We present a concept of the superconducting ReBCO dipole magnet for ramping range up to 10 kT/s as possibly required for the muon acceleration (Chance 2023) in a future Muon Collider presently under study (Palmer 2013), (Accettura et al., 2024), (Jindariani et al., 2025). This approach is based on the 6 kA CORC-like cable constructed with 12 ReBCO tapes of 2 mm width. Based on theoretical prediction (Solovyev et al., 2023) there is a linear scaling of the ReBCO cable hysteresis loss with the crossing magnetic field possibly generating power loss independent of the magnetic field ramping rate. This feature makes this ReBCO cable suitable for the construction of rapid-cycling magnets. In this work we outline the design of a dipole magnet for 2T gap magnetic field and discuss the helium coolant parameters for the minimal electric power.

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.

State-of-the-art Nb3Sn superconducting accelerator magnets are still prone to lengthy training. This study investigates whether direct heat from fractures in commonly used magnet impregnant is sufficient to cause the instabilities during training. To do so, the strain energy release rate of CTD-101 K epoxy is measured in liquid nitrogen at 77 K, together with the temperature of a nearby copper element representing a Nb3Sn strand in the magnet windings. This experiment provides evidence that a large part of the mechanical energy is converted into heat. An analytical model using strain energy release rate data of impregnates at 4.2 K shows that this heat can contribute to the first quenches during magnet training.

In the quest for climate neutrality in the aviation industry by 2050, technology development is one of the main pathways for Airbus. Owing to their high efficiency and current density, use of superconducting DC and AC distribution lines are a potential enabler for fully electric propulsion in a longer range aircraft, in particular in the scenario where liquid hydrogen provides a cold source on board of the aircraft. The ground-based Advanced Superconducting and Cryogenic Experimental power traiN Demonstrator (ASCEND) at Airbus intends to demonstrate the potential and feasibility of a cryogenic and superconducting powertrain as a breakthrough electric propulsion solution on future electric aircraft. A direct current distribution network is used in a generic propulsion system to transfer 500 kW power from the DC supply to an electrical converter, which transforms the energy into an alternating voltage/current to drive the superconducting motor. A relatively low voltage level of 300 V, and a current of 1700 A, is chosen to optimize the safety and installation in a future aircraft by operating at relatively low voltage. The DC link consists of a 10 m long two-pole superconducting Conductor on Round Core (CORC) cable, and demountable current leads, that transfer the power from the room temperature environment to the cryogenically cooled motor control unit. Downstream of this unit a 3-phase AC link operating at 500 Hz delivers power to a superconducting motor. Both the AC and DC links are cooled with a flow of subcooled LN 2 . The components of the DC and AC links have been designed, manufactured and recently integrated into the ASCEND test bench in Ottobrunn, Germany. We present the powering of the DC link up to nominal current, as well as commissioning and integration experience.

A very wide range of operational temperatures of the HTS (YBCO) superconductor makes it suitable for the construction of rapid-cycling magnets required for the muon acceleration. The measured [3] very low power loss of the 0.4 T magnet operating at 300 T/s suggested a realistic possibility of the HTS-based accelerator magnet with much higher magnetic field and ramp rate. The magnet core and the HTS cable designs for the 2 T field in the 30 mm beam gap are presented. The simulation of the HTS cable hysteresis power loss for the 1000 T/s ramp rate is discussed in terms of the operational temperatures and required cryogenic power.

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 paper investigates transport AC loss in CORC cables for the ground-based demonstrator ASCEND at Airbus, which studies the feasibility of a superconducting powertrain for electric aircraft. The demonstrator includes a three-phase AC link consisting of three parallel cables operating at 500 Hz and 2350 A peak current. The transport AC loss of the three-phase cable is estimated using a 2D model assuming equal current in all tapes. The model predicts an AC loss of 40 W at 77.5 K and 0.4 W at 65 K. A second model is proposed, which computes the current distribution between the tapes in a single cable using mutual inductance matrices for helical tape conductors. This model predicts that, at 500 Hz, the outer two layers of a CORC cable carry a disproportionate fraction of the current. This will lead to additional AC loss if the critical current in the outer layers is exceeded. AC transport loss was measured on single CORC cables. Both models significantly underestimate the measured loss. Also, a frequency-dependent quench current below the DC critical current was observed at 48 Hz and 96 Hz.

