Superconductor Science and Technology

Single-photon detectors based on superconducting nanowires (SSPDs or SNSPDs) have rapidly emerged as a highly promising photon-counting technology for infrared wavelengths. These devices offer high efficiency, low dark counts and excellent timing resolution. In this review, we consider the basic SNSPD operating principle and models of device behaviour. We give an overview of the evolution of SNSPD device design and the improvements in performance which have been achieved. We also evaluate device limitations and noise mechanisms. We survey practical refrigeration technologies and optical coupling schemes for SNSPDs. Finally we summarize promising application areas, ranging from quantum cryptography to remote sensing. Our goal is to capture a detailed snapshot of an emerging superconducting detector technology on the threshold of maturity.

A low-AC loss Rare-earth barium copper oxide (REBCO) cable, based on the VIPER cable technology has been developed by commonwealth fusion systems for use in high-field, compact tokamaks. The new cable is composed of partitioned and transposed copper 'petals' shaped to fit together in a circular pattern with each petal containing a REBCO tape stack and insulated from each other to reduce AC losses. A stainless-steel jacket adds mechanical robustness—also serving as a vessel for solder impregnation—while a tube runs through the middle for cooling purposes. Additionally, fiber optic sensors are placed under the tape stacks for quench detection (QD). To qualify this design, a series of experiments were conducted as part of the SPARC tokamak central solenoid (CS) model coil program—to retire the risks associated with full-scale, fast-ramping, high-flux high temperature superconductors CS and poloidal field coils for tokamak fusion power plants and net-energy demonstrators. These risk-study and risk-reduction experiments include (1) AC loss measurement and model validation in the range of ∼5 T s⁻¹, (2) an IxB electromagnetic (EM) loading of over 850 kN m⁻¹ at the cable level and up to 300 kN m⁻¹ at the stack level, (3) a transverse compression resilience of over 350 MPa, (4) manufacturability at tokamak-relevant speeds and scales, (5) cable-to-cable joint performance, (6) fiber optic-based QD speed, accuracy, and feasibility, and (7) overall winding pack integration and magnet assembly. The result is a cable technology, now referred to as PIT VIPER, with AC losses that measure fifteen times lower (at ∼5 T s⁻¹) than its predecessor technology; a 2% or lower degradation of critical current (I_c) at high IxB EM loads; no detectable I_c degradation up to 600 MPa of transverse compression on the cable unit cell; end-to-end magnet manufacturing, consistently producing I_c values within 7% of the model prediction; cable-to-cable joint resistances at 20 K on the order of ∼15 nΩ; and fast, functional QD capabilities that do not involve voltage taps.

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.

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.

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.

More than a century after the discovery of superconductors (SCs), numerous studies have been accomplished to take advantage of SCs in physics, power engineering, quantum computing, electronics, communications, aviation, healthcare, and defence-related applications. However, there are still challenges that hinder the full-scale commercialization of SCs, such as the high cost of superconducting wires/tapes, technical issues related to AC losses, the structure of superconducting devices, the complexity and high cost of the cooling systems, the critical temperature, and manufacturing-related issues. In the current century, massive advancements have been achieved in artificial intelligence (AI) techniques by offering disruptive solutions to handle engineering problems. Consequently, AI techniques can be implemented to tackle those challenges facing superconductivity and act as a shortcut towards the full commercialization of SCs and their applications. AI approaches are capable of providing fast, efficient, and accurate solutions for technical, manufacturing, and economic problems with a high level of complexity and nonlinearity in the field of superconductivity. In this paper, the concept of AI and the widely used algorithms are first given. Then a critical topical review is presented for those conducted studies that used AI methods for improvement, design, condition monitoring, fault detection and location of superconducting apparatuses in large-scale power applications, as well as the prediction of critical temperature and the structure of new SCs, and any other related applications. This topical review is presented in three main categories: AI for large-scale superconducting applications, AI for superconducting materials, and AI for the physics of SCs. In addition, the challenges of applying AI techniques to the superconductivity and its applications are given. Finally, future trends on how to integrate AI techniques with superconductivity towards commercialization are discussed.

