High-temperature superconducting (HTS) technology provides an alternative approach to achieve compact transformers. Addressing AC loss in the HTS winding is crucial for HTS transformer applications. Most numerical AC loss studies on HTS transformers have neglected the influence of iron cores. This work carries out an AC loss study to explore the impact of an iron core on the HTS windings in a 3-phase HTS 1 MVA transformer coupled with it. AC loss simulations for the transformer winding both with and without the iron core are conducted by adopting the three-dimensional (3D) T-A homogenization method. When the iron core is incorporated, the saturation magnetic fields of iron materials, flux diverters (FDs) with different geometries, and variations in turn spacings in the LV winding composed of Roebel cables are considered to investigate their influence on the AC loss of the transformer winding. The inclusion of the iron core leads to a 1.2% increase in AC loss for the transformer winding while simulating at the rated current. We attribute this slight difference to the non-inductive winding structure of the transformer winding, where a strong magnetic field generated in the space between the LV and HV windings effectively shields the influence of the iron core.

We systematically investigated the detection performance of Al nanostrips for single photons at various wavelengths. The Al films were deposited using magnetron sputtering, and the sophisticated nanostructures and morphology of the deposited films were revealed through high-resolution transmission electron microscopy. The fabricated Al meander nanostrips, with a thickness of 4.2 nm and a width of 178 nm, exhibited a superconducting transition temperature of 2.4 K and a critical current of approximately 5 μA at 0.85 K. While the Al nanostrips demonstrated a saturated internal quantum efficiency for 405-nm photons, the internal detection efficiency exhibited an exponential dependence on bias current without any saturation tendency for 1550-nm photons. This behavior can be attributed to the relatively large diffusion coefficient and coherence length of the Al films. By further narrowing the nanostrip width, the Al-SNSPDs remain capable of effectively detecting single telecom photons to facilitate practical applications.

(Re)Ba₂Cu₃O_7-x (REBCO) coated conductors (CCs) have attracted considerable concern because of their outstanding current carrying capacity in magnetic fields of high strengths. A huge electromagnetic force is generated in the superconducting coil when conducting large currents in strong magnetic field. Thus, management of stress and strain has become a key technical challenge for the stability and safety of superconducting coil during operation. To accurately predict the electro-magnetic and mechanical characteristics of superconducting coil in strong magnetic field, an electromechanical model on the basis of the H-formulation and arbitrary Lagrangian-Eulerian (ALE) method is proposed here with FE software. To verify the proposed model, the simulation outcomes of the coil during magnetization are compared with the experimental outcomes. The coupling effect of magnet at high field strengths is dependent on the position of the coil. To reduce the screening current effect, the overshoot method with plateau is found superior to the traditional overshoot method, and an increase in the stabilization time can decrease the maximum value of stress. Finally, the electromechanical behaviors of single winding coil and two-tapes co-winding coil are compared.

Superconductivity is a phenomenon arising from cooperative electron behavior. However, correlations among (1) the minimum tuning parameter required for emergence, (2) the superconducting transition temperature resulting from minimal tuning, and (3) the host's physical/chemical properties still elude the scientific community. Recent empirical investigations, such as those revealing ideal gas-like correlations at the onset of superconductivity in intercalated superconductors, motivate this study. Our investigation reports similar findings in systems (>170 compounds) exhibiting superconductivity through other perturbative means, such as single-element doping. In general, statistical measures, including distance correlation analyses (≠ linear regression fit) of thermodynamic variables, indicate the presence of empirical relationships near the superconducting onset of systematically tuned compounds. These relations involve unit cell volume (V), the number of valence electrons (N), and the superconducting transition temperature (T_c). Note: The author's primary aim is not to validate or challenge BCS theory; it is instead to focus on leveraging methodology led by available data to enhance the exploration and development of innovative and cost-effective superconductors.

REBa₂Cu₃O_7−δ (REBCO, RE = rare earth) tapes doped with 5% and 15% Zr have been scaled up to lengths more than 40 m in a pilot-scale advanced metal organic chemical vapor deposition (A-MOCVD) tool. The precursor compositions used for the long tapes were guided by a study of the influence of (Ba + dopant)/Cu content on the critical current density (J_c) of 5 and 15 mol.% Hf- and Zr-added tapes at 4.2 K and 13 T. The 40-m-long tapes exhibited a critical current (I_c) over 4,000 A/12 mm at 4.2 K and 13 T as well as over 1,400 A/12 mm at 20 K and 20 T. The critical current densities of a 40-m-long tape doped with 5% Zr at 4.2 K measured at the National High Magnetic Field Laboratory (NHMFL) were > 10 MAcm⁻² and >5 MAcm⁻² at 14 T and 30 T, respectively, which are over three times those of commercial REBCO tapes. The infield J_c of 5% Zr-added 40-m-long tapes was similar to those of previously-reported high-performance short samples made with 15% Zr or Hf. These results demonstrate the excellent potential of A-MOCVD for manufacturing high I_c REBCO tapes for use in ultrahigh-field magnet applications.

