In future electric aircraft applications employing all-superconducting rotating machines, round multifilamentary magnesium diboride (MgB2) wires are a preferrable material for lowering AC loss, due to their small filaments at the macron level and tight twist pitch. Our previous work has investigated AC loss behavior in a 54-filament MgB2 wire with a filament radius of 12.5 mu m, where the filament size was found not ideal for loss reduction. In this work, 3-D AC loss simulations of a twisted, nonmagnetic 114-filament MgB2 wire with a 5 mu m filament radius at 20 K are performed using H-formulation. Three types of AC losses are studied: 1) Transport loss only (Q(t0), with current levels up to 90% of its self-field critical current I-c0), 2) magnetization loss only (Q(m0), with AC field amplitudes and frequencies up to 2 T and 200 Hz, respectively), 3) total AC loss carrying AC current exposed to AC field (Q(total), with AC field also up to 2 T and current levels up to 40% of I-c0). Simulation results show that, for the Q(m0), the simulated hysteresis loss Q(h) of a 5-mm twist pitch, 114-filament wire at 50 Hz, and 200 Hz matches the analytical hysteresis loss equation for a cylindrical superconductor, scaled by 114 (the number of filaments), when B-m <= 0.5 T. Increasing the twist pitch (5 mm versus 10 mm) and filament size (5 mu m in the 114-filament wire versus 12.5 mu m in the 54-filament wire) leads to a higher Q(m0) due to the coupling effect. Moreover, the simulated Q(total) of the 114-filament wire range from 0.22 to 7.48 W/cm3 for i <= 0.4 and B-m <= 0.5 T operated at 200 Hz.

High temperature superconducting (HTS) magnets are the core for an adiabatic demagnetization refrigerator (ADR). However, the local positive-half magnetic field at end windings introduces AC loss (termed as magnetization loss), resulting in thermal loads in the cryogenic system. Previous work mainly focused on the AC loss under full sinusoidal field waveforms, lacking systematic analysis on AC loss under positive-half field waveforms. Therefore, this work investigates the magnetization loss of a 4 mm HTS tape exposed to various full/positive-half sinusoidal and non-sinusoidal perpendicular magnetic fields, such as trapezoidal and triangular fields, to compare the influence of different field waveforms, field amplitudes and frequency on magnetization loss. Simulation shows that a higher ramping rate dB/dt only leads to higher magnetization loss at low-B and the magnetization loss almost overlaps at high-B due to fully penetration. The use of positive-half field waveforms can reduce magnetization loss by 80% at low-B in comparison with those under full field waveforms, this is due to the lower penetration depth. It is also found that magnetization loss under positive-half magnetic fields decreases with frequency as f−2/n at low-B and increases with f1/n at high-B.

AC loss is a key factor in the design of twisted-stacked tape cables (TSTCs) for high temperature superconductor (HTS) fusion applications. Until recently, numerical analysis of AC loss in full-scale TSTCs has been limited by the computational demands of 3D models, which severely restrict tape number and mesh density. In this work, a 2D scanning method, assessed against 3D models and experimental measurements, is used to simulate the magnetization and dynamic losses in full-scale TSTCs. A simplified PIT-VIPER geometry with four stacks, each containing 20-100 tapes, is modelled under alternating external magnetic fields of up to 20 T, at a temperature of 20 K, with and without 50 kA DC transport current. The influence of field-dependent critical current on magnetization loss is examined by comparing tapes from different manufacturers. The critical currents of the cables are also simulated. Results show that, for low transport currents, reducing tape number can reduce AC losses, roughly in proportion with tape number. Furthermore, it is shown that the widely used 2/pi scaling of loss in flat stacks introduces moderate error until relatively high fields for practical tape numbers.

