Superconductor Science and Technology

In many high-temperature superconducting applications, the advantages of no-insulation (NI) coils, such as self-protecting capability and thermal stability, make them a promising alternative to insulated (INS) coils. Magnetisation loss will be generated when the coil is exposed to time-varying magnetic fields. This loss can vary with the applied field angle, magnitude, and frequency, resulting in parasitic heat loads. In this study, we investigate magnetization loss in NI and INS double-pancake and double-racetrack coils of identical dimensions, experimentally and numerically. Experiments were conducted at 77 K under external AC magnetic fields up to 100 mT, considering various field angles (0°–90°) and frequencies (73–146 Hz). The experimental results are compared with the finite element simulation results of the coils' three-dimensional models. Interestingly, NI coils exhibit no significant angular dependence of loss within a specific field range; however, beyond this range loss increases with increasing field angles. In contrast, the loss in INS coils consistently increases with decreasing field angles across the entire field range. Coil level shielding of the magnetic field is observed in NI coils under parallel fields which is similar to a bulk superconductor. The losses in INS and NI coils are comparable under a perpendicular magnetic field, which can be attributed to the dominance of superconducting currents, as confirmed by the current and field distributions observed in simulations.

Both electrical and magnetic properties of superconductors are determined by the vortex matter as well as its dynamics. The systematic understanding of the distribution and interaction of vortices in superconducting strips is important for the application of superconducting devices. Here, by using a low-temperature scanning Hall probe microscope, we performed direct visualization of vortex patterns in superconducting strips of different widths. A vortex lattice transition from 1D to 2D is observed and further confirmed based on the analysis of the intervortex distances. We have found that, at low magnetic fields, the 1D lattice formed due to strong domination of the confinement effect over vortex–vortex repulsion can be well fitted by the theoretical values, which take into account the full vortex expulsion field. At intermediate magnetic fields, there exists the phase with a zig-zag vortex lattice in narrow samples. Finally, at the high enough magnetic fields, the effect of vortex mutual repulsion becomes dominant, and the 2D Abrikosov lattice is formed. The results of numerical simulations well reproduce our experiments. A phase diagram of vortex pattern evolution with magnetic field is established. Our work illustrates how the vortex pattern evolves in narrow superconducting strips, and provides a new insight to design superconducting devices for practical applications.

We report on the design and implementation of adiabatic quantum flux parametron (AQFP) buffer gates utilizing cross-type Nb/AlO_x/Nb Josephson junctions with I_C of 20 μA, designed to operate at mK temperatures. We, therefore, discuss design considerations, circuit simulation and optimization and their technological implementation. The preliminary results of the test circuit at 4.2 K are demonstrated focusing on the performance. Particularly, we emphasize on the current sensitivity of the circuit based on the output switching probability. The measurement results, show a narrow grayzone width of 0.48 μA for low-speed operation, demonstrating a higher current sensitivity. Additionally, the designed AQFP circuit exhibits a wide operating margins, further endorsing their potential for high sensitivity based superconducting sensors and scalable interface circuits for quantum electronics.

High-temperature superconducting (HTS) flux pumps eliminate the need for bulky current leads and high-current power supplies when charging superconducting devices. In such systems, superconducting switches are essential for optimal performance. Typically, the switch critical current is designed above a certain threshold, such as twice the load critical current, to prevent operation in the overcritical regime where the switch current exceeds its critical current. However, due to limitations in the fabrication process and potential performance degradation during operation, the switches may fail to meet this condition, leading to changes in the performance of the flux pumps. This paper experimentally investigates the impact of the switch overcritical regime on the performance of an AC field-controlled transformer-rectifier HTS flux pump, revealing that how the output voltage and charging current vary with key operating parameters, including the amplitude and frequency of the transformer primary current, as well as the amplitude, frequency, and duration of the switch electromagnet (EM) current. No-load voltage tests show that when the switch enters the overcritical regime, the output voltage decreases as the transformer secondary current increases, due to the generation of flux flow resistive after the switch is switched off. Charging tests revealed that once the switch current reaches its critical current, the charging process halts prematurely. Afterward, increasing the EM current slightly boosts load current, while increasing the transformer current significantly reduces it. Additionally, we observed that the load was charged when only the switch was powered, suggesting the possibility of eliminating the transformer power supply. Based on experimental results, it is predicted that the switch critical current must be at least 1.66 times the load critical current to fully charge the load in our flux pump.

