ReBCO coated conductors are a promising solution to be integrated in superconducting electrical machines due to their high transport current under high magnetic fields. However superconducting armature windings will be subjected to AC fields and AC currents, resulting in non-negligible loss. These losses need to be estimated to achieve feasible designs since they strongly decrease the performance of the superconductors, affecting machine operation. In numerical models, ReBCO tapes are often represented by a superconducting thin sheet due to their high aspect ratio. Nonetheless, research shows that at high currents and/or frequencies, the influence of the stabilizing copper layers in the coated conductor's losses can become significant. In this paper, we propose a 2D electromagnetic model based on the T-A formulation to include the effect of copper layers on current distribution and on the evaluation of losses through Finite Elements Method models. A ReBCO tape is investigated when different currents and magnetic fields (perpendicular to the tape surface) are imposed, and the magnetization and transport losses of the superconductors show good agreement with homogenized T-A formulation, experimental and analytical results.

Distributed Fiber Optic Sensors (DFOS) are being considered as an alternative solution for Quench Detection in HTS fusion magnets. Their successful application is not straightforward due to the simultaneous need for high spatial and temporal resolution over long-length conductors operating in demanding cryogenic environments. In this work, we explore the potential of two different commercially available distributed sensing technologies, respectively based on the analysis of Rayleigh-backscattering through Optical Time Domain Reflectometry (OTDR) and Optical Frequency Domain Reflectometry (OFDR). The two techniques were used first to characterize the cryogenic temperature response of similar fibers between room temperature and 4 K. The temperature sensitivities were computed and compared to those of Fiber Bragg Grating sensors, showing comparable results. The performance of the investigated techniques in detecting local quenches was then experimentally assessed in operating conditions on a 2-meter-long, aluminum-stabilized HTS sample cooled by Liquid Nitrogen flow. While OFDR needs improvements in temporal resolution, the limited scale of the hot spot represents a challenge for the OTDR technique due to its lower spatial resolution.

To satisfy requirements of high operating current densities, compact layouts, and the possibility to reach magnetic field higher than 20 T , at temperatures from 4.2 K to 20 K , e.g., necessary for the development of next generation of colliders, the CORC (R) cable concept is of particular interest. Based on ReBCO high temperature superconducting tapes wound around a copper former, it exploits round cross-section guaranteeing electrical and mechanical isotropy. However, these cables can degrade as a result of the winding process and operating conditions, as ReBCO tapes are strain-sensitive. This paper presents a 3D multi-physics numerical model for characterizing the critical current ( Ic ) of bended ReBCO CORC (R) cables, based on a T-A formulation implemented in COMSOL Multiphysics (R) coupled with a thermal model of a straight cable, already validated against experimental results. The tape is approximated as a thin shell, taking advantage of its high aspect ratio, and the Ic scaling for the tape accounts for the local strain. A pure geometrical strain evaluation on the tape surface allow to properly account for the punctual degradation of Ic , as an input for the multi-physics model. The assessment of the voltage-current curve for the bent conductor has been compared to experimental results.

The study of superconducting tapes requires specialized formulations to account for the high aspect ratio of the tapes and the extremely high conductivity of the thin superconducting layer. This article presents a new formulation coupling the line integral of the magnetic vector potential a defined in the whole domain to the stream function psi defined on the nodes of the super conducting layer. Results on two benchmarks show that the proposed a-psi formulation is effective in solving problems where the currents are limited to thin layers also in case of a strong material nonlinearity.

High-temperature superconducting-slotted cables, including the VIPER cable, are being investigated as possible candidates for winding the toroidal field coils of compact nuclear fusion machines, such as ARC. The higher performance of HTS materials in terms of magnetic fields and currents allows them to reduce their size compared to machines based on Nb alloys and compounds. However, compactness also means a closer interaction between the plasma products and the coils, creating new technological challenges to be faced. Among the others, the thermal effects induced on the superconducting materials by direct particles (i.e., neutrons), secondary particles and gamma-ray heating, will be stronger than for low-field larger machines and must be quantified. In this paper, a detailed thermo-magnetic model is built up using the software COMSOL Multiphysics to simulate the consequences of the D-T plasma operation products on the first turn of a toroidal field coil of the ARC preliminary machine design. The irradiation-induced heat load on the (RE)Ba2Cu3O7-δ tapes, computed via Monte Carlo simulations, is used as input for the thermal analysis of the VIPER cable. At the same time, a homogenized T-A formulation is developed for checking the performance reduction in the current/field operating conditions.