REBa₂Cu₃O_7−x (REBCO) coated conductors, owing to its high tensile strength and current-carrying ability in a background field, are widely regarded a promising candidate in high-field applications. Despite the great potentials, recent studies have highlighted the challenges posed by screening currents, which are featured by a highly nonuniform current distribution in the superconducting layer. In this paper, we report a comprehensive study on the behaviors of screening currents in a compact REBCO coil, specifically the screening-current-induced magnetic fields and strains. Experiments were carried out in the self-generated magnetic field and a background field, respectively. In the self-field condition, the full hysteresis of the magnetic field was obtained by applying current sweeps with repeatedly reversed polarity, as the nominal center field reached 9.17 T with a maximum peak current of 350 A. In a background field of 23.15 T, the insert coil generated a center field of 4.17 T with an applied current of 170 A. Ultimately, a total center field of 32.58 T was achieved before quench. Both the sequential model and the coupled model considering the perpendicular field modification due to conductor deformation are applied. The comparative study shows that, for this coil, the electromagnetic-mechanical coupling plays a trivial role in self-field conditions up to 9 T. In contrast, with a high axial field dominated by the background field, the coupling effect has a stronger influence on the predicted current and strain distributions. Further discussions regarding the role of background field on the strains in the insert suggest potential design strategies to maximize the total center field.

Moiré superconductivity represents a new class of superconducting materials since the discovery of superconductivity in magic-angle (1.1°) twisted bi-layer graphene (MATBG), forming a Moiré lattice with a much bigger crystal parameter as the original lattice constant of graphene. Hence, experimentally changing the Moiré twist angle, 0.93° ⩽Θ⩽1.27, leads to a variation of the superconducting properties and enables a new way of engineering 2D superconducting materials. Details of the robust superconducting state of MATBG as function of charge carrier density, temperature and applied magnetic fields are reviewed. The influence of the top/bottom hexagonal boron nitride layer thickness on the superconducting properties of MATBG was also demonstrated in the literature. In all fabricated MATBG devices, changing of the charge carrier density leads to the appearance of insulating, metallic and even ferromagnetic states, which separate several superconducting domes in the phase diagram (longitudinal resistance, $R_{xx}$, as function of temperature T and charge carrier density, n). Further works have considered MATBG combined with WSe₂-layers, twisted bi-layer WSe₂, magic-angle tri-layer graphene (MATTG), and most recently, four-layer (MAT4G) and five-layer (MAT5G) stacks. The differences between the layered, cuprate high-$T_{c}$ superconductors and the Moiré superconductors are compiled together. The collected information is then used to apply the Roeser-Huber formalism to Moiré-type superconductivity to calculate the superconducting transition temperature, $T_{c}$, using only information of the Moiré lattice and the electronic configuration. To account for the different charge carrier densities in the experimental data sets and the low charge carrier mass demands that a new parameter $\eta $ must be introduced to the Roeser-Huber formalism to enable the description of several superconducting domes found in the phase diagram for a given Moiré angle. Doing so, the calculated data fit well to the correlation curve defined within the Roeser-Huber formalism.

In order to verify the feasibility of applying high-$J_{c}$ Nb₃Sn strand in fusion magnet, a full-size cable-in-conduit conductor (CICC) with short twist pitch (STP) cable pattern was manufactured and tested in SULTAN facility at SPC, Switzerland. Three levels of cyclic electromagnetic (EM) load were applied on the sample stepwise, no visible decrease of current sharing temperature ($T_{cs}$) was observed until the EM load increased to 80 kA × 10.8 T, after that the $T_{cs}$ decreased dramatically with the EM cycles, which suggested that irreversible deformation, causing a change in the strain state, or even damage has occurred in the superconducting strands. For investigating the reason which caused the conductor performance degradation, the tested conductor was dissected for metallographic observation. Eight segments which subjected to different EM loads were extracted from one of the legs, the geometric feature changes of the cable cross-sections were analyzed and compared. A good correlation was found between the decrease of the $T_{cs}$ and deformation of the cable cross section. A mass of cracks were found on the sub-elements of strands in the segment which subjected to highest EM load, but the amount of crack is much lower in other segments. Combining the analyses, it is speculated that the critical EM load which causes irreversible degradation is between 850 kN/m and 870 kN/m for this conductor. The results could be a reference in high-$J_{c}$ Nb₃Sn CICC design.

Since the discovery of MgB₂ as a superconductor, several research groups worldwide have studied the superconducting mechanisms due to the dual gap nature of MgB₂, as well as attempted to produce such a compound in wires, tapes, bulks, and thin films for a plethora of applications. While MgB₂ carries the promise of replacing Niobium-based superconductors in low-field applications, less-than-desirable performance and in-operation stability has slowed down such a progress. While the properties and nature of the superconductivity of MgB₂ are fairly known, the reproduction of its properties at manufacturing scales remains an unsolved problem. Therefore, this manuscript presents a systematic review on fundamental properties, phase formation, growth kinetics, and superconducting properties of MgB₂-based components such as multi- and mono-core wires, bulks, and thin films. Advances, challenges, and shortcomings are utilized in consolidating research questions and directions pertaining to the manufacturing of MgB₂ superconducting devices. Lastly, we evaluate the technological readiness of MgB₂-based devices for applications in fusion energy systems.

