Critical Current Reduction Research Articles

Intelligent estimation of critical current degradation in HTS tapes under repetitive overcurrent cycling for cryo-electric transportation applications

Overcurrent cycling refers to the procedure of imposing repetitive overcurrent to superconducting tapes/devices for characterizing their critical current reduction. Characterizing the overcurrent cycling behaviour of Rare Earth Barium Copper Oxide (ReBCO) tapes is a crucial step in the design process of High Temperature Superconducting (HTS) devices. Multiple overcurrent incidents during the operation of an HTS device can significantly decrease the total critical current, leading to potential quenches and failures. Data-driven models have been proposed in the literature to estimate the Critical Current Degradation Rate (CCDR) of ReBCO tapes under multiple overcurrent scenarios. However, these methods have exhibited notable errors in the range of 8%–11%, in the estimation of the critical current reduction. This paper proposed methods based on Artificial Intelligence (AI) techniques aimed at the challenges of conventional methods of CCDR estimation. Different AI-based techniques were proposed, tested, and compared to show the effectiveness of the proposed intelligent approach, including Support Vector Regression (SVR), Decision Tree (DT), Radial Basis Function (RBF), and Fuzzy Inference System (FIS). Experimental data on critical current values of ReBCO tapes subjected to multiple and repetitive overcurrent cycles were employed for this investigation. The results demonstrated that the Mean Relative Error (MRE) of the SVR method is 23%, for the DT model is approximately 0.61%, the MRE of the FIS model is well above 0.06%, and the MRE value for the RBF method is about 1.1 × 10−6%. Moreover, the proposed AI models offer fast test times, ranging from 1 to 11 ms. These findings highlighted the potential of using AI techniques to enhance the estimation accuracy of the risks associated with overcurrent events.

Design of HTS Excitation Coil for Homopolar Inductor Machine Considering Critical Current Reduction of Local Turn

Design of HTS Excitation Coil for Homopolar Inductor Machine Considering Critical Current Reduction of Local Turn

Computation of the Strain Induced Critical Current Reduction in the 16 T Nb3Sn Test Facility Dipole

A test facility dipole is being developed at LBNL, targeting a 16 T field in a 144 mm wide aperture. The magnet uses a block design, with two double-pancake coils. In order to minimize motion under the large Lorentz forces, the coils are preloaded against a thick aluminum shell and iron yoke using bladder and key technology. It is then crucial to verify that the performance of the magnet is not degraded due to strain induced on the Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn conductor during assembly, cool-down and powering. The critical current of extracted strands was measured in a varying background magnetic field and as a function of the applied longitudinal strain. Finite element analysis was used to extract the strain state inside the superconducting strands during magnet assembly and operation. This strain was then compared to the measurements to evaluate potential reversible and irreversible effects on the magnet performances. The results suggest that the magnet can reach 16 T with sufficient margin, with no irreversible degradation in the high field region.

Role of kinetic energy on Nb3Sn thin films by low-temperature co-sputtering

Nb3Sn is a promising thin film material for superconducting radio frequency (SRF) applications. Although surface resistivity, critical temperature, and critical field are advantageous in comparison to pure Nb, currently the performance of Nb3Sn is lacking behind due to its complex defect structure and phase inhomogeneities. In this work, the influence of the kinetic energy of the deposited particles on the defect structure in Nb3Sn thin films synthesized at low temperatures is investigated. A combination of extended x-ray absorption fine structure analysis, x-ray absorption spectroscopy mapping, and transmission electron microscopy reveals an improved local order and elemental homogeneity of the Nb3Sn films induced by higher kinetic energies of the elemental species during deposition. Even more, these process conditions lead to suppressed local inhomogeneities at grain boundaries, which can be one of the causes of critically reduced superconducting properties of low temperature sputter-coated Nb3Sn thin films. Finally, we show that the magnetic field-induced reduction of critical currents across weak-links formed at grain boundaries can be eliminated by the suggested materials’ synthesis.