Vanadium trioxide (V₂O₃) is an ideal candidate for electrical insulation materials in rare-earth barium copper oxide (REBCO) magnet applications owing to its metal-to-insulator transition (MIT) behaviour that is facilitated by its adjustable resistance, which shifts from high (at temperatures below 77 K) to low (above the transition temperature of ∼160 K). Optimising the turn-to-turn contact resistance (R_ct) in both normal and quenched states provides the benefits of both insulated and non-insulated (NI) winding methods. To implement V₂O₃ as a turn-to-turn insulator in REBCO magnets, ensuring responsive MIT activation between the turns is crucial. This study experimentally investigated the electrical behaviour of V₂O₃ insulation, which undergoes an electrical phase transition thermally triggered by transport current flow between the turns. Current–voltage (I–V) tests were performed on sandwiched REBCO tape samples with and without V₂O₃ insulation to analyse the electrical and thermal reactions. The I–V tests included stepped and pulsed current ramping to examine the repetitive behaviours under varying conditions. Furthermore, we verified the effect of mixing metal powder with V₂O₃ on the I–V characteristics. The results suggest that V₂O₃ insulation produces nonlinear I–V characteristics due to its negative temperature dependence, while the NI samples display linear I–V properties. The MIT characteristics of V₂O₃ insulation were reproducible across different current transport patterns and repeatable over thousands of cycles. Moreover, I–V measurements revealed that increasing the metal powder concentration reduced the R_ct values in the V₂O₃-insulated layer. Thus, maintaining high R_ct values (∼10⁷−∼10⁴μΩ cm²) in the normal operating range of below 77 K in REBCO magnets can effectively mitigate leakage current issues in the no-insulation winding technique. Conversely, transitioning to low R_ct values (∼10³μΩ cm²) in the transient operating range above 160 K is expected to minimise stability degradation caused by quenching or extended thermal runaway in the insulation winding technique. These findings provide valuable insights in designing V₂O₃-insulated REBCO magnets for diverse applications, such as rotating machines, accelerator and superconducting magnetic energy storage.

The high-temperature superconducting (HTS) closed-loop coil, characterised by shorted coil terminals and the low resistance of HTS conductors, can sustain a persistent DC current with minimal decay. These coils enable the generation of a DC magnetic field without the need for current leads or a power supply during operations, offering several advantages: (i) the development of compact, lightweight and portable DC magnet systems; (ii) the elimination of heat leakage and ohmic losses associated with current leads; and (iii) the removal of magnetic field harmonics caused by current supply. Recent advancements have revealed promising applications for HTS closed-loop coils, including maglev trains, nuclear magnetic resonance, scientific instruments, and energy storage systems. This paper firstly reviews various HTS closed-loop coils constructions, focusing on their distinctive characteristics. Then, the key research aspects of HTS closed-loop coils are overviewed, highlighting the latest advancements in persistent-current joint technologies, excitation methods, current control methods, current decay mechanisms and suppression techniques, simulation models, and quench detection and protection methods. Next, the applications of HTS closed-loop coils are analysed, emphasising their current status and future challenges. A detailed account is provided of our group's progress in developing an electrodynamic suspension train in Changchun, China, where all onboard magnets exclusively utilise HTS closed-loop coils. Finally, suggestions for future research directions are proposed.

The discovery of rare-earth barium copper oxide (REBCO) materials with high critical temperatures, and the continued advancements in the fabrication of REBCO coated conductors with extremely high critical current densities, has enabled the development of ultra-high-field (>20 T) compact and large-scale thermonuclear fusion devices. At present, around a dozen global commercial manufacturers are able to supply high-quality REBCO coated conductors with excellent performance. Significant advancements have been made for high-temperature, low-field applications such as motors, generators, long-length transmission cables, and so on using REBCO coated conductors. Nonetheless, multiple ongoing critical challenges under low-temperature, high-field conditions, such as irreversible degradation of the critical current, along with insufficient mechanical protection and inadequate reduction of AC losses, remain unsolved, collectively hindering their utilization in high-field thermonuclear fusion reactors. This paper provides a comprehensive theoretical and technical review of the current state-of-the-art, associated challenges, and prospects in the research and development (R&D) of REBCO coated conductors, cables, and magnet systems for high-field fusion. It highlights the significant enhancements in current-carrying capacity, mechanical protection, and AC loss reduction achieved over the past decade. The paper delves into detailed analyses of potential cabling solutions that offer exceptional current-carrying capacity while ensuring an optimal inductance balance for toroidal, poloidal, and central solenoid coils in tokamak devices. This work endeavours to lay the groundwork for the R&D of the next-generation REBCO magnets to facilitate the construction of ultra-high-field compact and large-scale tokamak reactors.