This study proposes a method for measuring the operational current of high temperature superconducting (HTS) non-insulation (NI) closed-loop coils, which operate in the steady persistent-current-mode (PCM). HTS NI closed-loop coils are promising for many easily-quenching direct-current (DC) applications, where their performance is determined by magnetomotive forces, total number of turns, and dimensions. As the primary interface parameter in an application system, the operational current must be accurately and rapidly measured. Generally, this is achieved by dividing the measured magnetic field by the coil constant. However, even if the influence of the screening current induced field (SCIF) is not considered, existing methods for the coil constant may be disturbed by the performance and location of Hall sensors, or experience a long measuring period. Therefore, a relatively accurate and fast method is proposed in this study, which is based on adjusting the output current of the adjustable power supply and monitoring the coil voltage as an indicator. The proposed method was validated through experiments and simulations using an equivalent circuit model coupled with a finite element method (FEM) model, and its current accuracy can be equivalent to the resolution of the employed power supply. It was demonstrated that this method reduced the requirements for Hall sensor's performance and location, and has a more reliable accuracy in contrast to the simulation method. Compared to the experimentally conventional method, the proposed method presents a significantly faster speed. The impact of the SCIF was considered and proven to be negligible for the tested pancake coils. Even for coils whose coil constant vibrates owing to the SCIF, this method can be adapted to directly measure various operational currents. Furthermore, it was demonstrated that the measurement error can be influenced by the current discrepancy among turns when the coil is not in the steady PCM, and a procedure for reducing this error was proposed.

Methods

PbMo₆S₈ superconducting materials are considered to have great potential for practical applications at low temperatures and high fields due to their high upper critical field, low anisotropy, and low preparation cost. In this work, PbMo₆S₈ bulks were prepared through a solid-state sintering process using PbS, Mo, and MoS₂ as raw materials. The phase evolution mechanism during the sintering of PbMo₆S₈ was studied in detail. It was found that during sintering at 750 °C for 24 h, both the S and Pb atoms diffuse into the Mo and MoS₂ particles, leading to the formation of the PbMo₆S₈ phase. After sintering at 950 °C for 72 h, a high superconducting phase content was obtained in the bulk; however, numerous pores remained. Therefore, in order to obtain a higher density for the bulk, a two-step sintering process was developed. Based on this technique, PbMo₆S₈ bulks with a higher bulk density and a higher superconducting phase content were obtained. This study provides an effective method for the fabrication of high-quality precursor powders, which can be the foundation for the future fabrication of PbMo₆S₈ superconducting long wires or tapes for practical applications.

A 10-MJ-class superconducting magnetic energy storage (SMES) magnet is designed and optimized in this study using quasi-isotropic strands and stacked-tape conductors. In order to ensure the stable operation of SMES systems, it is necessary to evaluate the mechanical properties risk caused by the Lorentz force. Therefore, in this study, the magnetic stress caused by the Lorentz force is analyzed using the finite element method. The results show that the tapes near the inner diameter of the magnet are subjected to a higher stress and require considerable support. Although the maximum stress is increased by two times due to the presence of the screening current, it is within the safety range. The screening current does not vanish after the discharge process. After discharge, the coil is still subjected to a stress on the other of a few MPa.

The homogeneity of the microstructure and composition are critical in determining the properties of rare earth-barium-cuprate, single grain bulk superconductors [(RE)BCO]. The magnitude of the trapped magnetic field achieveable in these technologically important materials, in particular, is influenced heavily by the size and distribution of (RE)₂BaCuO_x (RE-211) flux pinning inclusions in the bulk microstructure, whereas the size and distribution of silver agglomerates present within the bulk superconducting matrix correlate directly with improved mechanical properties. With careful engineering, these materials have significant potential for application in range of devices related to energy storage, medicine, electro-magnetic machinery and microelectronic technology. Fabrication of (RE)BCO bulk superconductors typically involves heating a powder compact above its peritectic decomposition temperature followed by slow cooling to facilitate the growth of a single grain. Each (RE)BCO composition has a different peritectic temperature and growth rate, which, therefore, necessitates different requirements in the heating profile. The fabrication temperature and growth rate, for example, may have an effect on the RE-211 and silver distribution, which may, in turn, affect the superconducting properties of the resulting single grain.

In this work we compare the distributions of silver and RE-211 in the single grain microstructures of YBCO-Ag, GdBCO-Ag, EuBCO-Ag and SmBCO-Ag bulk superconductors using optical microscopy, scanning electron microscopy and energy dispersive X-ray spectroscopy. We observe that the distributions are very similar along both the a/b-axis and c-axis of these materials. This suggests that factors other than the maximum temperature used to achieve peritectic decomposition and the rate of single grain growth are particularly influential in determining the properties of the as-processed samples in the top seeded melt growth process. This observation demonstrates there is freedom to use (RE) materials interchangeably between different applications as required, for example, for functional or economic reasons.

According to engineering experience, the axial shrinkage caused by the refrigerant seriously endangers the performance of long-distance conductor on round core (CORC) cables. Since outage maintenance of high-temperature superconducting (HTS) cables is inevitable, providing appropriate compensation for cyclic temperature is one of the key technologies in the actual application of power cables. Therefore, this paper presents an analytical solution for hollow CORC cables under thermo-mechanical loads. First, regarded as an axisymmetric composite structure, the radial temperature distribution of CORC cable under Dirichlet boundary or mixed boundary conditions was calculated. Then, assuming cable ends were axially fixed, a recursive method without variables is used to evaluate its displacement, strains, and stresses. Then, an algebraic method with axial strain as a variable is developed to analyze the mechanical behavior of the CORC cable more directly. Finally, concluded from the above derivation, a matrix equation is constructed based on continuity equations and boundary conditions, which applies to isotropic and orthotropic materials with orientations. Calculation results show that the analytical solution agrees with finite element method (FEM) results. Compared to the trial results of a 360 m CORC cable, the calculation error of axial shrinkage is within 1.63 cm, and the relative error is within 6.1%. In addition, the recursive method is the fastest to calculate axial strain, while the matrix method has a significant efficiency advantage in calculating the stresses and strains of each layer.

