Field Dependence Of Critical Current Research Articles

A platform to study defect-induced behavior in high-temperature superconductor cables

High-temperature superconductor (HTS) cables and magnets are enabling a range of high-current and high-field applications, including compact fusion devices aiming to achieve net energy. Defects in HTS pose manufacturing, cost, and operational challenges. A rigorous understanding and predictive capability for defect-induced behavior at relevant scale has not been established. To address this shortcoming, we have developed a cable-level defect characterization experimental platform coupled to high-fidelity computational modeling. The cable ( Ic∼ 438 A at 77.4 K, self-field) comprises a non-twisted 70 cm-long copper former containing a soldered stack of five rare-earth barium copper oxide (REBCO) tapes (each with Ic = 115.7 A/4 mm-w at 77.4 K, self-field), which can contain a variety of induced defects. Spatially-resolved electric fields are measured with a high-density voltage tap array and absolute current distribution with six custom-wound embedded Rogowski coils. 3D circuit modeling uses nodal analysis and self-consistently accounts for the magnetic field dependence of critical current. The model successfully predicts the experimentally measured spatial and operating current dependencies of electric field and current distribution with no defects, one defect, and two defects, validating the defect characterization platform as a tool for improving the design, cost, fabrication, and operation of REBCO cables.

Magnetic field dependence of critical currents of cross-type Josephson junctions with inhomogeneous critical current density under oblique magnetic fields

Abstract Studies of the magnetic interference of sandwich-type Josephson junctions in which perpendicular or oblique magnetic fields are applied to the junction plane have received less attention than those where the applied magnetic fields are parallel. Recently, it has been theoretically demonstrated that a variety of magnetic interferences of the critical currents appear when oblique magnetic fields are applied to a cross-type junction with homogeneous critical current density. We theoretically investigated the effect of the inhomogeneous critical current density in the junction plane, and found that more complicated magnetic interferences appeared. We considered the distribution of the current density flowing through the junction plane to explore the cause of these complex magnetic interferences.

Impact of strain on the SOT-driven dynamics of thin film Mn3Sn

Mn 3 Sn, a metallic antiferromagnet with an anti-chiral 120° spin structure, generates intriguing magneto-transport signatures such as a large anomalous Hall effect, spin-polarized current with novel symmetries, anomalous Nernst effect, and magneto-optic Kerr effect. When grown epitaxially as MgO(110)[001]∥Mn3Sn(01¯1¯0)[0001], Mn3Sn experiences a uniaxial tensile strain, which changes the bulk sixfold anisotropy to a twofold perpendicular magnetic anisotropy (PMA). Here, we investigate the field-assisted spin–orbit-torque (SOT)-driven dynamics in single-domain Mn3Sn with PMA. We find that for non-zero external magnetic fields, the magnetic octupole moment of Mn3Sn can be switched between the two stable states if the input current is between two field-dependent critical currents. Below the lower critical current, the magnetic octupole moment exhibits a stationary state in the vicinity of the initial stable state. On the other hand, above the higher critical current, the magnetic octupole moment shows oscillatory dynamics which could, in principle, be tuned from the 100s of megahertz to the terahertz range. We obtain approximate analytic expressions of the two critical currents that agree very well with the numerical simulations for experimentally relevant magnetic fields. We also obtain a unified functional form of the switching time vs the input current for different magnetic fields. Finally, we show that for lower values of Gilbert damping (α≲2×10−3), the critical currents and the final steady states depend significantly on α. The numerical and analytic results presented in our work can be used by both theorists and experimentalists to understand the SOT-driven order dynamics in PMA Mn3Sn and design future experiments and devices.

Weak spin-flip scattering in Pd89Ni11 interlayer of NbN-based ferromagnetic Josephson junctions

We studied niobium nitride (NbN)-based π-junctions with a diluted ferromagnetic Pd89Ni11 interlayer (NbN/PdNi/NbN junctions). In the NbN/PdNi/NbN junctions with various PdNi thicknesses, we observed a non-monotonic dependence of the critical currents on PdNi thickness, indicating the effects of the exchange interaction on the superconducting order parameter. From theoretical fitting of the experimental data, we found that the NbN/PdNi/NbN junctions showed a significantly smaller degree of spin-flip scattering in the PdNi interlayer than in the CuNi interlayer of NbN/CuNi/NbN junctions reported previously. The weak spin-flip scattering leads to a longer decay length of the Josephson critical current, so the critical currents were observed over a wide range of PdNi thicknesses (10–40 nm). We also fabricated superconducting quantum interference devices (SQUIDs) including the NbN/PdNi/NbN junction, using a PdNi thickness in which the π-state was expected. A half-flux-quantum shift, as evidence of the π-state, was observed in the magnetic field-dependent critical currents of the SQUIDs. This result represents an important step towards the practical application of NbN-based π-Josephson junctions.