Due to the excellent electrical conductivity, superconducting materials are playing an increasingly important role in high-field applications. Lots of superconducting applications rely on the electromagnetic interaction between the permanent magnet (PM) and superconductors in different forms of tapes, bulks and coils. Recently, an electromagnetic interaction between the closed superconducting coil (SC) and the moving PM has been researched with interest. This electromagnetic interaction can both induce and utilize the current in the closed SC, thus achieving the mutual conversion between mechanical and electromagnetic energy wirelessly. In this review, all recently published works about this electromagnetic interaction have been summarized, from aspects of interaction behaviors, mechanism, numerical models, key influence factors and applications. These studies have laid a solid foundation for the follow-up researches.

Superconducting (SC) magnets can generate exceptionally high magnetic fields and can be employed in various applications to enhance system power density. In contrast to conventional coil-based SC magnets, high-temperature superconducting (HTS) trapped field magnets (TFMs), namely HTS trapped field bulks (TFBs) and trapped field stacks (TFSs), can eliminate the need for continuous power supply or current leads during operation and thus can function as super permanent magnets. TFMs can potentially trap very high magnetic fields, with the highest recorded trapped field reaching 17.89 T, achieved by TFSs. TFMs find application across diverse fields, including rotating machinery, magnetic bearings, energy storage flywheels, and magnetic resonance imaging. However, a systematic review of the advancement of TFMs over the last decade remains lacking, which is urgently needed by industry, especially in response to the global net zero target. This paper provides a comprehensive overview of various aspects of TFMs, including simulation methods, experimental studies, fabrication techniques, magnetisation processes, applications, and demagnetisation issues. Several respects have been elucidated in detail to enhance the understanding of TFMs, encompassing the formation of TFBs and TFSs, trapped field patterns, enhancement of trapped field strength through pulsed field magnetisation, as well as their applications such as SC rotating machines, levitation, and Halbach arrays. Challenges such as demagnetisation, mechanical failure, and thermal instability have been illuminated, along with proposed mitigation measures. The different roles of ferromagnetic materials in improving the trapped field during magnetisation and in reducing demagnetisation have also been summarised. It is believed that this review article can provide a useful reference for the theoretical analysis, manufacturing, and applications of TFMs within various domains such as materials science, power engineering, and clean energy conversion.

The newly discovered family of titanium-based kagome metals, ATi₃Bi₅ (where A can be Rb or Cs), has been found to exhibit non-trivial band topology and fascinating electronic instabilities, including electronic nematicity and potential bulk superconductivity. Distinct from their vanadium-based counterparts (AV₃Sb₅), which display a charge density wave (CDW) phase that already breaks rotational symmetry, ATi₃Bi₅ shows no evidence of CDW, providing a unique platform to study nematicity in its pure form and its interplay with other correlated quantum phenomena, such as superconductivity. In this review, we highlight recent progress in both experimental and theoretical research on ATi₃Bi₅ and discuss the unresolved questions and challenges in this burgeoning field.

Superconducting devices are attractive technologies that could improve and increase the electrification of several industries. However, as superconductors have highly non-linear electromagnetic behavior, equipment based on such materials should be thoroughly investigated through experiments and simulations. For the latter, the finite element (FE) method is a common tool for simulation. However, this method often demands high computational resources, especially in transients. Moreover, the computation burden naturally increases with the number of degrees of freedom (DOF) involved in the solution. To alleviate this load, the magnetic vector potential $\mathbf{A}$ can be swapped for the magnetic scalar potential $\Phi$ in the existing formulations \textbf{T}-\textbf{A} and \textbf{J}-\textbf{A} where there are no electrically conductive or ferromagnetic materials. To show the relevancy of the approach and to quantify the gain in computational resources, two case studies in 2D are considered: a single superconducting tape and a pancake coil; both based on REBCO. The idea is to show the ease of implementation of the approach in COMSOL Multiphysics\textsuperscript{\textregistered}. The coupling between the scalar potential $\Phi$ and the vector potential $\mathbf{A}$ is detailed. An additional benefit of the proposed approach is the manual creation of a unique straightforward thin cut in the mesh, independently of the characteristics of the geometry. This method simplifies grandly the laborious generation of cuts in multiple connected domains. For both case studies, experimental data on AC losses are used to validate the models. The new formulations are also cross-checked with their respective older forms, showing a reduction of the computational time while keeping a fair accuracy.