Future collider accelerators will rely on high-temperature superconductors reaching high field up to 20 T and above. Among the existing high-temperature superconducting materials, the Rare-earth Barium Copper Oxide (ReBCO) tapes arranged according to the Conductor-on-Round-Core (CORC®) concept could be a viable solution to wound accelerator magnets such as Cosine Canted Theta (CCT) magnets. Dedicated experimental characterization of the critical current to quantify the degradation due to the winding process and operating conditions should proceed in parallel to the development of numerical models capable to reproduce and, in perspective, predict the cable performance. This paper presents the development of a new multi-physics model for a CORC® wound with ReBCO tapes together with its validation. The $T-A$ formulation has been used leveraging the high aspect ratio of tapes, suitably coupled with a conduction thermal model which for the first time properly accounts for the cable convective cooling. The model developed in this work can accurately simulate the thermal, electric and magnetic behaviors and the current sharing among tapes by using a set of self-consistent boundary conditions adopted for the first time in this kind of simulations. The model is verified and benchmarked against other well-established formulations on a set of test cases. The comparison of the computed $V-I$ characteristic of the straight cable to available experimental data shows that the main physics features of the cable are well captured by the model, including performance degradation due to cable tapering at the terminations.

Predicting the performance and reliability of high-temperature superconducting (HTS) cables and magnets is a critical component of their research and development process. Novel mixed finite element formulations, particularly the h - φ -formulation with thin-shell simplification, present promising opportunities for more efficient simulations of larger geometries. To make these new methods accessible in a flexible tool, we are developing the Berkeley Lab Finite Element Framework (BELFEM). This paper provides an overview of the relevant formulations, discusses the current state of the art, and discusses the main aspects of the BELFEM code structure. We validate a first 2D thin-shell implementation in BELFEM against selected benchmarks computed in COMSOL Multiphysics and compare the performance of our code with a comparable formulation in GetDP. We also outline the next steps in the development process, paving the way for more advanced and robust modeling capabilities.

In this work, we presented the design of a module of a 10 MW toroidal SMES, tailored for a charge/discharge time of 1 s aimed at compensating the intermittency of a solar photovoltaic system. The design is performed through an approach based on the functional analysis: first, the functions that must be satisfied by the SMES are identified, together with constraints such as the performance of commercial YBCO tapes. Then, the pre-conceptual design of, among the different components, the winding pack and the cryostat is performed, to cope with the constraints and comply with the assigned functions. Finally, the design is verified through a detailed numerical analysis, checking that the requested function is in fact satisfied. The design leads to a multi-layer coil with radius ∼ 0.45 m, wound using a stack of 7 commercial 12 mm-width tapes with 52 layers in parallel, each with 26 turns. The total inductance is ∼2 H and a maximum self-field below 4 T. Nine modules are needed for the entire SMES, which is designed to operate at 50 K.

At the ENEA's research center of Frascati, the DTT (Divertor Tokamak Test) facility is currently under construction. The activity of this experimental nuclear fusion reactor, will be focused on the optimization of the power exhaust management in view of DEMO. The project has been started during year 2015, when also the superconducting magnet system has been initially designed, basing on the available inputs coming from physics and on the desired goals for the machine. At present, the coils engineering design has almost been completed and the production of crucial components, such as the superconducting strands, conductors and toroidal field coils, have already been started. For the remaining superconducting elements, the engineering design is being finalized and other tenders are going to be launched soon. The result is a compact and flexible tokamak, with highly demanding requirements in terms of superconducting and structural performances, sometime close to the intrinsic mechanical limits of the adopted materials. Tight constraints on time, budget and resources forced the design team to walk through a complex path in these years for reaching a sound and satisfactory design of the complete magnet system. In fact, it was not possible to rely entirely on state-of-the-art and already assessed superconducting technologies, as was initially assumed. In particular, the trade-off between limiting the R&D phase and extending the performance demonstrated in other projects to the specific DTT requirements, pushed the team to take some risks, while providing a robust and fully performing magnet system design.

Super-conducting cables are an enabling technology for energy applications such as large magnetic-confinement nuclear fusion machine, and a promising key player in the power transmission of the next future, both in AC and DC conditions. While the thermal-hydraulic analysis of forced-flow superconducting cables for fusion application can only rely on commercial or proprietary numerical tools, such kind of tools for power transmission cables are not even available. Within the framework of Open Science, set as a priority by the European Commission in Horizon Europe, the novel software OPEN Super Conducting Cables (OPENSC2) has been developed to grant the entire research community the possibility to simulate thermal-hydraulic transients in forced-flow superconducting cables for energy applications. A Test-Driven Development has been adopted for the OPENSC2 within an object-oriented approach. Following the TDD approach, three test cases are considered of paramount interest for the OPENSC2 development, deriving the set of characteristics that the target object-oriented tool should comply with, and namely: 1) a heat slug propagation along an ITER-like 2-region cable-in-conduit conductor, with a thousand of mm-size low-critical-temperature superconducting (LTS) strands, cooled by supercritical helium (SHe); 2) the heat diffusion across the cross section of a twisted-slotted-core cable-in-conduit conductor, with high-critical-temperature (HTS) superconducting tapes, for fusion application, cooled by SHe and 3) the nominal operation of a single-phase HTS High-voltage, Direct Current power cable, with a 2-cryostat configuration and 2 different fluids adopted as primary coolant and thermal shield. In the object-oriented OPENSC(2 )the class "conductor " is defined, where each Conductor Object (CO) is the combination of different lower-level objects (both fluid and solid components) instantiated by the class. The choice of each component drives the automatic selection of the appropriate physical equation(s) in the code, as well as the possible interactions between them. Thermo-physical properties of different materials and cryogens can be attributed to the components of a conductor objects, taken form open datasets. A user-friendly GUI allows setting and monitoring the simulations while running. The software is tested in the three case studies targeted in the TDD, to show eventually how it allows modeling the three test cases presented here. The Verification and Validation of the CO methods performed through benchmarks against the 4C code is also presented and discussed.