Near-isotropic enhancement of the 20 K critical current of REBa2Cu3O7 coated conductors from columnar defects

Normal-incidence irradiation by 100 MeV Ag ions is used to improve flux pinning in previously optimised commercial REBCO tapes from the American Superconductor Corporation. We observe distinct critical-current anisotropy enhancements below and above 40 K. Above 40 K a strong c-axis peak appears in the angular dependence of the critical current, as is usually expected upon the introduction of columnar defects. The critical current is enhanced significantly but only for a limited range of field angles. Close to the parallel-field direction there is no enhancement or even a reduction in critical current. Below 40 K, on the other hand, the enhancement is much broader with respect to field angle, creating an almost isotropic response at 20 K, 3 T. The absence of a prominent c-axis peak does not indicate a lack of pinning, since the absolute value of the critical current still increases by a factor of 2.8 compared to an unirradiated sample. Instead, we postulate that pre-existing point-like pinning centres act to mediate an interaction between the existing planar and newly-introduced columnar pins, broadening both contributions. The point-like pins become less effective with increasing temperature as the coherence length increases, leading to a reduction in this interaction and a separation of the individual peaks relating to planar and columnar pins. At 20 K, we achieve an enhancement in the angular-minimum critical current by a factor of 2.7, in a material that had already been process-optimised for low-temperature pinning.

Influence of filament number and size on the basic properties of in situ made MgB2 wires

Monel-sheathed MgB2 wires with 6, 18 and 54 filaments of diameter 0.83 mm manufactured by Sam Dong Co., Ltd, have been subjected to twisting, drawing and rolling and measurements at low temperatures. R(T), I–V characteristics, critical currents and stress/strain tolerances of these wires were analyzed. Low reduction of critical current (⩽10%) by twisting between 50 mm and 12.5 mm was observed, especially for the wire with 54 filaments, which also showed the best strain tolerance to tension, ∼0.43% at 4.2 K. The engineering current density of the 18-filament wire was decreased by 56% by drawing from 0.83 mm to 0.4 mm, but improved by ∼24% by rolling from 0.83 mm to 0.64 mm. A small uninsulated coil was made from wire flattened from 0.83 mm to 0.64 mm by the wind and react process, resulting in a very high winding packing factor of 0.91 and also a high winding current density of 104 A cm−2 at B ⩽ 5.6 T. The presented properties are interesting for possible applications of these MgB2 wires in DC windings.

Numerical analysis of the mechanical and electrical properties of CORC cables under torsional loading

The type II high-temperature superconducting (HTS) ReBCO tapes have been widely used in high-field magnets. Conductors on round core (CORC) cables can carry very high currents in background magnetic fields exceeding 20 T, making it one of the most important types of HTS cables. However, the cables of the magnets in the fusion reactor are subjected to large mechanical and electromagnetic loads that may twist the CORC cables. The intrinsic strain of the superconducting cable is constrained by the brittleness of the HTS tape, which, if exceeded, will cause irreversible damage by producing cracks in the ReBCO layer. A finite element (FE) model was developed to predict how the CORC cable will perform in torsional cases. A comparison of numerical simulations with experiments for a single- and double-layer CORC cable is first performed to validate the model's reliability. For single-layer CORC cables, our model reduces the error between FE results and experiments from 46.7% to 6.7%. Variations in the winding angle, tape width, Poisson's ratio of the CORC cable core material, and core radius were made as part of the parametric analysis. The critical torsion angle is analyzed from the perspective of critical current density reduction. The results show that maintaining a small tape gap (smaller winding angle (26−30°), smaller core diameter, and larger tape width) and a small Poisson ratio can improve the strain limit of the ReBCO layer. The reason for the plateau phenomenon in the normalized critical current density curve of the double-layer CORC cable is reinterpreted. It is also confirmed that multi-layer CORC cables still need to maintain a small tape gap. The FE model can guide optimizing a cable design for specific application conditions.