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.

Re BCO racetrack coils may be used in high-dynamic superconducting linear motor systems, typically replacing either permanent- or electromagnets in the DC stator. Even so, in order to achieve a significant increase in force density, the superconductor needs to carry a high transport current while simultaneously experiencing the time-varying magnetic field from the copper mover coils. To aid with the design of such devices, a 2D numerical model has been developed that predicts the AC loss under motor-relevant conditions, i.e. under the combined influence of a stationary transport current and an alternating external magnetic field. The main aim of the experiments described in this paper is to validate this model with dedicated AC loss measurements. To this end, we constructed a set-up that simultaneously measures magnetization-, transport current- and overall AC loss. Two identical insulated sub-scale Re BCO racetrack coils were tested at 4.2 K while carrying a stationary transport current of up to 700 A in a sinusoidal, alternating magnetic field up to 1.5 T, applied perpendicular to the broad face of the windings. Just like with metallic superconductors, the transport current significantly increases the AC loss level and lowers the penetration field. The inductive, electric and calorimetric data were found to be consistent with each other, validating the experimental calibration methods involved. Furthermore, the numerical model accurately predicted all AC loss components in the coils without any fitting to the data and can thus reliably be used in the design of superconducting machines.

The ground-based Advanced Superconducting and Cryogenic Experimental power train Demonstrator (ASCEND) at Airbus intends to demonstrate the potential and feasibility of a cryogenic and superconducting powertrain as a breakthrough electric propulsion solution on future electric aircraft. A direct current distribution network is used in a propulsion chain to transfer 500 kW of power from the source to an electrical converter, which transforms the power into an alternating voltage/current to drive a superconducting motor. The working point of 1,700 A and 300 V is chosen for safety and installation reasons by operating at relatively low voltage. The direct current (DC) bus of ASCEND will be formed by a pair of high-temperature superconducting CORC cables inserted into a 10-meter-long narrow cryostat, resulting in a compact and lightweight solution. The 2-meter-long alternating current (AC) bus between the inverter and the electric motor is formed by a three-phase CORC cable. The challenge associated with 500 Hz operation in which a balance between AC loss in the cable and the size and mass of the system needs to be found, will be outlined. The AC and DC buses include several devices that connect the liquid nitrogen cooled power cables with the other system components that, in the case of the room temperature generator, operate at significantly higher temperatures. These devices thus include conduction-cooled current leads that are dimensioned to minimize the heat inleak from the warm to the cold environment. An overview of the design of the AC and DC buses and connecting devices will be provided and some of the design and operational challenges will be outlined.

Training of accelerator magnets is a costly and time consuming process. The number of training quenches must therefore be reduced to a minimum. We investigate training of impregnated Nb 3 Sn Rutherford cable in a small-scale experiment named BOX (BOnding Experiment). The test involves a Rutherford cable impregnated in a meandering channel simulating the environment of a canted-cosine-theta (CCT) coil. The sample is powered using a transformer and the Lorentz force is generated by an externally applied magnetic field. The low material and helium consumption enable the test of a larger number of samples. In this article, we present training of samples impregnated with alumina-filled epoxy resins, a modified resin with paraffin-like mechanical properties, and a new tough resin in development at ETH Zürich. These new data are compared with previous results published earlier. Compared to samples with unfilled epoxy resin, those with alumina-filled epoxy show favorable training properties with higher initial quench currents and fewer training quenches before reaching 80% of the critical current.

