Arjan Verweij

In this paper, we present the distributed inter-strand coupling current (DISCC) model. It is a finite element (FE) model based on a homogenization approach enabling efficient and accurate simulation of the transient magnetic response of superconducting Rutherford cables without explicitly representing individual strands. The DISCC model reproduces the inter-strand coupling current dynamics via a novel mixed FE formulation, and can be combined with the reduced order hysteretic magnetization and flux models in order to reproduce the effects of internal strand dynamics: hysteresis, eddy, and inter-filament coupling currents, as well as ohmic effects. The DISCC model offers a massive reduction of the computational time compared to fully detailed FE models and still accounts for all types of loss and magnetization contributions. As a result, Rutherford cables homogenized with the DISCC model can be directly included in FE models of magnet cross-sections for efficient electro–magneto–thermal simulations of their transient response. We present two possible FE formulations for the implementation of the DISCC model, a first one based on the h – φ -formulation, and a second one based on the h – φ – a -formulation, which is well suited for an efficient treatment of the ferromagnetic regions in magnet cross-sections.

A high-gradient (361 T/m) Nb₃Sn lattice quadrupole magnet (MQ) is being developed for the proposed Future Circular Collider hadron-hadron (FCC-hh) for operation at 1.9 K. The very high winding energy density of this magnet (61 MJ/m³) makes quench protection especially challenging. Limiting the hot-spot temperature and peak voltage-to-ground requires a system that rapidly transitions most of the windings into the normal state. This paper evaluates three protection methods: Quench Heaters (QH), the Coupling-Loss Induced Quench (CLIQ) system, and a novel method, Energy Shift with Coupling (ESC). ESC enables fast and effective quench initiation without direct electrical connection to the magnet coils. The scope includes analyzing hardware requirements, such as CLIQ and ESC unit energy, and ESC coil geometry. Failure cases for ESC were also studied to assess redundancy. Electromagnetic-thermal transient simulations were performed with the STEAM-LEDET. Results show that QH cannot protect this magnet, while CLIQ is effective only within a narrow energy range, limited by its switching current capability. ESC provides robust protection across the full current range with lower component stress and intrinsic redundancy from its per-pole implementation. ESC, therefore, emerges as the most promising candidate for FCC-hh MQ protection.

Volume 1 of the FCC Feasibility Report presents an overview of the physics case, experimental programme, and detector concepts for the Future Circular Collider (FCC). This volume outlines how FCC would address some of the most profound open questions in particle physics, from precision studies of the Higgs and EW bosons and of the top quark, to the exploration of physics beyond the Standard Model. The report reviews the experimental opportunities offered by the staged implementation of FCC, beginning with an electron-positron collider (FCC-ee), operating at several centre-of-mass energies, followed by a hadron collider (FCC-hh). Benchmark examples are given of the expected physics performance, in terms of precision and sensitivity to new phenomena, of each collider stage. Detector requirements and conceptual designs for FCC-ee experiments are discussed, as are the specific demands that the physics programme imposes on the accelerator in the domains of the calibration of the collision energy, and the interface region between the accelerator and the detector. The report also highlights advances in detector, software and computing technologies, as well as the theoretical tools/reconstruction techniques that will enable the precision measurements and discovery potential of the FCC experimental programme. The content and structure of this report are guided by the scope and priorities defined in the mandate of the FCC Feasibility Study. It is therefore not intended to serve as an exhaustive review of the full physics potential of FCC. Several topics, already covered in earlier reports such as the FCC CDR, are not reiterated here or are addressed only briefly, in alignment with the study’s focus. This volume reflects the outcome of a global collaborative effort involving hundreds of scientists and institutions, aided by a dedicated community-building coordination, and provides a targeted assessment of the scientific opportunities and experimental foundations of the FCC programme.

In this paper, we present the Reduced Order Hysteretic Flux (ROHF) model to describe the relationship between time-varying transport current and internal magnetic flux for composite superconductors. The ROHF model is parametrized using reference simulations of the conductor response, after which it enables the computation of macroscopic quantities such as voltage and power loss without requiring detailed electromagnetic field solutions. It is therefore suitable for the homogenization of transport current effects in large-scale superconducting magnets, avoiding a fine discretization of the composite strand small-scale structures, allowing to drastically reduce the computational effort. The approximation can be implemented either (i) as a rate-independent model, neglecting eddy current effects in the normal conducting matrix, or (ii) as a rate-dependent model, including those eddy current effects. In this paper, the complete modeling workflow, including parameter identification, coupling with the other fields (temperature and magnetic field), and post-processing of the results, is described and verified using a twisted multifilamentary strand as an example.