Ba0.6K0.4Fe2As2 superconductors have been identified as potential candidates for magnet applications through their very high upper critical field, relatively high superconducting transition temperature and manufacturability through the powder-in-tube (PIT) route. Recent studies have reported that these conductors have a deep minimum critical current (Ic dip) near zero field, and this anomalous property exhibits hysteresis sometimes. However, little attention has been paid to AC loss in these conductors; a clear understanding of the loss behaviors is required for practical applications. In this work, preliminary AC loss simulations were performed at 15 K for stainless steel/silver double-sheathed nonfilamentary Ba0.6K0.4Fe2As2 tapes. A hypothetical tape without Ic dip was further used to investigate the influence of low-field Jc characteristics on the overall AC loss response. The simulation results indicate that the low-field anomaly causes a slight increase in magnetization loss at low fields and significantly impacts dynamic loss in the presentence of DC currents approaching Ic.

Abstract All-superconducting motors are promising for high-power-density aviation applications. Multifilamentary magnesium diboride (MgB 2 ) wires are attractive for armature windings due to their AC-loss reduction potential. However, most existing AC-loss studies focus on transverse standing-wave magnetic fields (SWs), while AC loss under rotating magnetic fields (RMFs), which are more relevant to armature-winding conditions in some superconducting motors, remain insufficiently investigated. In this work, magnetization loss Q m in a MgB 2 single cylindrical filament and twisted two-filament wire under SWs and RMFs is numerically investigated using 3D finite-element-method (FEM) models based on the H -formulation. At the two-filament wire level, the effects of twist pitch, frequency, and matrix resistivity on magnetization loss and coupling behaviour are systematically investigated. The models use the measured critical current density J c and n -value data of MgB 2 wire at 20 K as interpolated inputs, with operating conditions of field amplitudes from 0.05 to 2 T and frequencies of 50 and 200 Hz. At the filament level, the simulated hysteresis loss Q h agrees well with analytical calculations at low fields in both the SW and RMF models. At high fields, the SW result deviates from the analytical calculations, while the RMF result is better captured by the analytical calculation considering field-dependent critical current density J c ( B ). Meanwhile, the SW–RMF comparison shows a reversal in Q h , from Q h (SW) < Q h (RMF) at low fields to Q h (SW) > Q h (RMF) at high fields. At the two-filament wire level, stronger inter-filament coupling, promoted by longer twist pitch, higher frequency, and lower matrix resistivity, increases both Q h and Q m . In most cases, the coupling loss Q c reaches its peak as the field increases in both the SW and RMF models, with the RMF peak shifted to lower fields.

AC loss in REBCO coils is one of the critical issues for applications such as superconducting rotating machines and fast-ramping magnets. One approach to reducing AC loss is to concentrically place open-loop superconducting shielding coils (SSC) near the ends of the REBCO coil assembly, thereby shielding it from time-varying magnetic fields. However, there is no experimental validation on the effectiveness of SSC. In this work, AC loss in a REBCO coil assembly was measured and numerically calculated at 77 K with and without SSC. The coil assembly consists of three double pancake coils (120 turns in total). The coils assembly and SSC are wound from 4-mm-wide SuperPower and 12-mm-wide Fujikura coated conductors, respectively. Both the simulation and experiment show that SSC effectively reduces loss by 30-50%. Through experimental benchmarking, we found that accurate loss prediction requires considering the uniformity of the lateral critical current density in the coated conductors used in SSC.

No-insulation (NI) coils are considered as an alternative to insulated (INS) coils in some applications due to their enhanced thermal stability and self-protecting capability. However, NI coils generate magnetization loss (Qm) under time-varying magnetic fields, and the loss varies with operating conditions. In this work, the magnetization loss of 5-turn and 10-turn NI double-pancake coils (NI-DPC) is simulated at 40 K and 77 K. The amplitude of the AC magnetic fields varies from 0.03 T to 1 T, with frequencies ranging from 10 to 200 Hz, and the magnetic fields are applied both in parallel and perpendicular directions. The simulation results show that Qm (J/m/cycle) for 5-turn NI-DPC is greater than 10-turn NI-DPC, owing to the stronger shielding effect in the 10-turn coil. Under parallel magnetic fields, Qm exhibits a sudden increase with increasing magnetic fields, as the coil reaches the fully penetrated state, leading to flux-flow.