Numerical Study on Ring-shape Superconducting Trapped Field Magnet Based on Circuit Model

The so-called ring-shape superconducting trapped field magnet has been proved as a potential candidate to replace commercial permanent magnets in practical industrial applications on account of its jointless structure. In this paper, a circuit method based on Bean model, E-J power law and Faraday law has been built to investigate the magnetization mechanism of ring-shape magnet. The field dependent critical current of superconducting materials has been taken into consideration for further optimization. The numerical model was verified by both finite element method (FEM) and experiments. Compared with other methods, the circuit-based simulation method has the advantages of high efficiency, fast speed and wide applicability. On basis of this method, the paper also studied characteristics of ring-shape magnets under different working conditions to provide a guideline for the magnet design.

Influence of field-dependent critical current on harmonic AC loss analysis in HTS coils for superconducting transformers supplying non-linear loads

There are two main obstacles in front of the development of high temperature superconducting (HTS) technology for electric power network applications; tape price and cooling cost. In order to reduce cooling cost, it is vital to evaluate AC transport current loss of the tapes precisely and then reduce it by some design innovative approaches. In addition, AC transport current loss in HTS material is a critical design variable for large-scale power network applications such as HTS transformers, superconducting fault current limiters, and power cables, since they are continuously carrying the network/load current during their operating life. In existing power networks, harmonic production sources are commonly used and thus, currents are distorted. Therefore, the effect of nonsinusoidal current on the critical apparatus in the network such as transformer must be studied. In this paper, AC transport current loss of a single-turn 2G YBCO HTS coil was modeled and numerically calculated under nonsinusoidal transport current using finite element method. Furthermore, influence of dependency of critical current density to magnetic field on the AC transport current loss of HTS coil when carries distorted currents was considered. It was observed that nonsinusoidal current causes excessive losses in HTS coil. On the other hand, a case study on an HTS transformer supplying non-linear load was considered to study the loss increment as well as heat load change. It was observed that current harmonics increases the AC loss, and heat load of transformer and decreases the efficiency, consequently.

Effect of swift heavy ions irradiation on the microstructure and current-carrying capability in YBa2Cu3O7-δ high temperature superconductor films

YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7−<i>δ</i></sub> (YBCO) high temperature superconductor materials have many promising applications in energy, transportation and so on. Nonetheless, the application of YBCO in high magnetic field was limited because of low critical current. One-dimensional latent tracks produced by swift heavy ions irradiation can be effective pinning centers, thus enhancing superconductivity in external field. YBCO high temperature superconducting films were irradiated with 1.9 GeV Ta ions at room temperature and vacuum condition. Structure damages in irradiated samples were characterized by transmission electron microscopy (TEM). Continuous amorphous latent tracks, with diameter from 5 nm to 15 nm, throughout the whole superconducting layer can be observed from TEM images. Physical property measurement system (PPMS) was used to measure superconducting properties of samples before and after irradiation. When irradiated at optimal fluence of 8 × 10<sup>10</sup> ions/cm<sup>2</sup>, critical current reaches its maximum value and pinning force was twice of unirradiated sample, while critical temperature almost unchanged. The analysis of experimental results shows that latent tracks produced by swift heavy ions irradiation can enhance in-field current-carrying capability, without decreasing critical temperature. In the power-law regime <inline-formula><tex-math id="M2">\begin{document}${J_c} \propto {B^{ - \alpha }}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191914_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191914_M2.png"/></alternatives></inline-formula> values of <i>ɑ</i> decreased with the increasing of fluence, indicating a weaker magnetic field dependence of critical current. <i>ɑ</i> reaches its lowest value 0.375 when irradiated at a fluence of 5.0 × 10<sup>11</sup> ions/cm<sup>2</sup>, corresponding to a lowest in-field <i>J<sub>c</sub></i>. This result may be a combination of increasing pinning centers and decreasing superconductor volumes that work together. Normalized pinning force <i>f</i><sub>p</sub> = <i>F</i><sub>p</sub>/<i>F</i><sub>p,max</sub> of sample irradiated with different fluence as a function of magnetic field <i>h</i> = <i>H</i>/<i>H</i><sub>max</sub> was analyzed using Higuchi model. Fitting results show that planar defects are main source of pinning when <i>h</i> > 1, independent of irradiation. Whereas, dominate pinning centers shifting from surface pinning to isotropic normal point pinning with increasing fluence when <i>h</i> < 1. Given that latent tracks produced by Ta ions irradiation act as strong anisotropic pinning centers, the reason of the dominate pinning centers change with increasing fluence remains to be further studied.