High-temperature superconductors (HTS) promise to revolutionize high-power applications like wind generators, DC power cables, particle accelerators, and fusion energy devices. A practical HTS cable must not degrade under severe mechanical, electrical, and thermal conditions; have simple, low-resistance, and manufacturable electrical joints; high thermal stability; and rapid detection of thermal runaway quench events. We have designed and experimentally qualified a vacuum pressure impregnated, insulated, partially transposed, extruded, and roll-formed (VIPER) cable that simultaneously satisfies all of these requirements for the first time. VIPER cable critical currents are stable over thousands of mechanical cycles at extreme electromechanical force levels, multiple cryogenic thermal cycles, and dozens of quench-like transient events. Electrical joints between VIPER cables are simple, robust, and demountable. Two independent, integrated fiber-optic quench detectors outperform standard quench detection approaches. VIPER cable represents a key milestone in next-step energy generation and transmission technologies and in the maturity of HTS as a technology.

This paper presents the design of a non-insulated (NI) high-temperature superconductor (HTS) 15 T solenoid with a 72 mm diameter warm bore, intended for use in the Paul Scherrer Institute positron production (P³) experiment. The P³ experiment, scheduled to start in Q3 2026, aims to demonstrate a high-yield positron source that is relevant in the context of FCC-ee. The coils will be solder-impregnated using techniques developed with a small-bore HTS NI coil stack. This magnet produced a magnetic field of 18 T at 12 K and 2 kA, in a cryogen-free, conduction-cooled setup. Similarly, the P³ magnet will be conduction-cooled by two cryocoolers. This larger-bore magnet is designed to operate at 15 K with a nominal operating current of 1.2 kA. To ensure the protection of the NI magnet, quench prevention is the preferred strategy. Several potential failure modes are analyzed, including thermal runaway in the event of failures in the current leads, power supply, or cryocoolers. By enhancing the cold mass' heat capacity through the addition of a large lead mass, the stored magnetic energy can be safely dissipated in the cold mass through the electrical path formed by the superconductor and the solder. Mechanical analysis indicates that the hoop, radial and axial stresses are kept below allowable limits.

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.

Superconducting technology applications in electric machines have long been pursued due to their significant advantages of higher efficiency and power density over conventional technology. However, in spite of many successful technology demonstrations, commercial adoption has been slow, presumably because the threshold for value versus cost and technology risk has not yet been crossed. One likely path for disruptive superconducting technology in commercial products could be in applications where its advantages become key enablers for systems which are not practical with conventional technology. To help systems engineers assess the viability of such future solutions, we present a technology roadmap for superconducting machines. The timeline considered was ten years to attain a Technology Readiness Level of 6+, with systems demonstrated in a relevant environment. Future projections, by definition, are based on the judgment of specialists, and can be subjective. Attempts have been made to obtain input from a broad set of organizations for an inclusive opinion. This document was generated through a series of teleconferences and in-person meetings, including meetings at the 2015 IEEE PES General meeting in Denver, CO, the 2015 ECCE in Montreal, Canada, and a final workshop in April 2016 at the University of Illinois, Urbana-Champaign that brought together a broad group of technical experts spanning the industry, government and academia.

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 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 involved in the solution. To alleviate this load, the magnetic vector potential A can be swapped for the magnetic scalar potential Φ in the existing formulations T–A and J–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 (rare earth barium copper oxide) REBCO. The idea is to show the ease of implementation of the approach in COMSOL Multiphysics^®. The coupling between the scalar potential Φ and the vector potential 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.

The advantages of low loss and high power density in high-temperature superconducting (HTS) power cables render them promising candidates for urban power transmission applications. Numerical simulation models, especially field-circuit coupling models, are adept at capturing the interactions between cables and power grids during transient short-circuit faults. However, a significant limitation in current research is the lack of integration of cable thermal-hydraulic behavior into these models. In finite element model models, kilometer-long cables present challenges due to their large geometric aspect ratios, and high-current short-circuit faults can further complicate computational convergence. Addressing this, this paper proposes a simulation framework that enhances field-circuit coupling models by incorporating a scaled-length thermal-hydraulic model and optimizing the E-J relationship of HTS tapes under fault conditions. This paper also investigates the fault endurance of the cable in given power grid, explores reclosing strategies based on the maximum self-recovery temperature, and evaluates load recovery capability, finding that backup overheating protection and reclosing strategies utilizing non-electrical quantities can drastically reduce the cable outage duration while boosting the equipment utilization of the cable by 99.71%.