Reducing AC loss is a critical issue in the design of high-temperature superconducting (HTS) transformers. Owing to the diamagnetism of superconductors, superconducting shielding coils (SSCs) provide an effective means of reducing the perpendicular magnetic field component and AC loss. This work systematically investigates the influence of the SSCs on AC loss in a 1 MVA HTS transformer, using two-dimensional T-A homogenization method. The effects of key parameters are analyzed, including the SSC turn number (up to 12), tape width (4, 6, 12 mm, including combination of different widths), vertical distance h above the top of the transformer windings (0.1-4 mm), and the radial gap g between the SSCs and the transformer windings (0.5-5 mm). The AC loss in the 1 MVA HTS transformer is calculated under these configurations. The simulation results indicate that incorporating SSCs significantly reduces AC loss. For example, employing four 12 mm wide turns of SSCs for both the LV and HV windings at rated current achieves a reduction of 35.2%. This effectiveness arises from the suppression of perpendicular magnetic field component to the end parts of the transformer windings.

Large superconducting windings can be considered as assemblies of many arrays consisting of high-temperature superconductor (HTS) tapes. In HTS applications, they will be exposed to external fields with various orientations, resulting in magnetization loss (Q(m)). Understanding the magnetization loss behaviors of HTS arrays is crucial for those HTS applications. In this work, we measure Q(m) of single- and four-row arrays with one, two, and four columns at 72.23 and 145.51 Hz. We refer an array as a/b, where "a" and "b" represent the number of columns and rows, respectively. Q(m) of the 4/1 and 4/4 arrays with various magnetic field angles is also measured. All measured Q(m) results are compared with corresponding finite-element method simulations. Notably, the measured Q(m) per tape in the single-column arrays is smaller than that of the two-column arrays, while the four-column arrays exhibit the highest loss at low field (e.g., below 60 mT for the four-row array). On the other hand, simulation results on the arrays with up to eight rows and columns show that as the column count increases, the magnetization loss values become saturated due to the dominance of magnetization loss in the inner columns.

A 10 T fast-ramping high-temperature superconducting (HTS) magnet is being designed to characterize new rare-earth permanent magnet materials. However, AC loss associated with the fast-ramping process is one of the key technical challenges. This study focuses on evaluating the effectiveness of loss-reduction strategies-superconducting shielding coils (SSC) and magnetic flux diverters (MFD)-both individually and in combination. As the first step of the project, AC loss in a small-scale magnet was numerically studied, resulting in loss reduction of approximately 32%, 71%, and 90% with SSC, MFD, and their combination, respectively. By analyzing the correlation between critical current and AC loss, we found that the frequency and amplitude of the transport current significantly influence the effectiveness of SSC. In the subsequent simulation for the 10-T magnet, AC loss reduction is up to 34%, 57%, and 71% when using SSC, MFD and both. The simulation results indicate that the effectiveness of SSC is less sensitive to high magnetic fields than that of MFD; MFD is still effective for the 10-T magnet, even beyond its saturation field; the combined configuration of SSC and MFD is the most efficient method for AC loss reduction.