The high-temperature superconducting (HTS) dynamo enables injection of large DC currents into a superconducting coil, without the need for thermally-inefficient current leads. Because of this important advantage, there is significant interest in using such technology to energise superconducting coils in superconducting rotating machines and NMR/MRI magnets. Despite the extensive experimental work carried out over the past decade, there was - until very recently - considerable confusion and debate regarding the physical origin of the HTS dynamo’s DC output voltage. Numerical modelling has played a key role in elucidating the underlying physics of such devices and several different numerical models have now been developed as useful and cost-effective tools to not only explain and further examine experimental results, but also optimise and improve dynamo designs. This review summarises all of the developments in this important area over recent years, including modelling the open-circuit voltage behaviour in 2D and 3D, the definition of a new benchmark problem for the HTS modelling community, investigating key dynamo parameters, modelling dynamic coil charging behaviour and calculating losses. A view towards the future is provided, including the outstanding challenges and the developments required to address these.

An array of three GdBa₂Cu₃O_7-δ bulk high-temperature superconductors (HTS) that mimic the field pole of a high-power superconducting motor had been magnetized by pulsed field magnetization (PFM) while cooled by liquid nitrogen. The bulk array was magnetized by a passive PFM technique using three vortex-type coils placed over each individual bulk and connected in series. The trapped magnetic flux density distribution was comparable to the distribution obtained with more traditional quasi-static magnetization such as field-cooling. This suggests that the use of PFM technique on arrays of HTS bulks is possible. PFM has also been performed using each coil individually, to magnetize each bulk sequentially. The magnetization sequences showed a maximum reduction of the peak trapped magnetic flux density of 12% due to the demagnetization effect of the magnetization sequence, while the trapped magnetization distribution was improved.

For an accurate estimation of the AC losses of superconducting triaxial cables, in this paper we present a two-dimensional model capable to provide a global assessment of multi-layer triaxial cables, validated against the reported AC-losses measurements on single-phase cables provided by the Russian Scientific and Research Institute of the Cable Industry (VNIIKP). Four models are presented, the first being a single-phase cable of 50 tapes and the others being three triaxial cables made of up to 135 coated conductors distributed in up to 9 layers. A systematic study is devised, where the number of layers per phase increases from 1 to 3, with at least 14 tapes distributed across each layer of the first (innermost) phase, 15 in the secondary (middle) phase, and 16 in the third (outermost) phase, respectively. Remarkably, our results reveal that the simple strategy of considering an unbalanced distribution for the amplitudes of the applied current, can generally balance the magnetic field between the three phases even for the bilayer and trilayer cables, resulting in negligible magnetic leaks in all situations. Besides, our high-resolution simulations allow to see for the first time how the transport and magnetization currents distribute across the thickness of all the superconducting tapes, from which we have found that the AC-losses of the 2nd phase is generally higher than at the other phases at low to moderate transport currents, $I_{t r}<0.8 I_{c}$, being $I_c$ the critical current of the corresponding tapes. Nevertheless, depending on whether the $I_c$ of the SC tapes at the 3rd phase layers is lower than the one at the 2nd phase, the layers at the third phase can exhibit a considerable increment on the AC losses. This is result of the considered magneto angular anisotropy of the superconducting tapes, which lead to intriguing electromagnetic features that suggest a practical threshold for the applied transport current, being it 0.8Ic. Likewise, the relative change in the AC-losses per adding layers, per phase, and as a function of the entire range of applied transport current is disclosed.

In this study a novel method was presented to parameterize the critical current of Yttrium Barium Copper Oxide (YBCO) tapes based on their width, thickness, magnetothermal operational conditions, and the applied strain. For this purpose, a fuzzy-logic-based model was developed that take tapes structures and their operational conditions as inputs to calculate their critical current, as output. The results of critical current parameterization by fuzzy-logic-based model showed that the relative error of the proposed model is less than 3% comparing to experimentally acquired data. Then, the results of presented model was compared to results of semi-analytical fitting-based models and fully-analytical fitting based models. The comparisons showed the better performance in terms of accuracy and error of fuzzy logic model over fitting-based methods. At last, the results were also compared with the Artificial Neural Network (ANN)-based parameterization model and Adaptive Nero-Fuzzy Interference System (ANFIS)-based parameterization model. The proposed method had 6% to 8% higher accuracy and about 47% to 54% lower root mean squared error.

Since the discovery of high-temperature superconductors (HTS), superconducting magnetic bearings (SMB) have attracted much attention for practical applications such as flywheel energy storage systems, electrical machines, gyroscopes, etc., because of their ability to provide passive stable levitation under high-load conditions. Despite providing contactless linear and rotational motion, SMBs gradually decelerate by AC losses mainly generated by magnetic field inhomogeneity. The main component of AC losses at low rotational speeds is hysteresis loss, which is said to be independent of rotational speed, intrinsic to HTS, and proportional to the cube of magnetic field inhomogeneity. Although the state-of-the-art analytical expression of hysteresis loss in SMBs captures the general physics of the loss mechanism, it ignores the periodicity of the magnetic field in one complete rotation of the bearing. In this paper, the analytical expression of hysteresis loss is modified, taking into account the impact of magnetic field periodicity and the distribution of loss over the bearing surface. The new expression is tested by performing spin-down experiments with magnets of different levels of inhomogeneity in an actual SMB environment. The impact of magnetic field inhomogeneity on the dynamic behaviour of the bearing is also investigated. The results show consistency between modified analytical calculations and experimental data.