The use of laser cutting technology to subdivide the superconducting layer of commercial REBCO tapes into narrow and parallel filaments, resulting in a multi-filamentary tape that can significantly decrease shielding currents and AC losses, while effectively maintaining the critical current (I_C). In order to prevent the superconducting layer in the prepared REBCO multi-filamentary tapes from hydrolysis reaction with water when directly exposed to air, leading to the degradation of superconducting properties. Therefore, re-encapsulation is necessary to the REBCO multi-filamentary tapes. This research involved the re-encapsulation of filament wire tapes with different filament counts (2-filament, 6-filament, and 10-filament) using a reel-to-reel copper plating device, along with relevant performance validation. The results show that when the copper plating thickness on each side is 10 μm, the grooves generated during laser cutting (where the groove width × groove height = 20 μm × 30 μm) have been basically filled. Meanwhile, the current-carrying performance of the REBCO multi-filamentary tapes encapsulated with copper plating again was tested at different temperatures and magnetic fields, and no further reduction of the critical current was found. In addition, the mechanical properties of REBCO multi-filamentary tapes before and after electroplated copper re-encapsulation at room temperature and in the liquid nitrogen temperature were verified. It is found that the mechanical properties of the multi-filamentary tape after laser cutting are not decay significantly, and the mechanical properties of the multi-filamentary tape after re-encapsulation were significantly improved, especially under low-temperature conditions.

YBCO superconducting ceramic fibers doped with Ni or Zn were produced using the solution blow spinning (SBS) technique. Precursor solutions were prepared with acetates of yttrium, barium, copper, nickel, and zinc, and reduced and stabilized with polyvinylpyrrolidone (PVP) of different molar masses (360 000 g mol⁻¹ and 1300 000 g mol⁻¹). All reagents were dissolved in a solution with methanol, acetic and propionic acids. The samples were prepared with a stoichiometric ratio of YBa₂Cu$_{3-x}M_x$O$_{7-\delta}$ (M = Ni or Zn and x = 0.01, 0.02 and 0.04). The morphology of the samples was evaluated by scanning electron microscopy, revealing the formation of fibers on a sub-micrometer scale and an influence of the molar mass of PVP on the average fiber diameter. X-ray diffraction evidences the formation of the desired superconducting phase while not indicating the presence of the doping elements, supporting the idea that doping occurs at the copper site. This hypothesis is strengthened by the experimental observation that the critical temperature varies with x for both dopant materials. The observed properties are aligned with the expected behavior for samples produced by alternative methods, thus establishing SBS as a viable route to fabricate doped YBCO ceramic nanofibers.

Twisted, stacked cable-in-conduit-conductors, including VIPER cables, have emerged as a popular choice for high temperature superconductor 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 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. A semi-empirical method is proposed to estimate the loss in VIPER cables from 2D simulations of flat stacks, supplementing the established $2/{\pi}$ 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 ${I_{\text{c}}}$.

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.

High-T_c superconducting (HTS) flux pumps are capable of wirelessly powering HTS magnets, and are becoming promising alternatives of driven mode excitation which requires thermally inefficient current leads. HTS transformer-rectifiers, also considered as a type of HTS flux pumps, have drawn broad attention in recent years, since they enabled a number of novel HTS magnet applications. Compared to other types of HTS flux pumps, these devices are clear in physics and circuit topologies, easily controllable, and superior in some key performances. In this work, we aim to give a comprehensive overview on the thriving field of HTS transformer-rectifiers, especially those unconventional ones which do not involve superconducting-to-normal state transition. The work starts with explaining the working principle, including the underlying physics of induction-rectification effect, circuit topologies, and switching methods; followed by introducing design methods and construction considerations for engineering devices; and ends with summarizing research and development status, as well as potential applications of HTS transformer-rectifiers.

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.

Several superconducting motor designs with a power density exceeding 20 kW/kg have been proposed and are under development. However, maintaining the stable operation of superconducting coils in a rotating environment remains a partially unresolved challenge. The no-insulation (NI) high-temperature superconductor (HTS) winding technique, which deliberately removes insulation materials between turns, has emerged as a potential solution for superconducting motors. NI HTS coils have demonstrated current bypassing characteristics, making them stable under external field disturbances and robust against local critical current drops. However, contact resistivity, which largely governs the ``NI behavior," has been reported to fall within a broad range in prior studies, making it challenging to consistently obtain specific values. As a result, understanding and managing contact resistivity has become a significant area of research. This is especially critical in motors where the field winding is subjected to periodic external harmonic fields, and maintaining pole-to-pole balance is crucial. In this study, we investigated the influence of contact resistivity on the performance of field windings through simulation as part of our efforts to assess the potential risks associated with NI HTS motors. Torque, voltage, and current were analyzed using the finite element method coupled with a lumped parameter circuit model, and the results were compared.