An overview of the main peculiarities of the models currently available in the literature for the thermal-hydraulic analysis of the cooling of the high critical temperature superconducting power transmission cables, mainly in nominal operating conditions, is performed. Several models address specific issues such as the temperature distribution along or across the cables, and their pressure drop, typically with a simplified approach. The verification and validation of the models has not been systematically addressed so far. From analysis of the available literature, the lack of a general model, capable to address thermal-hydraulic transients for the cooling of the different possible cable designs, with the capability to capture both the behaviour of the cable solid components and different cryogens, is highlighted. The main ingredients that such a general thermal-hydraulic model should not miss are presented, also based on the know-how on, and comparison to, similar tools for low critical temperature cables for nuclear fusion applications.

In the framework of Open Science, the OPENSC 2 open-source object-oriented software for multi-physics analysis has been developed to simulate the operating transients in forced-flow superconducting cables for fusion and power applications. Due to high magnetic fields and transport currents involved, the dissipated power by Joule effect and AC losses can compromise the thermal stability of the superconductors, so that the electromagnetic problem comes intrinsically with the thermal-hydraulic one. The numerical current distribution model, recently developed for OPENSC 2 , is reported here. After the solution verification and validation, followed by benchmarks against other software and experimental data, a first coupling with the thermal-hydraulic transients has been tested and reported in this work.

Colliders are built on a foundation of superconducting magnet technology that provides strong dipole magnets to maintain the beam orbit and strong focusing magnets to enable the extraordinary luminosity required to probe physics at the energy frontier. The dipole magnet strength plays a critical role in dictating the energy reach of a collider, and the superconducting magnets are arguably the dominant cost driver for future collider facilities. As the community considers opportunities to explore new energy frontiers, the importance of advanced magnet technology - both in terms of magnet performance and in the magnet technology's potential for cost reduction - is evident, as the technology status is essential for informed decisions on targets for physics reach and facility feasibility.

The Divertor Tokamak Test (DTT) facility, under construction in Frascati, Italy, will rely on a fully-superconductive magnetic system. Superconductive feeders, designed as Nb-Ti cable-in-conduit conductors, will run into the cryostat from the cold boxes to the magnet winding terminations. They will be cooled by Supercritical Helium at 0.6 MPa and 4.5 K, entering the cables at the location of the peak field. The feeders will be subject to AC losses during plasma operation, as well as radiative parasitic load from the thermal shield and Joule heating in the terminations. The minimum temperature margin, computed for the different feeders in the worst operating condition, is presented and discussed in this paper, showing the conservativeness of the design for such components.

High-field superconducting magnets with a dipole field of 16 T and above enable future energy-frontier circular particle colliders. Although we believe these magnets can be built, none exists today. They can also be a showstopper for future high-energy machines due to a prohibitively high price tag based on the current conductor and magnet fabrication cost. The high-temperature superconducting REBCO coated conductor can address both the technical and cost issues, a silver bullet to lay both monsters to rest. The challenges and unknowns, however, can be too arduous to make the silver bullet. We lay out a potential road forward and suggest key action items. As a contribution from the accelerator community, we attempt to clarify for our theorist and experimenter colleagues a few aspects about the future high-field superconducting magnets. We hope to stimulate an effective plan for the 2023 P5 process that can lead to a cost-effective high-field magnet technology for future colliders and the exciting physics they can steward.

The design of the superconducting magnet system of the EU-DEMO tokamak reached the end of the preconceptual design phase, and a careful investigation of the parasitic heat load from the room-temperature environment is needed. A possible route for the parasitic heat to enter the toroidal field (TF) coils is by conduction through their Gravity Supports (GSs), which provide mechanical support to the TFs, the Vacuum Vessel (VV) and attached coils, acting as a thermal bridge to the TF casing. A thermal anchoring of the GS using Supercritical helium (SHe) at 4.5 K, re-routing a fraction of the coolant from the TF casing cooling loop, downstream of the casing, is addressed in this study. A 3D thermal model is developed for a plausible design of the EUDEMO GS, coupled to fluid lines that account for the active cooling by SHe. The effect of the location of the Thermal Anchor (TA) at different heights of the GS plates is investigated parametrically and the beneficial reduction of the parasitic heat load to the TF coil is demonstrated. The reduction of the static heat load to the TF winding pack, when the TA is enabled, is computed and discussed.