Power transformers are key elements for the safe and reliable delivery of electrical energy generated by renewable energy resources to consumers via transmission lines. Fault-tolerant current-limiting High Temperature Superconducting (FTCL HTS) transformers are type of superconducting transformers that tolerate fault for seconds and limit the fault current without the threat of burnout or delamination of tapes and deformation of windings. In this paper, the fault performance of a FTCL HTS transformer in a standard IEEE power system is investigated. The studied transformer is a 50 MVA 132 kV/13.8 kV transformer where both windings are made up of HTS tapes. The understudied power system consists of two microgrids with distributed generators. Part of the power in microgrids is supplied by the upstream grid which is connected to the microgrids through the HTS transformers. Two fault scenarios have been considered in this power system, in each one of these scenarios, a fault happens in one of the microgrids. Two considered fault scenarios have an approximate fault current of 18x to 23x of the rated current in the secondary windings. Results showed that insulated windings in FTCL HTS transformers could substantially reduce the peak temperature of the HTS windings, compared to bare windings. Afterwards, post-fault loading is imposed on the HTS windings, to observe their performance against the current increase after fault clearance. In this case, for the first scenario of the faults, the FTCL HTS transformer could tolerate 192% of post-fault overloading, while this number for the second fault scenario is 170%. Finally, the impact of post-fault loading on the full recovery time was discussed.

We show a conceptual structure for a wave energy converter, which features a direct-drive linear power generator with REBaCuO high-temperature superconducting (HTS) bulk field poles and driven by a heaving buoy. A dual translator power generation system of the proposed concept structure is a linear generator in which both the HTS bulks and armature copper coils move in opposite directions simultaneously. A performance analysis of our linear generator was conducted using a finite-element electromagnetic field analysis method. The results of the analysis were compared between the HTS dual translator linear power generator and the HTS single translator linear power generator. The maximum electromagnetic force and the average output power of the HTS dual translator are around 5 % and 11 % higher than that of the HTS single translator. We further present the results of the analysis regarding the influence of reducing the stroke length of the linear generator translator on the output power, where the output power for the HTS dual translator system increased up to a factor of two, in comparison to the HTS single translator counterpart, for the same reduction of stroke length.

The pinning of quantized magnetic vortices in superconducting YBa₂Cu₃O_{7- δ}(YBCO or Y123) thin films with Y₂BaCuO₅ (Y211) nanoinclusions have been investigated over wide temperature range (4.2-77 K). The concentration of Y211 nanoinclusions has been systematically varied inside YBCO thin films prepared by laser ablation technique using surface modified target approach. Large pinning force density values (F_p ∼ 0.5 TNm⁻³ at 4.2 K, 9 T) have been observed for the YBCO film with moderate concentration of Y211 nanoinclusions (3.6 area % on ablation target). In addition, uniform enhancement in critical current density (J_c) was observed in the angular dependent J_c measurement of YBCO+Y211 nanocomposite films. Y211 nanoinclusions have been found to be very efficient in pinning the quantized vortices thereby enhancing the in-field J_c values over a wide range of temperature. Increasing the concentration of Y211 secondary phase into Y123 film matrix results into agglomeration of Y211 phase and observed as increased Y211 nanoparticle size. These larger secondary phase nanoparticles are not as efficient pinning centers at lower temperatures as they are at higher temperatures due to substantial reduction of the coherence length at lower temperatures. Investigation of the temperature dependence of J_c for YBCO+Y211 nanocomposite films has been conducted and possible vortex pinning mechanism in these nanocomposite films has been discussed.

Nb₃Sn triple-helical structure is the elementary structure in the superconducting cable of ITER magnets and undergoes prolonged fatigue loading in extreme environments leading to serious damage degradation. In this paper, the fatigue behaviors of the Nb₃Sn triple-helical structure have been investigated by the strain cycling fatigue experiments at liquid nitrogen temperature. The results indicate that Nb₃Sn triple-helical structures with short twist-pitches possess excellent fatigue damage resistance than that of long twist-pitches, such as longer fatigue life, slower damage degradation, and smaller energy dissipation. Meanwhile, a theoretical model of damage evolution has been established to reveal the effects of twist-pitches on fatigue properties for triple-helical structures, which is also validated by the present experimental data. Furthermore, one can see that the Nb₃Sn superconducting wires in a triple-helical structure with the shorter twist-pitches have a larger elongation of helical structure and less cyclic deformation, which can be considered as the main mechanism of better fatigue damage properties for the triple-helical structures during the strain cycling processes. These findings provide a better understanding of the fatigue properties and damage mechanisms for Nb₃Sn triple-helical structures in superconducting cables of ITER magnets.