In this paper, we investigate the superconducting critical temperature, morphology and structural properties of NbN ultra-thin films (5–7 nm) deposited by reactive sputtering on top of silicon nitride (SiN) over 200-mm silicon wafers. We demonstrate the effectiveness of a 10-nm thick spacer layer of AlN in raising the superconducting critical temperature from 5.0 K to 7.2 K and from 7.3 K to 9.3 K for 5-nm and 7-nm NbN thickness respectively. By combining investigations with X-ray diffraction and transmission electron microscopy, we highlight significant modifications of the crystalline properties of the NbN film on top of the AlN spacer layer. When directly deposited on SiN, the grains of the NbN polycrystalline layer are randomly oriented. In contrast, when deposited on top of the AlN (0001) spacer layer, the NbN layer is textured along the (111) direction, leading to increased critical temperatures. As AlN is a CMOS-compatible material, these findings are particularly relevant in view of the future integration of high-performance Superconducting Nanowire Single Photon Detectors (SNSPDs) on large-scale quantum photonic chips.

This study investigates the impact of heavy ion irradiation on the superconducting performance of second-generation high-temperature superconducting (2G-HTS) wires in strong magnetic fields. We performed irradiation experiments using 18MeV Au, 12MeV Ni and 15MeV O ions accelerated by a tandem ion accelerator, targeting 2G-HTS wires composed of YBCO, EuBCO/BHO, GdBCO, or (NdEuGd)BCO. The superconducting properties of these wires were measured under various magnetic fields and temperatures. Our results indicate that oxygen ion irradiation had minimal effect on Ic(B) characteristics. In contrast, nickel ion irradiation at doses of 1.2x1011 ions/cm² significantly improved Ic(B), particularly at lower temperatures (20-30K), without quick material degradation at higher doses. Similarly, gold ion irradiation enhanced Ic(B) across a wide range of temperatures and fields. TRIM simulations suggested that ion penetration and energy loss varied by ion type, affecting defect formation and superconducting performance. The presence of heavy rare-earth elements in the HTS material increased susceptibility to ion irradiation, leading to more pronounced improvements in Ic. These findings demonstrate the potential of ion irradiation as a practical method for enhancing the superconducting properties of 2G-HTS wires, paving the way for their industrial application in high-field environments.

We present a non-return-to-zero (NRZ) superconductive voltage driver (SVD) for interfacing single flux quantum (SFQ) circuits with semiconductor circuits. The NRZ SVD design consists an encoding module, splitter networks, sixteen RS flip-flops (RSFFs), and a sixteen-stage DC SQUID array (DSA). By employing an asymmetric SQUID structure, the SVD achieved a simulated output swing of 4.3 mV. The impedance and quality factor formulas of the DSA were provided. We solved the issue of slower fall time caused by the asymmetric SQUID by inserting a termination resistor into the DSA to reduce its quality factor. By using this damped asymmetric DSA, the NRZ SVD can reach up to 30 Gbps in simulation. The test chip of the NRZ SVD was fabricated using the SIMIT's Nb03P process (J_C = 6 kA/cm²) and measured in a liquid helium dewar. The SVD achieved a measured output swing of up to 6.8 mV, which is relatively high compared to the published reports. Eye diagrams at 5 Gbps and 10 Gbps were clearly opened, demonstrating a very low bit error rate (BER). The test circuit for the NRZ SVD can support up to 15 Gbps with a 2⁹ − 1 pseudo-random bit sequence (PRBS-9) input and 20 Gbps with a sinusoidal input.