Analytical approximations for the self-field distribution of a superconducting tape between iron cores

Magnetic switches apply AC magnetic fields to DC current-carrying high temperature superconducting (HTS) tapes to generate DC voltages and are commonly used in the persistent current switches (PCSs) and flux pumps to charge HTS-coated conductor magnets. Normally, they are made of copper field coils and iron cores with narrow air gaps for the HTS tape to pass through. However, the perpendicular components of the self-field of the HTS tape in the air gap can be enhanced by the iron cores and cause a critical current reduction of up to 40% to the tape. If ignored, this reduction, rather than the magnets themselves, will limit the current carrying capability of the HTS magnets. To tackle this problem, we present analytical approximations to calculate the self-field distribution of a superconducting tape between iron cores. The approximate solutions are based on the method of images in electromagnetics to simplify the derivation and are then verified by the experiments and 3D finite element method models using the T–A formulation. The solutions are universal and can be applied to almost all the magnetic switches currently in use. A case study of typical magnetic switches shows that the solutions can be used to determine the critical current reduction quickly and accurately, analyse the influence of different parameters, and simplify the design process of magnetic switches. The results can significantly benefit the design and optimisation of PCSs and flux pumps for HTS magnet charging systems in the future.

Magnetization loss of CORC cables under axial tensile loading

As a highly flexible and fully isotropic cable structure, CORC (Conductor on Round Core) cable wound with high-temperature superconducting (HTS) tapes has promise for giant magnets, including fusion magnets, high-energy accelerator magnets, and nuclear magnetic resonance. CORC cables are subjected to mechanical, thermal, and electromagnetic loadings during preparation and operation. Axial tension is one of the basic deformation modes of CORC cables. To investigate the impact of axial tension loads on the electromagnetic performance of CORC cables, a mechanical-electromagnetic model is created in this study. A comparison of numerical simulations and experiments was first performed for single straight tape and single-layer CORC cables to verify the model's reliability, with particular attention to the critical current reduction and the variation of magnetization loss during axial tension. The model developed in this paper may evaluate electromagnetic performance under applied AC magnetic fields with small amplitudes and mechanical response to axial tension loads. On this basis, the strain distribution of CORC cables under axial tension and their magnetization loss characteristics under various strain states are presented. The effects of different cable design parameters on the critical current and magnetization loss are discussed. The results show that the strain affects the magnetization loss of CORC cable significantly, especially for ones with larger winding angles. The magnetization loss can be reduced by choosing a narrower tape, a smaller winding angle, or a cable core material with a higher Poisson ratio. This study can provide a theoretical basis for the structure optimization design and practical application of CORC cables.

Investigating the effect of transverse compressive loads on the electromagnetic performance of superconducting CORC® cables

High-temperature superconductor (Re)Ba2Cu3O x (ReBCO) conductor on round core cable (CORC®) has a large current carrying capacity for high field magnets. Lorentz forces acting on CORC conductors, cause a reduction of the critical current, or even permanent degradation of their performance when exceeding critical values. Transverse compressive stress is one of the principal mechanical stresses when CORC cables are bundled to cable-in-conduit conductors (CICC) conductors capable of operating at currents up to 100 kA in magnetic fields of up to 20 T. In this research, a mechanical-electromagnetic model is developed to study the effect of transverse compressive loads on the electromagnetic performance of CORC cables. A mechanical transverse load on the cable is implemented to simulate the electromagnetic force. A comparison of numerical simulations with experiments for a three-layer CORC cable is first performed to validate the model’s reliability, with particular attention to critical current reduction during the transverse compression process. A novel feature of this paper is that the model developed can analyze both mechanical response under transverse compressive loads and electromagnetic performance under applied AC magnetic fields with low amplitudes. On this basis, the model investigates the effects of winding parameters on the axial strain and critical current reduction of the ReBCO layer in a single-layer CORC cable. The numerical analysis shows that increasing the winding angle can reduce the axial strain and critical current reduction of the ReBCO layer in the contact area. Subsequently, a detailed comparative study is carried out studying the axial strain of the ReBCO layer in the non-contact area with and without taking the winding core into account. In addition, a sudden increase in the magnetization loss is explained when the transverse compressive load reaches a certain level. Finally, a six-layer CORC cable’s electromagnetic analysis is performed, and each tape layer’s critical current reduction is investigated and discussed. The comparison of magnetization loss and current density between six- and single-layer CORC cables in the no-strain case is also given. This finite element model can guide optimizing a cable design for specific application conditions.