K-doped BaAs₂Fe₂ (K-Ba122) superconductor is a promising material for applications.
However, it has been found challenging to achieve high critical current density (J_c) in untextured bulk sample. In this paper we investigated bulk samples prepared by varying the milling energy density which affects the grain and grain boundary microstructures, and we investigate their magnetic performance to better understand what causes their different J_c. We found that in our samples, which all have small grain size, T_c does not appear directly correlated to J_c. Moreover, AC susceptibility reveals in at least one case obvious signs of multiscale supercurrents, not caused by granularity but that directly influence the overall J_c performance. Considering the microstructural features and the magnetization response we ascribed the J_c differences to lack of connectivity on a larger scale due to nano-cracks at some grain boundaries, which subdivided the samples into macroscopic regions and inevitably limited the overall performance. We discuss possible routes to overcome those extrinsic current-blocking defects.

This paper proposes a new systematic design method based on coupling matrix theory and non-resonant structure for HTS (high-temperature superconducting) filters, which can introduce more transmission zeros (n + X) than the conventional coupling matrix theory. The proposed approach not only introduces transmission zeros at the near end of the passband through a coupling matrix, but also introduces transmission zeros at the far end of the passband through a new non-resonant structure. The non-resonant structure is realized by a grounded microstrip line (GML) structure, and the exact expression of the non-resonant structure is derived through the equivalent circuit. To demonstrate the proposed method, two-order, four-order and six-order filters are designed. The effectiveness of the methods is verified through simulations and experiments, with results that closely match theoretical calculations.

The High Magnetic Field Laboratory of China (CHMFL) is developing high-temperature superconducting(HTS) magnets for the upgraded 55~60 T magnet. This is the first Bi2212 cable-in-conduit conductor (CICC) fabricated in the CHMFL with a rectangular-shape to serve the hybrid magnet. The fabrication of the Bi2212 CICC has technical challenges that must be overcome to optimise the critical performance in engineering applications. This paper details the fabrication technology, including cabling, jacketing, heat treatment (HT), and leakage detection, with critical current (Ic) tests at low temperatures. The Bi2212 conductor has the characteristics of rectangular, long twist pitch (LTP), low void fraction (VF), and large deformation of the wires and sub-cables. It has no central cooling channel and soft-silver tube, smaller in size and higher in engineering current density (Je), similar to the real conductor. The rectangular Bi2212 CICC, including 60 SC wires, exhibits 34.5 kA at 15 K and exceeds 40 kA at 4.2K. The current sharing temperature (Tcs) was up to 40 K at 10kA, and no quench occurred. The resistance of the terminal joints reaches the nΩ-level. This paper presents a detailed fabrication technology of the Bi2212 CICC for the future engineering design of HTS magnets.

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.

K-doped BaAs₂Fe₂ (K-Ba122) superconductor is a promising material for applications.
However, it has been found challenging to achieve high critical current density (J_c) in untextured bulk sample. In this paper we investigated bulk samples prepared by varying the milling energy density which affects the grain and grain boundary microstructures, and we investigate their magnetic performance to better understand what causes their different J_c. We found that in our samples, which all have small grain size, T_c does not appear directly correlated to J_c. Moreover, AC susceptibility reveals in at least one case obvious signs of multiscale supercurrents, not caused by granularity but that directly influence the overall J_c performance. Considering the microstructural features and the magnetization response we ascribed the J_c differences to lack of connectivity on a larger scale due to nano-cracks at some grain boundaries, which subdivided the samples into macroscopic regions and inevitably limited the overall performance. We discuss possible routes to overcome those extrinsic current-blocking defects.

Twisted, stacked cable-in-conduit-conductors, including VIPER cables, have emerged as a popular choice for high temperature superconductor 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 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. A semi-empirical method is proposed to estimate the loss in VIPER cables from 2D simulations of flat stacks, supplementing the established $2/{\pi}$ 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 ${I_{\text{c}}}$.

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.

Stochastic computing (SC) is a form of probabilistic computation that encodes information in the probability of a '1' occurring 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. 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. High-speed operation up to 33.2 GHz was confirmed. 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 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.

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 Q₀. 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 in situ, immediately after the thermal treatment without disassembly of heating elements. Moreover, the air exposure that causes partial degradation of Q₀ by surface reoxidation is avoided. The heat treatment of a single-cell 1.3 GHz niobium cavity at 230 ^∘C for 24 h demonstrated the doubling of Q₀ at $E_\mathrm{acc}$ = 10 MV m⁻¹ (from $1.20\times10^{10}$ to $2.4\times10^{10}$) and retained the maximal accelerating field of 35 MV m⁻¹ 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 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.

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.

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.