Bi₂Sr₂CaCu₂O_8+δ (Bi-2212) superconducting round wires exhibited great potential for use in high-field applications. The purity of the precursor powders is critical for the transport current of the wires. However, the role of the residual secondary phase in the precursor powders is not fully understood. Here, the origin of the secondary phase was investigated in precursor powders that were prepared using ultrasonic spray pyrolysis (USP) and calcination processing. The microstructure and phase evolution of the precursor powders during the crystallization process were analyzed. Moreover, the effects that the residual secondary phase has on melting behavior, morphology properties, and the supercurrent flow of Bi-2212 multi-filamentary wires are systematically discussed. The residual secondary phase in the filament caused further crystallization, and this led to the formation of more and larger Bi-2201 grains at the onset of the melting process. The poor microstructure and low critical current of the final Bi-2212 wires can be attributed to the presence of the residual copper-rich phase. Bi-2212 wires that were prepared with fully crystallized powders had a high critical current density (J_c) of 6773 A/mm² at 4.2 K, self-field. It was revealed that control of the secondary phases in precursor powders is greatly significant for achieving superior values of J_c.

Resistances of grain junctions of bulk polycrystalline YBa₂Cu₃O_7−δ (YBCO) and DyBa₂Cu₃O_7−δ (DyBCO) superconductors have been extracted following (i) Ambegaokar- Baratoff (AB) and (ii) de Gennes (dG) equations. Current–voltage (IV) below the critical temperature ($T_c$) has been used to extract transport critical current density ($J_c$). The variations of the junction resistances, ($R_N$) with temperature (T) exhibit that below a critical value of the normalised superfluid density (NSD), junctions become very low resistive and exhibit metallicity. Dependence of this feature of $R_N$ on the energy gaps has also been explored. Weak scattering limit is found to be compatible with the maximum of $R_N$ (T) as is observed from the corresponding NSD.

Transformer-rectifier flux pumps are DC superconducting power supplies capable of charging superconducting magnets to high currents and stored magnetic energies. Here, we demonstrate a full-wave superconducting flux pump assembled from high-temperature superconducting (HTS) wire that utilizes superconducting switches controlled by applied magnetic field. A negative DC offset occurs in the superconducting secondary of the circuit during operation which is related to the output load current. A feedback control system is proposed and demonstrated to account for the negative DC offset. Increasing the primary current proportional to the load current during operation allowed for the maximum output of the flux pump to be increased from 35 A to more than 275 A. These results are reproduced using a coupled electrical- and magnetic-circuit model formulated in the MATLAB Simulink® package.

In flux pumps, motors and superconducting magnets, the high temperature superconductor (HTS) coated conductor frequently carries a DC transport current when an oscillating magnetic field is present in the background. Under this circumstance, the interesting effect of dynamic resistance takes place, which can affect the operating performance of superconducting devices: heat accumulation can contribute to the rising temperature of the HTS tape and the dynamic resistance voltage can change accordingly. This article explores the time-dependent development of the dynamic resistance voltage using a numerical modeling considering the thermal effects. After a validation against experimental results, this work investigates the effects of several factors on the structure of the HTS tape on the time-dependent development of the dynamic resistance, thus providing insights toward a better understanding of the time-dependent behavior of HTS tapes under external magnetic fields.

We report a superconducting nanowire single-photon detector (SNSPD) array aiming for a near-infrared 1550-nm wavelength that consists of 32 × 32 nanowire pixels and an area of 0.96 mm × 0.96 mm. Unlike most reported large-scale SNSPD arrays with amorphous films, NbN superconducting nanowires are employed in our array, which allows the detector operation at 2.3 K provided by a compact two-stage Gifford-McMahon cryocooler. Thermally coupled row-column multiplexing is employed in our arrays to avoid current redistribution and loss of electrical signal occurring in the electrically coupled row-column architecture. The fabricated detector array shows a pixel yield of 94% and maximal intrinsic efficiencies of 77% and 96% at 1550 nm and 405 nm, respectively. The timing jitter and the thermal coupling probability are also investigated.

As an elegant and fast numerical tool for solving time-dependent electromagnetic field problems in hard superconductors, Brandt’s method has played an important role in understading the magnetic behavior of superconducting strips, discs, bars and cylinders in various aspect ratios. However, the application of this convenient method was mainly in magnetization processes. Traditionally, the solution of current transport problem needs to introduce a driving electric field $E_{a}$, which requires a low efficiency iterative process and $E_{a}$ itself was not clearly explained. In this work, three integral algorithms based on the Brandt’s method are developed to deal with current transport problems, which directly adopt the applied current as a boundary condition. Namely the current (I)-driven version and two current-field-driven versions A and B. Moreover, the arbitrary applied magnetic field can also be included in the I-driven version. The derivation with all necessary formulas for the methods are given in this work. As an example, the new methods, as well as the traditional method are used for calculating transport ac loss Q of a superconducting cylinder or strip obeying a power-law relation of $E \propto J^{n}$ as a function of a given $I(t)$. Derived from the Ampère law and the differential rather than the integral expression of the Faraday law, the current-driven version can be used for more accurate and much quicker computation. Being an intermediate quantity, $E_{a}(t)$ in the two current-field-driven versions is accurately calculated under the given $I(t)$, but version B is much quicker than A. Problems relating to $E_{a}(t)$ and Q stabilization process are discussed.