REBCO Coils With Variable Co-Wind Dimensions Under Static and Cyclic Axial Pressure Loads at 77 K

An investigation into the effects of high cycle fatigue on REBCO coils along their axis of rotation was performed to establish design limits. Three coils were tested in liquid nitrogen via a hydraulic materials testing machine. The coils were fabricated with the same type of REBCO tape but had different co-wind materials and dimensions. The results showed that for a coil with REBCO tape wider than its co-wind, where the loads bear directly on the conductor, had 5% permanent critical current degradation at pressures near 100 MPa. A significant improvement was observed in a wax impregnated coil, which aided to distribute loads, with a 1.2% permanent critical current reduction after 50,000 load cycles to 125 MPa. Additionally, a coil with co-wind wider than its REBCO tape was also improved and reached 5% reduction after 50,000 cycles at pressures up to 100 MPa and continued loading to 151 MPa.

Current Crowding in Nanoscale Superconductors within the Ginzburg-Landau Model

The current density in a superconductor with turnarounds or constrictions is nonuniform due to a geometrical current-crowding effect. This effect reduces the critical current in the superconducting structure compared to a straight segment and is of importance when designing superconducting devices. We investigate the current-crowding effect in numerical simulations within the generalized time-dependent Ginzburg-Landau (GTDGL) model. The results are validated experimentally by measuring the magnetic field dependence of the critical current in superconducting-nanowire structures, similar to those employed in single-photon detector devices. Comparing the results with London theory, we conclude that the reduction in critical current is significantly smaller in the GTDGL model. This difference is attributed to the current redistribution effect, which reduces the current density at weak points of the superconductor and counteracts the current-crowding effect. We numerically investigate the effect of the fill factor on the critical current in a meander and conclude that the reduction of the critical current is low enough to justify fill factors higher than 33% for applications where the detection efficiency is critical. Finally, we propose a meander design that can combine a high fill factor and low current crowding.

Current–voltage curve of the high temperature superconductor with local reduction of critical current

Particular feature of the 2nd generation of conductors, based on the high-temperature superconducting compounds and produced nowadays in industrial process, is the fluctuation of properties along the conductor length. As a consequence, the voltage appearing at approaching the maximum transportable DC current could come from just one single weak spot. In such a place, characterized by the critical current reduced with respect to the rest of the conductor, the excess dissipation results in a locally elevated temperature. We developed an analytical theory predicting the experimentally observed current–voltage characteristics of such conductor, based on the weak spot properties and the cooling conditions. It extends our previous work, that was focused on forecasting the value of current at which would happen the thermal runaway, accompanied by an abrupt growth of the measured voltage. Here we derive the analytical expression that provides prediction for the current–voltage curve in wider range of currents, without necessity to reach thermal runaway. Then, a more reliable determination of the superconductor properties, in particular the flux creep exponent, can be achieved. Use of the model in the analysis of experimental data is illustrated, and its limitations resulting from the simplifications, introduced in order to reach the analytical predictions, are discussed.

On the mechanisms governing the critical current reduction in Nb3Sn Rutherford cables under transverse stress

