviors at a very high current. This short model provides an opportunity to study quench protection concepts which will be needed for the full-scale FCC magnets. Both quench heaters and CLIQ (coupling loss induced quench) are under study. This paper presents the research work on the CLIQ protection. The work includes CLIQ design methods and configurations, and comparative studies of various CLIQ configurations for maximizing the CLIQ effectiveness. The results show that the most effective CLIQ configuration is able to quench 80% of the coil turns at the nominal current within 3 ms, leaving 20 ms for detection and validation time while keeping the maximum hotspot temperature within 350 K. The study shows that protection of R2D2 using only CLIQ may be feasible under certain assumptions.

The quench protection for the Future Circular Collider (FCC) 16 T Nb 3 Sn dipoles was based either on the CLIQ (Coupling Loss Induced Quench) system, or on resistive quench protection heaters. Several heater designs were sketched during the iterative magnet design processes. This led to identifying some rules about an effective heater design in the full-scale 14-m-long magnets. Following the FCC study, short dipole magnet models are being built to test the novel features that were envisioned for the FCC magnets. In this work, we review the principles of effective heater design, and then apply this methodology to the graded block dipole short model R2D2, which is being designed at CEA Saclay. This magnet has high current density in copper after quench, which makes the protection challenging and requires pushing the heater technology to its limits.

In the framework of the NEWGAIN project, which aims to build a second injector with a mass to charge-state ratio A/q = 7 for the SPIRAL2 linear accelerator at GANIL, CEA is developing in collaboration with LPSC and GANIL a new superconducting 28 GHz ECR Ion Source Magnet named ASTERICS. The magnetic design is based on an advanced concept of the VENUS ECR ion source operating at Berkeley and the FRIB source under commisionning at MSU. The ion source superconducting magnet consists of a sextupole inside three solenoids to confine the plasma and a shell-based support structure to apply a preload to the sextupole coils. The confinement coils will be made in Nb-Ti and will be operated at 4.2 K. The cryogenic environment will be ensured by liquid helium thermosiphon closed loop thanks to six in-situ cryocoolers. Specific HTS current leads are being designed to power the magnet. A cold integrated He buffer will also allow He almost-lossless quenches. The preliminary design choices of the ASTERICS superconducting magnet are presented here from the magnetic, mechanical and protection design to the cryogenic definition emphasizing the global approach used to obtain the final magnet configuration.

In the framework of studies for high energy particle colliders, design concepts for high field dipoles are being explored. In particular, relatively compact 20 T magnets can be achieved in a hybrid configuration, combining a High Temperature Superconductor (HTS) and a Low Temperature Superconductor (LTS). Preliminary concepts have been previously proposed using Bi2212 for the HTS and Nb 3 Sn for the LTS. One of the main difficulties of 20 T magnets is the management of the very high stresses developing during operation. The design concepts rely on a rectangular block-coil layout, which offers the advantage of aligning the conductors with the main magnetic field, therefore submitting the conductors to a perpendicular electromagnetic force for a better control of the stresses. In addition, the layout allows a specific stress management, with adequate horizontal and vertical plates to intercept the stresses. The paper presents the improvements provided to the initial concept. In terms of magnetic design, the field quality has been improved. In terms of mechanical design, the stress management has been optimized to provide a compact coil with a reduced peak stress on the HTS. Concepts for flared-end coils with joints in the coil-ends are finally presented.

The most effective way to achieve very high collision energies in a circular particle accelerator is to maximize the field strength of the main bending dipoles. In dipole magnets using Nb-Ti superconductor the practical field limit is considered to be 8-9 T. When Nb3Sn superconductor material is utilized, a field level of 15-16 T can be achieved. To further push the magnetic field beyond the Nb3Sn limits, High Temperature Superconductors (HTS) need to be considered in the magnet design. The most promising HTS materials for particle accelerator magnets are Bi2212 and REBCO. However, their outstanding performance comes with a significantly higher cost. Therefore, an economically viable option towards 20 T dipole magnets could consist in an hybrid solution, where both HTS and Nb3Sn materials are used. We discuss in this paper preliminary conceptual designs of various 20 T hybrid magnet concepts. After the definition of the overall design criteria, the coil dimensions and parameters are investigated with finite element models based on simple sector coils. Preliminary 2D cross-section computation results are then presented and three main layouts compared: cos-theta, block, and common-coil. Both traditional designs and more advanced stress-management options are considered.