Twisted, stacked cable-in-conduit-conductors, including VIPER cables, have emerged as a popular choice for High Temperature Superconductor (HTS) fusion applications. The time-varying magnetic fields these cables are exposed to can generate significant AC losses, which are important to quantify for the design of fusion magnets. Although AC loss in twisted tapes and stacks—including VIPER cables—has been the subject of increasing research, many studies focus on higher temperatures and low fields outside the range applicable to fusion, while those considering higher fields tend to provide a less detailed analysis of the loss. This work provides a fundamental examination of the hysteresis loss characteristics of VIPER tapes, stacks and cables under conditions relevant to fusion applications. 3D finite element method (FEM) models implemented with H-ϕ formulation are used to simulate the loss at 20, 40 and 77 K, under applied magnetic fields of up to 20 T. Cables with up to 10 tapes per stack are considered. The field-angle dependence of critical current and n-value are accounted for, based on measured data from 4 mm Faraday Factory tape. Results show that hysteresis loss in VIPER strands is independent of pitch length and winding radius, a valuable result for shortening simulation time. An empirical method is proposed to estimate the loss in VIPER cables from 2D simulations of flat stacks, supplementing the established 2/π relationship. It is also shown that hysteresis loss in VIPER geometries can be scaled across temperatures by normalizing with the self-field critical current of a single tape, surprisingly irrespective of cable Ic.

In many high-temperature superconducting applications, the advantages of no-insulation (NI) coils, such as self-protecting capability and thermal stability, make them a promising alternative to insulated (INS) coils. Magnetisation loss will be generated when the coil is exposed to time-varying magnetic fields. This loss can vary with the applied field angle, magnitude, and frequency, resulting in parasitic heat loads. In this study, we investigate magnetization loss in NI and INS double-pancake and double-racetrack coils of identical dimensions, experimentally and numerically. Experiments were conducted at 77 K under external AC magnetic fields up to 100 mT, considering various field angles (0°–90°) and frequencies (73–146 Hz). The experimental results are compared with the finite element simulation results of the coils' three-dimensional models. Interestingly, NI coils exhibit no significant angular dependence of loss within a specific field range; however, beyond this range loss increases with increasing field angles. In contrast, the loss in INS coils consistently increases with decreasing field angles across the entire field range. Coil level shielding of the magnetic field is observed in NI coils under parallel fields which is similar to a bulk superconductor. The losses in INS and NI coils are comparable under a perpendicular magnetic field, which can be attributed to the dominance of superconducting currents, as confirmed by the current and field distributions observed in simulations.

Twisted, stacked cable-in-conduit-conductors, including VIPER cables, have emerged as a popular choice for High Temperature Superconductor (HTS) fusion applications. The time-varying magnetic fields these cables are exposed to can generate significant AC losses, which are important to quantify for the design of fusion magnets. Although AC loss in twisted tapes and stacks—including VIPER cables—has been the subject of increasing research, many studies focus on higher temperatures and low fields outside the range applicable to fusion, while those considering higher fields tend to provide a less detailed analysis of the loss. This work provides a fundamental examination of the hysteresis loss characteristics of VIPER tapes, stacks and cables under conditions relevant to fusion applications. 3D finite element method (FEM) models implemented with H-ϕ formulation are used to simulate the loss at 20, 40 and 77 K, under applied magnetic fields of up to 20 T. Cables with up to 10 tapes per stack are considered. The field-angle dependence of critical current and n-value are accounted for, based on measured data from 4 mm Faraday Factory tape. Results show that hysteresis loss in VIPER strands is independent of pitch length and winding radius, a valuable result for shortening simulation time. An empirical method is proposed to estimate the loss in VIPER cables from 2D simulations of flat stacks, supplementing the established 2/π relationship. It is also shown that hysteresis loss in VIPER geometries can be scaled across temperatures by normalizing with the self-field critical current of a single tape, surprisingly irrespective of cable Ic.