Within the framework of the HiLumi-LHC project, CERN is currently manufacturing 11 T dipole and quadrupole accelerator magnets using state-of-the-art Nb3Sn Rutherford cables. Even higher magnetic fields are considered by the Hadron Future Circular Collider (FCC-hh) design study, which plans to develop 16 T Nb3Sn bending dipoles. In such high-field magnets, the design pre-stress can reach considerable values (150–200 MPa) and, since Nb3Sn is a brittle compound, this can constitute a technological difficult challenge. Due to the significant impact that a transverse load can have on the performances of a Nb3Sn magnet, CERN has launched a campaign of critical current measurements of reacted and impregnated Nb3Sn cables subjected to transverse pressure up to about 210 MPa. In this paper, results obtained on 18-strand 10-mm-wide cable sample based on a 1-mm-diameter powder-in-tube (PIT) wire are presented. The tests were carried out on a 2-m-long sample by using the FReSCa test station, at T = 4.3 K and background magnetic fields up to 9.6 T. For applied pressures below ≈ 130 MPa, only reversible reductions of the critical current, Ic, are observed. At higher pressures, a permanent Ic reduction occurs; such irreversible behaviour is due to the residual stresses generated by the plastic deformations of the copper stabilizer. This type of current reduction, whether reversible or not, is fully governed by the strain-induced variations of the upper critical field, Bc2. At higher pressures, estimated between 180 and 210 MPa, it is indeed plausible to believe that cracking of filaments occurs, with detrimental consequences for the Nb3Sn cable’s electrical performances. The complete set of critical current data here presented, collected at different pressures and as a function of the applied magnetic field, allows for the first time to investigate the evolution of superconducting parameters such as the upper critical field Bc2 in the irreversibility region, where both the effects of Cu matrix plasticization and/or cracking of filaments may occur. The experimental approach and data interpretation have a general value and can be applied to any typology of Rutherford cable.

Stability of DC transport in HTS conductor with local critical current reduction

A common feature of commercially available conductors based on high-temperature superconducting compounds is the fluctuation of critical current along the length. Fortunately, the practice adopted by manufacturers nowadays is to supply the detailed I c(x) data with the conductor. Compared to knowing just the average of critical current, this should also allow a much better prediction of the conductor performance. Statistical methods are suitable for this purpose in the case when the fluctuations are regular at the low end of critical current distribution. However, a different approach is necessary at the presence of ‘weak spots’ that drop out of any statistics. Because of the strong nonlinearity of the current–voltage curve, such a location could transform into a ‘hot spot’ at transporting direct current (DC), with an abrupt increase of temperature endangering the conductor operation. We present a set of analytical formulas including the prediction of the maximum DC that could be carried sustainably before the thermal runaway appears. It is necessary to know the cooling conditions as well as the properties of the conductor constituents and their architecture. A formula for the voltage appearing on a weak spot, and its dependence on the DC, is also proposed. For this purpose the result of previous theoretical work has been slightly modified after comparing it with numerical iterative computations and finite element modeling. We demonstrate that the derived model allows a powerful analysis of experimental data comprising an estimation of the weak spot parameters i.e. its critical current and the length of the defect zone.

A methodology to compute the critical current limit in Nb3Sn magnets

Numerous experiments have shown that the loads applied to Nb3Sn strands and cables can reduce their critical current. Experiments, performed on uniaxially loaded strands, allowed to define clear laws to describe the evolution of the critical surface as a function of the applied current, field, temperature and strain. It is, however, still unclear how these laws can be applied to superconducting magnets. The present paper proposes a methodology to estimate the critical current and temperature margin reduction on superconducting magnets due to stress on the superconducting material. The methodology is tested on the MQXF magnets, a quadrupole developed for the High Luminosity LHC project, and successfully validated by comparing computed strain with data from strain gauge measurements. Results suggested that, because of the stresses arising in winding during assembly, cool-down and powering, the current limit of the magnet is lower than the expected short sample limit, and that the most critical region does not coincide with the peak field location.

Transverse-pressure susceptibility of high-Jc RRP and PIT types of Nb3Sn Rutherford cables for accelerator magnets