No-insulation (NI) high-temperature superconductor (HTS) coils possess inherent advantages compared with their insulated (INS) counterparts, including enhanced current density, improved mechanical integrity, thermal stability, and self-protecting properties, making them a more appealing technological choice for high-field magnets, rotating machines, and linear propulsion applications. In many such applications, the coils are exposed to time-varying magnetic fields which results in magnetization loss. This loss, which creates a heat load that could significantly impact the cryogenic system, has yet to be well characterized and understood for NI coils. In this study, magnetization loss in a double-pancake, solder-impregnated NI coil wound HTS-coated conductor is investigated both experimentally and numerically at 77 K. The amplitude of the applied ac field is varied between 10 and 100 mT with frequency varying from 72 to 145 Hz and field orientation varying between parallel to perpendicular with respect to the normal vector of the conductor surface of the coil. The experimental results showed no frequency dependence and no clear angular dependence with the loss essentially equal between parallel and perpendicular fields, in striking contrast to INS coils. Numerical analysis carried out in a 2D configuration for parallel fields was able to reproduce the relevant experimental data. The current density and magnetic field distributions calculated from the analysis show that the NI coil can completely shield its inner turns, attributed to the effective shielding provided by the radial and screening currents. As such the magnetization loss characteristics of NI coils are better understood as those of an HTS bulk, rather than of a coil.

In the pursuit of enabling the application of all-superconducting rotating machines in electric aviation, high AC loss in the armature windings where superconductors carry AC currents and exposed to AC/rotating magnetic fields is a critical stumbling block. For lowering AC loss, multifilamentary magnesium diboride (MgB2) wires with fine filaments and tight twist are one promising candidate for aviation applications. In this paper, 3D AC loss simulations of a 54-filament MgB2 wire with a non-magnetic matrix at 20 K are carried out based on the H-formulation. The transport loss carrying AC current without external field, Q(t0), of 12-, 30- and 54-filament wires is firstly obtained, where the current amplitudes range from 20% to 90% of its self-field critical current I-c0. Then the magnetization loss exposed to field amplitudes up to 2 T without current, Q(m0), is presented, where the operational frequency, the twist pitch and resistivity of the matrix are varied to investigate their impacts on Q(m0) and its three loss components (hysteresis loss Q(h), coupling loss Q(c) and eddy current loss Q(e)). Lastly, the total loss, Q(total), of the 54-filament wire with various twist pitches and frequencies is compared, where the current amplitudes vary from 30% to 70% of I-c0 and the field amplitudes are up to 2 T. All simulations use the measured J(c)(B, 20 K) and n(B, 20 K) data of the 54-filament wire. Simulation results show that, the use of the 5 mm twist pitch wire can significantly reduce Q(m0) due to the decoupling of the filaments, where the simulated Q(h) matches well with the analytical hysteresis loss for a cylindrical superconductor multiplied by 54 (the number of filaments). With increasing twist pitch, the filaments become coupled, resulting in a greater increase in both Q(c) and Q(h). Surprisingly, the simulated Q(total) values in the wires with different twist pitches agree well with the sum of Q(m0) and Q(t0) for all different current levels. This implies that Q(total) in an MgB2 wire carrying an AC current exposed to an AC magnetic field can be accurately predicted by knowing Q(m0) and Q(t0) values which are more easily obtained.

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-phi 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 Ic.

We measured the frequency-dependent magnetization losses of twisted multifilament MgB2 wires subjected to ac transverse magnetic fields with a small amplitude, under which coupling loss dominates magnetization loss, and then, we determined their coupling time constants as well as their geometry factors of coupling losses at various temperatures. We also measured the hysteresis loops of their magnetizations using a vibrating sample magnetometer, and then, we calculated the hysteresis losses at various magnetic field amplitudes and at various temperatures. Note that such calculated values represent the hysteresis losses in completely decoupled filaments in a twisted multifilament MgB2 wire. Using these values obtained experimentally, we calculated the magnetization losses of twisted multifilament MgB2 wires under practical operating conditions, i.e., at various magnetic field amplitudes, at various magnetic field frequencies, and at various temperatures, considering the saturation of the filamentary region in the wire, which occurs at magnetic fields with high frequencies and large amplitudes.