tochastic computing (SC) is a form of probabilistic computation that encodes information in the probability of a ``1'' appearing within a finite-length binary sequence. SC has been investigated for applications in various fields that do not require deterministic and precise computation. A superconducting single-flux-quantum (SFQ) circuit is considered a promising candidate for implementing SC hardware due to its high-speed operation and probabilistic behavior. In this study, we propose a novel large fan-out signal splitter to enable large-scale SFQ-based stochastic arithmetic circuits, addressing the issue of computation accuracy degradation caused by correlations between binary sequences. The proposed signal splitter generates uncorrelated output binary sequences by utilizing superconductor random number generators frequency-synchronized to the input binary sequence. Moreover, the fan-out can be easily increased by simply adding more superconductor random number generators. We implemented a four-output stochastic number signal splitter using the 10 kA/cm^2 Nb four-layer superconducting circuit fabrication process. Its operation was successfully demonstrated by measuring the average voltage at the input and outputs under continuous high-speed binary sequence input. Correct operation was confirmed at the input frequency of up to 32.4 GHz. The proposed signal splitter uniquely leverages the properties of superconducting circuits, where flux quanta determined by fundamental physical constants serve as the information carrier. We believe this development will significantly advance the realization of practical SFQ-based SC systems.

The vortex dynamics of an undoped uniaxially textured YBa₂Cu₃O_7−δ (YBCO) superconducting film grown onto a MgO (100) substrate was inspected by applying the vortex glass and collective-pinning models. The texture and structural characterization studied by X-ray diffraction revealed a uniaxially (00 l) YBCO layer, which coexists with minor Y₂BaCuO₅ and CuO phases. The temperature dependence of the magnetization in the superconducting state revealed a critical temperature ${T_{\text{C}}}$ = 88 K. By measuring the hysteresis loops ($M\left( H \right)$) at 10–70 K, the critical fields ${H_{{\text{C}}1}},{\text{ }}{H_{{\text{C}}2}},{\text{ }}{H_{\text{P}}}$ and ${H_{{\text{irr}}}}$ were estimated and a vortex matter diagram was sketched. By using the Bean model, the critical current density values ${J_{\text{C}}}\left( {T,H} \right)$ were obtained and the typical peak effect is observed. The vortex dynamics mechanism is discussed taking into account four vortex feature regimes in the double-logarithmical ${J_{\text{C}}}\left( H \right)$ curves. The vortex pinning mechanism is discussed by obtaining the pining force, ${F_{\text{P}}}$, its normalization, $f\left( h \right)$, and magnetic relaxation $M\left( t \right)$ measurements taken in field cooling mode at 10–60 K. The glassy exponent $\mu$ and the characteristic energy $U\left( {J,{\text{ }}T} \right)$ in the vortex glass model were estimated following the Maley method. The collective-pinning model is used to discuss the possible vortex regimes mechanism (individual flux lines, small bundles and large bundles of pinned flux). Eventually, the $E\left( J \right)$ curves, expressed from the swept field and creep measurements, show a power-law behaviour, in agreement with the vortex matter.

Upon reviewing the published version of our work, we identified misprints in the equations, which are corrected here. Additionally, we re-evaluated the oxygen concentration depth profiles. This re-evaluation does not affect the validity of the paper's statements or conclusions.

Vacuum thermal treatments (baking) are known to improve the superconducting properties of the RF surface layer of niobium cavities, and are employed as a last processing step to increase their efficiency determined by intrinsic quality factor Q$_0$. A specific method to perform the baking has been used. It consists in annealing of an evacuated cavity with the local heaters installed on its outer surface in a cryostat which ensures an exterior vacuum and protects the outer cavity surface from oxidation. Such a set-up has a number of advantages as it does not require to cool the cavity flanges during baking, and allows to perform the "cold" RF characterization of the cavity \textit{in situ}, immediately after the thermal treatment without disassembly of heating elements. Moreover, the air exposure that causes partial degradation of Q$_0$ by surface reoxidation is avoided. The heat treatment of a single-cell \SI{1.3}{\giga\hertz} niobium cavity at \SI{230}{\degreeCelsius} for \SI{24}{\hour} demonstrated the doubling of Q$_0$ at $E_{acc}$=\SI{10}{\mega\volt\per\meter} (from \SI{1.20e10}{} to \SI{2.4e10}{}) and retained the maximal accelerating field of \SI{35}{\mega\volt\per\meter} without quenching. The selection of treatment parameters is based on our previous XPS studies. This treatment ensures incomplete dissolution of the native oxide by oxygen diffusion, thereby preventing interaction of niobium surface with external contaminants. We propose to bake the cavities directly in a cryomodule, which would allow to use the treatment to improve their performance. The potential impact of material parameters on the components of surface resistance has been briefly examined.