Thermal transient responses of superconducting magnets can be simulated using the finite element (FE) method. Some accelerator magnets use cables whose electric insulation is significantly thinner than the bare electric conductor. The FE discretisation of such geometries with high-quality meshes leads to many degrees of freedom. This increases the computational time, particularly since non-linear material properties are involved. In this work, we propose to use a thermal thin-shell approximation (TSA) to improve the computational efficiency when solving the heat diffusion equation in two dimensions. We apply the method to compute the thermal transient response of superconducting accelerator magnets used for CERN’s Large Hadron Collider (LHC) and High-Luminosity LHC (HL-LHC). The TSA collapses thin electrical insulation layers into lines while accurately representing the thermal gradient across the insulation’s thickness. It allows considering cryogenic cooling via a temperature-dependent heat transfer coefficient and multi-layered quench heater (QH) regions. The TSA is implemented in the multipole module of the open-source Finite Element Quench Simulator (FiQuS), which can generate the multipole magnet models programmatically from input text files. The modifications implemented in FiQuS when constructing the geometry and mesh for the TSA model are discussed. First, the TSA approach is verified by comparison to classical FE simulations with meshed surface insulation regions for a simple block of four superconducting cables and a detailed model of the single-aperture Nb₃Sn magnet bending high field (MBH) dipole. The results show that the TSA approach reduces the computational time significantly while preserving the accuracy of the solution. Second, the QH delay, i.e. the time between activation of the QH and the point in time where the transport current density exceeds the homogenised critical current density in one of the superconducting half turns, computed with the TSA method is compared to measurements for the MBH magnet. To this end, the thermal transient simulation is coupled to a magnetostatic solution to account for magneto-resistive effects. Third, the TSA’s full capabilities are showcased in non-linear magneto-thermal simulations of several LHC and HL-LHC superconducting magnet models. The full source code, including input files to recreate all simulations, is publicly available.

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.

The Fusillo project at CERN aims to design and build a demonstrator magnet with multi-harmonic corrected fields in a 90°, curved, Canted-Cosine-Theta magnet. Two subscale magnets are built with 30° bending, about 1/30 of the demonstrator conductor length, and increased current to reach coil stresses equivalent to those of the demonstrator. These magnets enable qualification of the technology developments, fabrication methods, winding and assembly procedures, magnetic and quench protection design and measurement setups. The second Fusillo subscale magnet had dedicated instrumentation, including temperature sensors, a heater on the aluminium formers, and a set of sensing coils positioned in the curved bore. The magnet voltage and current were also measured. A specific powering sequence was applied to the magnet, including forced energy extractions. The eddy currents and heat propagation in the formers and the windings are simulated in three dimensions. A cooperative simulation approach was used, which involves tools developed at CERN as part of the STEAM framework: FiQuS, a finite element-based tool, and LEDET, a finite difference-based tool. The measurement results are compared with simulations, and the key aspects of the magnet transient behaviour are discussed. The simulation model inputs are refined using the measurement results, and the methodology for doing this is presented.

The Large Hadron Collider (LHC) includes eight main dipole circuits, each containing 154 superconducting magnets. We are carrying out simulations of the electromagnetic thermal behavior of these circuits, together with experimental tests and continuous monitoring, to ensure their safe operation and to further improve our understanding. Accurately modeling these eight circuits is very challenging. This is due to the interactions between the 154 magnets in each circuit and due to small variations in the physical properties of the magnets, e.g. due to component tolerances which introduce numerous unknown parameters into the model. In this contribution, we propose a method to optimize these large parameter sets efficiently, using a novel software module that combines our previously in-house developed circuit simulation framework with Dakota, an open-source parameter optimization toolkit. We demonstrate the effectiveness of this approach by optimizing a new simulation model of the dipole magnet by-pass diodes. Improving the accuracy of the model may in the future allow the identification of magnets and circuit components with non-conform behavior, and the reconstruction of failure cases for which no measurement data are available.