In the frame of the High-Luminosity Large Hadron Collider construction and Future Circular Collider development program, the magnetic field in the accelerator dipole magnets is being enhanced to 11 T, and 15 T to 16 T level, respectively. Advanced Nb3Sn superconductors with a non-copper critical current density exceeding 2500 A mm−2 at 4.2 K and 12 T, are being developed using the Restacked-Rod-Process (RRP) and Powder-In-Tube (PIT) wire technologies. However, since Nb3Sn is extremely brittle, it is a significant challenge to construct the high-field dipole magnets with such very strain-susceptible superconductor. The high-level of stress acting on the wide face of the Rutherford cables in the coils of 120 MPa to 200 MPa generated by the Lorenz’ force, causes initially a reversible reduction and eventually at some stress level followed by permanent degradation of the critical current when strain goes to high. This study sets out to examine the critical current and upper critical field performance of state-of-the-art RRP and PIT Nb3Sn Rutherford cables in terms of transverse pressure. The variation of the critical current and upper critical field due to the thermal- and mechanical load-cycling was investigated as well. For reference, the critical current of witness wires characterized on standard ITER type barrels were also measured. The results indicate that the RRP type of Nb3Sn Rutherford cables, when fully impregnated with epoxy resin, are able to withstand a transverse stress of 170 MPa to 250 MPa without noticeable irreversible critical current reduction. For the transverse pressure limit for present PIT type of Nb3Sn Rutherford cables somewhat lower values are found at the level of 50 MPa to 120 MPa. Therefore, given the present cables, the high-field dipole magnet construction can be realized using the RRP Nb3Sn Rutherford cables, while for PIT type cables more cable development is requested to enhance the onset of irreversible degradation. The reversible critical current reduction in RRP type of cables of 10% at 150 MPa to 250 MPa needs to be taken into account when predicting magnet performance. Finally, extreme care needs to be taken into account for Nb3Sn coil fabrication, since the experimental results show significant critical current reduction due to stress concentrations already at 0.2° misalignment angles between the pressure applying surface and the surface of the impregnated cable.

A 3D Finite Element Model of the Reversible Critical Current Reduction Due to Transverse Load in Nb$_3$Sn Wires

A 3D Finite Element Model of the Reversible Critical Current Reduction Due to Transverse Load in Nb$_3$Sn Wires

Pressure-induced critical current reduction in impregnated Nb3Sn Rutherford cables for use in future accelerator magnets

The measured critical current reduction in Nb3Sn Rutherford cables under magnet-relevant transverse pressure levels is analyzed in terms of the strain state of the filaments inside their strands. Several straightforward mechanical 2D FE models of the cables’ cross-section are used to translate the stress that is applied to the surface of the impregnated cables into a strain distribution on its strands. The resulting critical current reduction of the cable is then estimated from the average deviatoric strain in the strands’ filamentary zone, using the well-established strain scaling relations obtained for isolated strands. This allows to identify the main factors that influence the pressure response of impregnated Nb3Sn accelerator cables. The analysis is presented for state-of-the-art cable samples that were measured at the University of Twente and shows how especially stiff and incompressible resins reduces the deviatoric strain in the filamentary zone of the cable strands, but also how relatively small alignment errors can lead to stress concentrations that reduce the critical current density significantly.

Impact of critical current fluctuations on the performance of a coated conductor tape

Coated conductor (CC) tapes often exhibit critical current, Ic, which fluctuates along the length coordinate, x, leading to an Ic(x) dependence. The need to reduce the price of these tapes does not favor a decrease in the variation of Ic in the near future. Therefore, it is reasonable to develop a method for estimating the possible impact of such fluctuating transport ability on the performance of superconducting devices. Fortunately, providing Ic(x) data together with the delivered conductor is becoming a standard approach among CC tape producers, and in-depth analysis of such data is now possible. Extrapolation of the short sample testing methodology to the case of a device incorporating many meters of CC tape leads to the introduction of an ‘overall critical current’ as a value generating 1 μV cm−1 of electric field over the whole conductor. We show that in the case of Ic(x) fluctuations obeying the Gaussian distribution one can predict the value of the overall critical current from the mean value and the variance of the Ic(x) data set. Deviation from the Gaussian distribution found in real tapes would cause a further reduction of the overall critical current. Conversely, in the case of strong dropouts in the critical current value, a statistical approach is useless and one must analyze the probability of the weakest location developing in a hot spot with a dramatic increase of temperature. Extending the analysis for a single tape to cables and coils results in a rather simple summary: when current sharing is possible, the reduction of overall critical current with respect to its mean value is significantly depressed. This favors the parallel arrangement of tapes with low contact resistance allowing current migration from tape to tape. On the other hand, the insulation of tapes leads to the same overall critical current reduction as observed for a single tape.