Bulk high-temperature superconductors (HTSs) are capable of generating very strong magnetic fields while maintaining a compact form factor. Solenoids constructed using stacks of ring-shaped bulk HTSs have been demonstrated to be suitable for low-resolution nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI). However, these stacks were magnetised via field cooling, which typically requires a secondary superconducting charging magnet capable of sustaining a high magnetic field for a long period. A more economical alternative to field cooling is pulsed-field magnetisation (PFM), which can be carried out with an electromagnet wound from a normal conductor, such as copper. In this work, we present an additional advantage of PFM, where the trapped field in a stack of ring-shaped bulk HTSs is iteratively homogenised by manipulating the spatial profile of the applied pulsed field. Compared to field cooling with a uniform applied field, the variation in field along the central 10~mm of the solenoid is halved using this technique. If PFM of HTS rings could be advanced further to trap higher fields, this technique could be instrumental in magnetising HTS solenoids for NMR/MRI applications.

In this paper, we propose the Reduced Order Hysteretic Magnetization (ROHM) model to describe the magnetization and instantaneous power loss of composite superconductors subject to time-varying magnetic fields. Once the parameters of the ROHM model are fixed based on reference simulations, it allows to directly compute the macroscopic response of composite superconductors without the need to solve the detailed current density distribution. It can then be used as part of a homogenization method in large-scale superconducting models to significantly reduce the computational effort compared to detailed simulations. In this contribution, we focus on the case of a strand with twisted superconducting filaments subject to a time-varying transverse magnetic field. We propose two variations of the ROHM model: (i) a rate-independent model that reproduces hysteresis in the filaments, and (ii) a rate-dependent model that generalizes the first level by also reproducing dynamic effects due to coupling and eddy currents. We then describe the implementation and inclusion of the ROHM model in a finite element framework, discuss how to deduce the model parameters, and finally demonstrate the capabilities of the approach in terms of accuracy and efficiency over a wide range of excitation frequencies and amplitudes.

The attenuation of magnetic fields is crucial for various application fields, including health, space exploration, and fundamental physics, to name just a few. Superconductors are key materials for addressing this challenge. In this review, we mainly focus on the shielding and screening of quasi-static magnetic fields using superconductor-based passive layouts. After providing a brief overview of the principles of magnetic shielding and screening using superconductors, we outline commonly used procedures for measuring the field attenuation. Next, we give an insight into analytical and numerical models able to reproduce experimental results and predict the performances of new designs. Key challenges and achievements in employing low temperature or high temperature 
superconducting bulk and tape-based structures for reducing a given applied field are then discussed. Additionally, hybrid designs combining superconducting and ferromagnetic materials, aimed at enhancing the shielding ability or fabricating magnetic cloaks, are described. Finally, we highlight future challenges and potential advancements in this technology.

The discovery of rare-earth barium copper oxide (REBCO) materials with high critical temperatures, and the continued advancements in the fabrication of REBCO coated conductors with extremely high critical current densities, has enabled the development of ultra-high-field (>20 T) compact and large-scale thermonuclear fusion devices. At present, around a dozen global commercial manufacturers are able to supply high-quality REBCO coated conductors with excellent performance. Significant advancements have been made for high-temperature, low-field applications such as motors, generators, long-length transmission cables, and so on using REBCO coated conductors. Nonetheless, multiple ongoing critical challenges under low-temperature, high-field conditions, such as irreversible degradation of the critical current, along with insufficient mechanical protection and inadequate reduction of AC losses, remain unsolved, collectively hindering their utilization in high-field thermonuclear fusion reactors. This paper provides a comprehensive theoretical and technical review of the current state-of-the-art, associated challenges, and prospects in the research and development (R&D) of REBCO coated conductors, cables, and magnet systems for high-field fusion. It highlights the significant enhancements in current-carrying capacity, mechanical protection, and AC loss reduction achieved over the past decade. The paper delves into detailed analyses of potential cabling solutions that offer exceptional current-carrying capacity while ensuring an optimal inductance balance for toroidal, poloidal, and central solenoid coils in tokamak devices. This work endeavours to lay the groundwork for the R&D of the next-generation REBCO magnets to facilitate the construction of ultra-high-field compact and large-scale tokamak reactors.