No-insulation coils are self-protecting and can therefore generally be operated at higher current densities. However, the electrical turn-to-turn connections may cause additional AC loss when charging the coil or when it is exposed to a time-dependent magnetic field. In this work, we study the case of a no-insulation Re BCO tape racetrack coil exposed to a uniform AC field applied parallel to the tape surface. We show that an anisotropic continuum model allows to formulate analytical approximations for coupling loss in the low- and high-frequency limits. For intermediate frequencies, the continuum model needs to be evaluated numerically. The model was validated with representative measurements of AC loss in the coils, measured calorimetrically as well as magnetically using pick-up coils. The validation experiment confirms the predicted frequency dependence of the coupling loss, which is P ∝ f 2 at low frequencies and P ∝ f at high frequencies, due to the skin effect. The transition between low- and high-frequency regimes occurs around a characteristic frequency f c that is directly related to the characteristic time constant τ = 1 / 2 π f c associated with the current decay in (dis)charge experiments.

The development of ever smaller medical particle accelerators is motivated by a desire to make proton therapy accessible to more patients. Reducing the footprint of particle accelerators and subsequently proton therapy facilities allows for cheaper and broader usage of proton therapy. By employing superconducting technologies for field shaping, the size of particle accelerators can be reduced further below what is possible with saturated iron. This article discusses experiments on a first-of-its-kind double pancake (DP), and an assembly of six DP coils, designed to be used as a so-called ‘flutter coil’ for a compact isochronous cyclotron for proton therapy, fabricated from high-temperature superconducting (HTS) Bi 2 − x Pb x Sr 2 Ca 2 Cu 3 O y (Bi-2223) tape. The coils were mounted under pre-stress within a stainless-steel structure to maintain mechanical stability during the experiments. The critical current as a function of the temperature of both coils was measured in a conduction-cooled setup. A model describing the coils, based on tape data, was created and revealed that the measurements were in excellent agreement with the predictions. Additional experiments were performed to study the quench and thermal runaway behaviour of the HTS coils, determining whether such coils can be protected against fault scenarios, using realistic quench-detection levels and discharge extraction-rates. These experiments demonstrate that the coils are very robust and can be well protected against quenches and thermal-runaway events using common quench-protection measures with realistic parameters.

ReBCO coils are developed as DC field coils in linear motor systems to increase the force density, in favor of permanent magnets. Such coils have to sustain a relatively large heat load stemming from the AC magnetic field environment in which they operate. The use of no or partial turn-to-turn insulation can make them more stable against the effects of local heating. Conversely, the radial electrical connections in no-insulation (NI) coils allow for large coupling currents, causing additional AC loss on top of the already significant heat load. Here we report on the AC loss in sub-scale NI, 4 mm wide single-tape, ReBCO racetrack coils exposed to parallel-to-the-tape magnetic field in the frequency range of 10(-4) to 1 Hz at 77 K and 4.2 K, while carrying a DC transport current. AC loss is measured magnetically and electrically. The main goal of these experiments is to validate our 2D numerical model, which provides more insight into the origin of the AC loss. At low frequencies, inter-turn coupling currents are spread more or less homogeneously throughout the winding pack. Whereas at high frequencies, the skin effect causes shielding of the interior of the coil and large induced currents only occupy the coil's outer surface.

Training of accelerator magnets is a costly and time consuming process. The number of training quenches must therefore be reduced to a minimum. We investigate training of impregnated Nb3Sn Rutherford cable in a small-scale experiment. The test involves a Rutherford cable impregnated in a meandering channel simulating the environment of a canted-cosine-theta (CCT) coil. The sample is powered using a transformer and the Lorentz force is generated by an externally applied magnetic field. The low material and helium consumption enable the test of a larger number of samples. In this article, we present training of samples impregnated with alumina-filled epoxy resins, a modified resin with paraffin-like mechanical properties, and a new tough resin in development at ETH Zürich. These new data are compared with previous results published earlier. Compared to samples with unfilled epoxy resin, those with alumina-filled epoxy show favorable training properties with higher initial quench currents and fewer training quenches before reaching 80 current.