High-temperature superconductors are a powerful technological option to be applied in the current scenario of energy transition. Their applications include fault current limiters, power electrical cables, and electrical machines, for example. Due to the non-linearities of superconductors, it is computationally costly to run real models of superconducting equipment. Therefore, it is of paramount importance to have a reliable and fast formulation to model superconducting devices. This paper proposes a new hybrid J-A formulation to simulate superconducting devices. The new formulation is validated with 5 case studies, some of which are benchmarks. The J-A formulation agrees in all cases and has a smaller computation time when compared with the T-A formulation. Moreover, due to the simple implementation, the proposed formulation allows the possibility of running the J and A formulations in the same order and presents itself as a potential feature to speed up and help the design of the superconducting devices.

Self-regulating high-temperature superconducting (HTS) flux pumps enable direct current injection into a closed-loop superconducting coil without any electrical contact. In this work, the process of charging a coil by a self-regulating HTS flux pump is examined in detail by numerical modeling. The proposed model combines an $H$-formulation finite element method (FEM) model with an electrical circuit, enabling a comprehensive evaluation of the overall performance of self-regulating HTS flux pumps while accurately capturing local effects. The results indicate that the proposed model can capture all the critical features of a self-regulating HTS flux pump, including superconducting properties and the impact of the secondary resistance. When the numerical results are compared to the experimental data, the presented model is found to be acceptable both qualitatively and quantitatively. Based on this model, we have demonstrated how the addition of a milliohm range, normal-conducting secondary resistance in series with the charging loop can improve the charging process. In addition, its impact on the charging performance is revealed, including the maximum achievable current, charging speed, and the generated losses. The modeling approach employed in this study can be generalized to the optimization and design of various types of flux pumps, potentially expediting their practical application.

In order to utilize high-temperature superconducting Yttrium Barium Copper Oxide (YBCO) tapes to develop superconducting cables for high magnet field applications, it is critical to ensure the stable operation of the YBCO cable under challenging mechanical and thermal conditions. A new type of cable featuring the winding of YBCO and copper tapes around a spiral stainless steel tube has been proposed to increase flexibility and cooling. Experiments are performed to confirm that its critical current varies with the bending diameter. The cables wound with nine YBCO tapes in three layers show a critical current degradation of less than 5% for a bending diameter of 30 mm. The performance of the cable degrades as the number of wound layers increases. The critical current degradation of cable specimens wound from 15 tapes in five layers reached approximately 12% for a bending diameter of 30 mm. In addition, when compared to traditional CORC cable specimens, the developed cable specimens show better-bending flexibility and achieve a lower critical bending diameter. The finite element models show that the higher elasticity coefficient and lower plasticity of the stainless steel spiral tube results in a lower strain on the YBCO tapes of the HFRC cable than that of the CORC cable, and the maximum strain on the YBCO tapes of the HFRC cable was only about 10% of that of the CORC cable. Therefore, it is less likely that the YBCO tape in this type of cable will reach the irreversible strain limit during bending, resulting in a degradation in current carrying performance. Furthermore, the cooling efficiency can be improved by flowing the cooling medium inside the central core, which can significantly improve its thermal stability. These advantages indicate the possibility of using it in future high-field magnets with high current carrying capacity at fields greater than 15 T.

The application of High-Temperature Superconductor (HTS) coils made of coated conductors has been investigated for many years. A possible configuration for such coils is the jointless loop, also known as the ring coil. The double crossed loop coil (DCLC) has been successfully applied in superconducting magnetic bearings (SMBs). The design of SMBs with DCLCs requires flexible modelling to allow all parts of the device to be represented. This work proposes the T-A formulation with a thin-film approximation for modelling SMB with DCLCs in the finite element analysis framework. A 2D representation of the system is coupled with an external electric circuit to model the continuity of the lines that represent the parts of each jointless loop. To couple the T-A formulation and the circuit, an average of the total electric field, with both resistive and inductive components, is applied to the circuit. The total current computed by the circuit is applied to the T-A formulation. The proposed methodology was validated by comparison with levitation force experimental data. Two types of tests were simulated: five levitation force tests and three guidance force tests. It is shown that there is a limit to the behaviour of the levitation force related to the high-loss state. Below this limit, the stack of DCLCs behaves as an equivalent bulk. Beyond this limit, a high-loss state appears as a linear growth of the levitation force. It is also shown that this high-loss state in vertical displacement influences the lateral force.

Iron-based superconductors (IBSCs) are a class of material under investigation for the development of superconducting wires in the low-temperature-high magnetic fields power application. Among the various families of IBSCs, the 1144 CaKFe₄As₄ compound is a promising material able to achieve outstanding superconducting properties with a cheap and simple chemical composition. Oxidation, in these compounds, is considered an obstacle for high intergranular critical current density, J_c,GB. A study devoted to the evaluation of oxidation phenomena and their effects on the superconducting properties is thus needed in order to fully understand the involved mechanisms. From the evaluation of polycrystalline samples obtained by a mechanochemically assisted synthesis route, a degradation of the critical temperature and critical currents has been observed concurrently with oxygen accumulation at grain boundaries in open porosities. However, the crystalline structure at an atomic level seems not affected, as well as intragranular superconducting properties assessed by means of calorimetric methods. These results suggest that loss of superconducting properties in Ca/K-1144 compounds following oxidation is significantly associated with the worsening of grain connectivity.