R2D2, the Research Racetrack Dipole Demonstrator, is a short model being developed within a collaboration between CEA Paris-Saclay and CERN. The goal of the program is to develop key technologies for future high field 16 T Nb3Sn magnets for particle colliders. In the particular case of block-coil designs, two different cable grades are wound in the same coil layer, in order to maximize the current density, therefore to minimize the size of the magnet and the use of superconductor. One of the most challenging technologies with this grading concept, is the connection between two cables grades. CEA Paris-Saclay has proposed a concept of external joints, for which the cable exits are guided outside of the coil to perform the connections between the cable grades. The R2D2 project is aimed at demonstrating this technology in a representative demonstrator magnet, while simplifying and reducing the risks when possible, as an intermediate step towards 16 T magnets. In particular, the magnet is composed of single-layer racetrack coils, mainly to reduce the use of conductor and simplify some fabrication steps. However, the complexity inherent to the external joints requires a special focus in the design of the coil ends. To do so, the design of the magnet has been performed using a combination of CAD (Computer Aided Design), magnetic and mechanical 3D FEM (Finite-Elements Models). This paper will explain the design choices leading to a safe operation of the magnet in terms of peak fields and peak stresses.

The 2020 update of the European Strategy for Particle Physics emphasised the importance of an intensified and well-coordinated programme of accelerator R&D, supporting the design and delivery of future particle accelerators in a timely, affordable and sustainable way. This report sets out a roadmap for European accelerator R&D for the next five to ten years, covering five topical areas identified in the Strategy update. The R&D objectives include: improvement of the performance and cost-performance of magnet and radio-frequency acceleration systems; investigations of the potential of laser / plasma acceleration and energy-recovery linac techniques; and development of new concepts for muon beams and muon colliders. The goal of the roadmap is to document the collective view of the field on the next steps for the R&D programme, and to provide the evidence base to support subsequent decisions on prioritisation, resourcing and implementation.

Future high energy particle colliders are under study, with a first goal of 16 T dipoles, which is believed to be the practical limit of Nb3Sn magnets. Another more ambitious goal is to aim for 20 T dipoles. This very high field would require High Temperature Superconductors (HTS), such as Bi2212 or REBCO. Their substantially higher cost necessitate anyways the use of Nb3Sn for an affordable accelerator application. Therefore, hybrid designs can be proposed, where the HTS are used in the high field (16–20 T) area, and Nb3Sn are used in the low field (<16T) area. Rectangular block-coil designs are particularly well adapted to this concept, since the separation between high field and low field can be made parallel to the cable turns, inside each layer of the coil. However, the large forces accumulating on the cable turns generate a high transverse stress detrimental to the coil. The paper presents a conceptual Hybrid Nb3Sn-HTS design generating 20 T in the bore with margin, using a block-coil concept. Several conductor options are discussed. The design also proposes stress-management solutions to deal with the large stress developing in the coils.

The European Laboratory Directors Group (LDG) was mandated by CERN Council in 2021 to oversee the development of an Accelerator R&D Roadmap. To this end, a set of expert panels was convened, covering the five broad areas of accelerator R&D highlighted in the ESPPU. The High Field Magnet (HFM) Panel is proposing a programme to demonstrate Nb3Sn magnet technology for large-scale deployment and to investigate the suitability of high temperature superconductors (HTS) for accelerator magnet applications. A summary of this programme is presented here.

For the Future Circular Collider hadron-hadron (FCC-hh), a 100 TeV post Large Hadron collider machine, 750 main quadrupoles with a 360 T/m gradient over a magnetic length of 7 m are required. They consist of a double aperture based on a laminated collar structure similar to the LHC MQ technology. In this paper, a preliminary 3D finite element analysis is performed to evaluate the stresses and strains of the complete magnet structure, with particular emphasis on maintaining coil pre-stress at the pole-coil interfaces under operation. Numerical results during preload, cool-down, and energization are presented in detail and discussed. The peak stress is of the order of 160 MPa in the Nb 3 Sn coil with a localized gap of less than 6 μm at the coil-pole interface under nominal operation. The stress in the mechanical structure is bearable with only high stress values confined to very small areas.