Resin-impregnated high-field Nb3Sn type of accelerator magnets are known to require extensive training campaigns and even may exhibit performance-limiting defects after thermal or electromagnetic cycling. In order to efficiently explore technological solutions for this behaviour and assess a wide variety of impregnation material combinations and surface treatments, the BOnding eXperiment (BOX) sample was developed. BOX provides a short-sample test platform featuring magnet-relevant Lorentz forces and exhibits associated training. Here we report on the comparative behaviour of BOX samples comprising the same Nb3Sn Rutherford cable but impregnated either with common resins used in high-field magnets, or with less conventional paraffin wax. Remarkably, the two paraffin wax-impregnated BOX samples reached their critical current without training and are also resilient to thermal and mechanical cycling. These rather encouraging results strongly contrast to those obtained with resin impregnated samples, which show the characteristic extensive training and at best barely reach their critical current value.

For 30 years, training and unpredictable degradation in accelerator type high-field Nb3Sn magnets have seriously hampered Nb3Sn application. Training and deterioration have to be solved or at least better controlled. The global picture shows that most of the R&D and short model magnets start to train at some 40%–70% of the critical current and then creep up to almost the critical current within some 10–50 training steps. A typical class of failures leading to quenches is largely characterized by cracking and debonding at the interfaces between cable and glass-resin insulation, as well as between insulation and coil former. The study of training by means of testing demonstrator coils is rather expensive and time consuming. However, advances in magnet design and fabrication can also be assessed and benchmarked using BOX, the bonding experiment presented here, that produces maximum uniaxial Lorentz forces at some 7.5 T in a controlled experiment performed in 11 T solenoid facility at the University of Twente. BOX samples use only one meter of Nb3Sn cable inserted in a three-wave meandering slot in a flat metallic sample holder, reproducing magnet-relevant interactions between cable, insulation, impregnated materials and coil former. The meander shape exposes seven straight cable sections to a transverse magnetic field, thereby generating a representative level of shear stress at the interfaces. In this way, characteristic training curves of magnets can be mimicked and solutions studied. We aim to demonstrate with various samples failure mechanisms of high-field Nb3Sn magnets without the need to manufacture complete magnets. BOX may thus be expected to allow for quick and affordable testing of novel insulations, impregnation materials, coatings and interfaces for Nb3Sn magnets achieved by investigating various resins, fillers and more.

When exposed to time-dependent magnetic fields, REBCO Roebel cables generate AC loss resulting from both magnetic hysteresis and induced inter-strand coupling currents. Until now, the AC loss has been computed in a two-dimensional approximation assuming fully coupled or decoupled strands, and a finite inter-strand resistance could be simulated only with three-dimensional models. In this work, we propose a homogenization procedure that reduces the three-dimensional geometry of the Roebel cable to two dimensions, without ignoring connections between the strands. The homogenized cable consists of two parallel 'monoblocks' with an anisotropic resistivity. The proposed model enables computation of AC coupling loss without the need for complex three-dimensional simulations. For experimental validation, a Roebel cable with soldered strands was prepared. The inter-strand resistance was determined by applying a transverse current and measuring the voltage profile. Additionally, the AC magnetization loss of the cable was measured in fields of 1 to 50 mT with frequencies of 1 to 2048 Hz using a calibration-free technique. With the measured inter-strand resistance as input parameter, the monoblock model gives a good estimate for the AC loss, even for conditions in which the coupling loss is dominant.

The current distribution in a superconductor is commonly calculated by solving the Maxwells equations in differential form. An alternative method based on an integral form of Maxwells equations was proposed by E. H. Brandt. Since the integral formulation needs to be solved in the conductor volume only, this method can be easily implemented in a programming language such as MATLAB. Brandts approach has been used by several authors over the years, but no ready-to-use implementations are available. In this article, we present a step-by-step derivation of the method for a thin strip, a rectangular bar, and a cylindrical bulk. The results are validated using a comparison with exact solutions of the critical state model and a finite element solution of the $H$-formulation.