Assembled conductor on round core (CORC) cables are a promising candidate for future fusion magnets to meet high DC demands. In high-temperature superconductors (HTS) fusion applications, HTS tapes in poloidal field coils are exposed to high magnetic fields (similar to 20 T), high currents (> 25 kA), and low temperatures (20 K). Under these conditions, the superconductors can generate AC losses that may potentially lead to the magnet quenching. Here, considering the HTS layer of the coated conductor, AC losses include magnetization loss from external AC magnetic fields and dynamic loss from the interaction between AC fields and a DC current. The sum of magnetization loss and dynamic loss equals the total loss. In this work, 3D finite element method simulations are used to investigate the averaged AC loss of HTS tapes (Faraday/Theva), used either in a spiral tape or in multilayer CORC cables. The simulations are carried out under AC magnetic fields, with/without DC current, where the magnetic field amplitude reaches up to 8 T at 20 and 50 K. An eight-layer CORC cable exposed to magnetic fields up to 20 T at 20 K is also investigated as a specific case study. The simulation results show that magnetization loss decreases with increasing number of layers at low and medium magnetic fields, due to the shielding effect. However, at high magnetic fields, the magnetization loss of multilayer cables becomes similar due to the shielding effect becoming insufficient to prevent flux penetration at high fields, as the shielding currents reach their critical limits. In addition, the eight-layer CORC cable shows consistency with the other cables at 8 T and follows the same trend up to 20 T at 20 K. Then, a temperature scaling law for the CORC cables is explored, showing that magnetization loss (without current) and total loss of multilayer CORC cables at different temperatures can be scaled using the self-field critical current.

No-insulation (NI) coils emerged as a viable alternative to traditional insulated (INS) high temperature superconducting (HTS) coils primarily due to their inherent ability to self-protect during quench and enhanced mechanical stability. When coils carrying direct current (DC) are exposed to an external alternating current (AC) magnetic field, total loss in the coil is the sum of magnetisation loss due to the AC field and dynamic loss arising from the interaction between the DC current and the AC field. In this work, we numerically study the total loss and its components in NI and INS double-pancake coils (DPCs) of identical dimensions, wound with 4 mm wide SuperPower Rare-earth barium copper oxide (ReBCO) coated conductor (CC) tapes at 77 K. The analysis is carried out for external AC magnetic fields up to 200 mT at 72.73 Hz, with the coil carrying DC current up to 90 % of the coil self-field critical current. The results show that under a perpendicular magnetic field, the total loss and its components in the INS-DPC are higher than in the NI-DPC, which is attributed to the presence of insulation which hinders the current bypass. The NI-DPC and INS-DPC coils show similar electromagnetic behaviour under the perpendicular field, and the evolution of dynamic resistance, which gives rise to dynamic loss, is also similar. Under parallel field the loss in the NI-DPC is higher than that for the perpendicular field, and the coil level shielding similar to bulk superconductor is also observed. Surprisingly, under parallel fields, a dynamic resistance higher than that under perpendicular fields is evident in the NI-DPC, arising from a finite average electric field over a cycle.

AC loss estimation in REBCO high-temperature superconductor (HTS) coils is crucial in ac applications. The finite-element method (FEM) modeling is an efficient and widely-used approach to simulate ac loss in HTS coils. However, such models can become time-consuming and resource-intensive due to the high aspect ratio and anisotropic field-angle-dependent critical current properties of REBCO tapes. In addition, HTS coils with complex geometry, such as saddle-shaped coils, further increase the complexity of models because the 3D rotational asymmetry must be considered. This work presents a detailed demonstration of a 3D 10-turn saddle coil to overcome these simulation challenges. More importantly, the loss behaviors in an HTS saddle coil carrying currents under external magnetic fields are characterized for the first time. Frenet-Serret equations are utilized within the finite element analysis software to construct the 3D structure of a 10-turn saddle coil wound with REBCO tape. The dimensions of the coil are approximately 200 mm in length and 70 mm in width. The T-A formulation is employed, and measured I-c (B,theta) data is interpolated in the FEM model to simulate the electromagnetic behaviors of HTS tapes. The critical current of the saddle coil, along with magnetization loss at various magnetic field amplitudes, dynamic resistance, and total loss at different dc levels, are analyzed. Additionally, a race-track coil model with a similar size to the saddle coil is constructed and simulated for comparison purposes. Simulation results indicate that for both types of coils, the loss is mainly generated in the straight parts rather than the curved end portions.