The critical current density ($J_c$) of the body centered cubic (bcc) V_0.6Ti_0.4 alloy enhances significantly after the addition of rare earth Gd as the latter is immiscible in the matrix [S. Paul, et.al, IEEE Trans. Appl. Supercond. 31, 5 (2021)]. Very low solubility of Gd in other bcc elements like Ta and Nb is also well known [Jr. KA Gschneidner in Prog Sci Technol Rare Earths, vol. 1, pp. 222–258, 1964 & M Neuberger, et.al in Handbook of Electronic Materials, Vol 4, 1972]. We use these facts to find the effect of adding 1 at.% Gd into the Nb_0.6Ti_0.4 and Ta_0.4Ti_0.6 alloys on the superconducting properties e.g., the transition temperature ($T_c$), Jc, flux pinning force density ($F_p$) and the microstructure. In spite of Gd being ferromagnetic, the $T_c$ in these alloys change only marginally (increase by 0.3 K in Ta_0.4Ti_0.6 and decrease by 0.15 K in Nb_0.6Ti_0.4 after Gd addition. The $J_c$ (H=1 T, T = 4 K) increases by 5 and 1.5 times respectively in the Gd containing Nb_0.6Ti_0.4 and Ta_0.4Ti_0.6 alloys, which is quite small as compared to the increase observed in the V_0.6Ti_0.4 (20 times) system. With Gd addition, the grain size reduces approximately by 65% and 10% respectively in Nb_0.6Ti_0.4 and Ta_0.4Ti_0.6. Our analysis indicates that grain boundaries are the major flux line pinning centres in these alloys and the role of Gd in increasing the $J_c$ depends on the effectiveness of Gd in reducing the grain size. The grain boundary density depends strongly on the distribution of Gd precipitates, which is quite different from each other for two alloy systems under study. Moreover, our results suggest that the addition of Gd to commercial Nb-Ti (Nb_0.37Ti_0.63) alloy is a new promising route for achieving higher $J_c$ values.

Low-temperature superconducting (LTS) wires are of significant importance in high-field magnet applications. Current developments of the LTS wires are attributed to many studies. Particularly, Nb₃Sn is an attractive superconductor with substantial potential for performance improvement in view of an ideal microstructure that maximizes flux pinning properties. To date, various reviews have been reported on the physical properties of low-temperature superconductors. Therefore, this review focuses on understanding the fundamental phase formations and microstructural controls of low-temperature superconductors from the perspectives of growth kinetics, nucleation theory, and chemical potentials to facilitate the syntheses of these superconductors and advancement of wire production. Taking Nb₃Sn as an example, the effect of Cu addition to Nb₃Sn on Nb/Sn reactive diffusion is briefly described. Then, representative Nb₃Sn formations are schematically summarized to broaden our understanding of the development behaviors of Nb₃Sn. These behaviors are qualitatively reviewed in terms of Sn chemical potential. After mentioning the potential for performance improvement of Nb₃Sn, the influences of element additions, specifically those of Zr and Hf additions, resulting in breakthrough microstructural refinements, on Nb/Sn diffusion are investigated. Subsequently, strengthening of the matrix via element additions is reviewed. Thereafter, taking Nb₃Al as an example, the features of Nb₃Al formation and basic development processes, including low-temperature processes, metastable phase transformations, and microstructural control, are described. Strain sensitivity, one of the most important properties of Nb₃Al, is also briefly reviewed. Then, taking Nb alloy as an example, α-Ti precipitation in a binary Nb-Ti system is concisely summarized. Subsequently, recently reported new artificial pin incorporation based on a powder method is introduced, followed by a unique study of the application of high-temperature-tolerable Nb superconducting alloys in superconducting joints. This review makes a novel contribution to the literature as it provides a comprehensive understanding of phase formation in low-temperature superconductors.

AC loss is one of the greatest obstacles for high-temperature superconducting (HTS) applications. In some HTS applications, coated conductors carry non-sinusoidal currents. Thus, it is important to investigate the effect of various waveforms on AC loss in coated conductors. In this work, transport AC loss in a 4 mm - wide REBCO coated conductor carrying sinusoidal and non-sinusoidal currents, is numerically investigated. The current amplitudes, the frequency of the transport current, and n-value are varied. Non-sinusoidal transport current waveforms studied include square, five types of trapezoidal, and triangular waveforms. Simulated results show that, for a given current amplitude, AC loss for the square current waveform is the greatest, that for the triangular waveform is the smallest. The sequence of AC loss in the conductor for different current waveforms coincides with the penetration depth, which implies the penetration depth determines the AC loss of the coated conductor. Furthermore, the transport AC loss in the conductor was found to decrease with frequency as f-2/n for non-sinusoidal transport current.

Superconducting flux pumps (FP) are capable of supplying superconducting circuits with high currents by additively supplying current over a number of cycles without introducing large amounts of heat into the cryogenic environment. Superconducting FPs can be broadly classified into two types: dynamo and transformer rectifier. Modelling the behaviour of these systems is an emerging field. In this work a model of a half wave magnetically switched transformer rectifier FP created in MATLAB/Simulink/Simscape is presented. Unlike existing models, the characteristics of all circuit elements are fully integrated allowing all superconducting elements to be accurately incorporated. The presented method uses pre-calculated look-up tables, populated with experimentally derived material qualities to simulate these superconducting elements. The thermal evolution of the switches, calculated simultaneously to the magnetic field switching interaction has also been included. This model is compared to the performance of a real world FP during the pumping of a load coil and is found to be accurate. Furthermore, the presented model illustrates how small amounts of heating at a magnetic switch can profoundly affect a FPs performance over many cycles.