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 degrees-90 degrees) 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.

In high-temperature superconducting (HTS) coil applications, such as field coils for superconducting motors, HTS tapes in vertical stacks carry a DC transport current under an external AC magnetic field. In such a complex electromagnetic situation, HTS tapes generate AC losses consisting of magnetization loss and dynamic loss, when the amplitude of the ripple fields exceeds the threshold field (Bth). Understanding and predicting the Bth and dynamic loss in HTS tapes is crucial for the design of field coils with high stability and efficiency. In this study, Bth, dynamic loss and magnetization loss for a single tape and 2-, 6-, 10- and 20-tape vertical stacks are numerically studied in detail under external perpendicular magnetic fields ranging from 10 mT to 1 T. The transport DC current level (IDC) is varied from 11.6 A to 254 A, corresponding to i0 (=IDC/Ic0) ranging from 0.03 to 0.7, where Ic0 is a self-field critical current of 362.9 A at 65 K. The analytical equation for a single tape, Bth = Bp(1 - i0), is extended to the average and individual Bth for multi-tape stacks by modifying i0 and Bp. Here, Bp is the effective penetration field of the HTS tapes, which can be found from the maxima of Gamma m0 (the normalized magnetization loss without DC current by the square of the external magnetic field). Comparison of the simulation results shows that not only the average Bth of the stacks but also the Bth of individual tapes can be predicted by the extended analytical equation for stacks. The edge tapes have the lowest Bth and highest AC loss values in the stacks due to the large shielding current that expels the external magnetic fields.

High-power density all-superconducting rotating machines have potential for application in electrical aircraft motors. However, superconductors in the armature windings of such rotating machines carry AC currents under AC/rotating magnetic fields, resulting in AC losses. For reducing AC loss, low-cost, round magnesium diboride (MgB2) wires are one promising material due to their multifilamentary structure, fine filament size and tight twist. To date, previous 3D AC loss simulations have focused on MgB2 wires with a magnetic matrix operating at low frequency and 4.2 K, which are not relevant to aviation applications. In this work, 3D simulations of magnetization loss at 20 K of twisted 2-filament and 54-filament wires with a non-magnetic matrix are carried out using the finite element method, based on the H-formulation, with AC field amplitudes from 0.1 T to 2 T and frequencies up to 200 Hz. The measured J(c)(B, 20 K) and n(B, 20 K) data of a non-magnetic MgB2 wire manufactured by Hyper Tech Research is assumed as input parameters. For the 2-filament wire, the operational frequency, the twist pitch, the filament size, the matrix resistivity, and inter-filament gap have been varied to systematically study their impacts on magnetization loss and its loss components (hysteresis loss, coupling loss and eddy currents). The simulation results show that the 2-filament wire with a 5 mm twist pitch and a higher resistivity matrix operated at 50 Hz has the lowest magnetization loss through decoupling the filaments. Furthermore, a lower coupling loss at 200 Hz for field amplitudes exceeding 1 T is observed, this is because critical coupling frequency f(c) shifts to small values with increasing field amplitudes. For the 54-filament MgB2 wire, the magnetization loss of a 5 mm twist pitch and a higher resistivity matrix wire operated at 50 Hz is estimated. The simulations show that the hysteresis loss of the 54-filament wire can be well predicted by the analytical hysteresis loss equation for a cylindrical superconductor multiplied by 54 (the number of filaments) because the filaments are in an uncoupled state. Good agreement is also observed between the simulated coupling loss and the analytical coupling loss equation from Wilson book for a circular-arranged multifilamentary superconducting wire.