Superconducting properties of YBCO thin films grown on [001] quartz substrates by pulsed laser deposition

We present an investigation of the superconducting properties of thin YBa2Cu3O7-x (YBCO) films grown on [001] single-crystalline quartz substrates by pulsed laser deposition (PLD) technique. The growth of YBCO on quartz is challenging due to large crystal lattice mismatch between YBCO and quartz. We obtained highly c-oriented textured films with superconducting transition at about 85 K, transition width of 1 K, and critical current density jc ≈ 104 A cm−2 at 77 K. Analysis of the temperature dependences of the resistivity and current-voltage characteristics has shown the presence of the thermally-assisted flux flow at temperatures above 70 K. From the temperature and magnetic field dependences of critical current, vortex activation energy, U0(H), was estimated for both parallel and perpendicular orientation of magnetic field. Second critical field, Hc2(0), was estimated from extrapolation of the Hc2(T) dependences. The obtained results are an important step towards realization of YBCO thin films on amorphous silica fibers for the third generation (3 G) of the HTS long wire with low losses in alternative current applications.

Numerical modelling of dynamic resistance in high-temperature superconducting coated-conductor wires

The use of superconducting wire within AC power systems is complicated by the dissipative interactions that occur when a superconductor is exposed to an alternating current and/or magnetic field, giving rise to a superconducting AC loss caused by the motion of vortices within the superconducting material. When a superconductor is exposed to an alternating field whilst carrying a constant DC transport current, a DC electrical resistance can be observed, commonly referred to as ‘dynamic resistance.’ Dynamic resistance is relevant to many potential high-temperature superconducting (HTS) applications and has been identified as critical to understanding the operating mechanism of HTS flux pump devices. In this paper, a 2D numerical model based on the finite-element method and implementing the H-formulation is used to calculate the dynamic resistance and total AC loss in a coated-conductor HTS wire carrying an arbitrary DC transport current and exposed to background AC magnetic fields up to 100 mT. The measured angular dependence of the superconducting properties of the wire are used as input data, and the model is validated using experimental data for magnetic fields perpendicular to the plane of the wire, as well as at angles of 30° and 60° to this axis. The model is used to obtain insights into the characteristics of such dynamic resistance, including its relationship with the applied current and field, the wire’s superconducting properties, the threshold field above which dynamic resistance is generated and the flux-flow resistance that arises when the total driven transport current exceeds the field-dependent critical current, Ic(B), of the wire. It is shown that the dynamic resistance can be mostly determined by the perpendicular field component with subtle differences determined by the angular dependence of the superconducting properties of the wire. The dynamic resistance in parallel fields is essentially negligible until Jc is exceeded and flux-flow resistance occurs.

Universal scaling of the self-field critical current in superconductors: from sub-nanometre to millimetre size

Universal scaling behaviour in superconductors has significantly elucidated fluctuation and phase transition phenomena in these materials. However, universal behaviour for the most practical property, the critical current, was not contemplated because prevailing models invoke nucleation and migration of flux vortices. Such migration depends critically on pinning, and the detailed microstructure naturally differs from one material to another, even within a single material. Through microstructural engineering there have been ongoing improvements in the field-dependent critical current, thus illustrating its non-universal behaviour. But here we demonstrate the universal size scaling of the self-field critical current for any superconductor, of any symmetry, geometry or band multiplicity. Key to our analysis is the huge range of sample dimensions, from single-atomic-layer to mm-scale. These have widely variable microstructure with transition temperatures ranging from 1.2 K to the current record, 203 K. In all cases the critical current is governed by a fundamental surface current density limit given by the relevant critical field divided by the penetration depth.

Vortex shaking study of REBCO tape with consideration of anisotropic characteristics

The second generation high temperature superconductor, specifically REBCO, has become a new research focus in the development of a new generation of high-field (>25 T) magnets. One of the main challenges in the application of the magnets is the current screening problem. Previous research shows that for magnetized superconducting stacks and bulks the application of an AC field in plane with the circulating current will lead to demagnetization due to vortex shaking, which provides a possible solution to remove the shielding current. This paper provides an in-depth study, both experimentally and numerically, to unveil the vortex shaking mechanism of REBCO stacks. A new experiment was carried out to measure the demagnetization rate of REBCO stacks exposed to an in-plane AC magnetic field. Meanwhile, 2D finite element models, based on the E–J power law, are developed for simulating the vortex shaking effect of the AC magnetic field. Qualitative agreement was obtained between the experimental and the simulation results. Our results show that the applied in-plane magnetic field leads to a sudden decay of trapped magnetic field in the first half shaking cycle, which is caused by the magnetic field dependence of critical current. Furthermore, the decline of demagnetization rate with the increase of tape number is mainly due to the cross-magnetic field being screened by the top and bottom stacks during the shaking process, which leads to lower demagnetization rate of inner layers. We also demonstrate that the frequency of the applied AC magnetic field has little impact on the demagnetization process. Our modeling tool and findings perfect the vortex shaking theory and provide helpful guidance for eliminating screening current in the new generation REBCO magnets.

Dynamic resistance of a high-Tc coated conductor wire in a perpendicular magnetic field at 77 K

Superconducting high-Tc coated conductor (CC) wires comprise a ceramic thin film with a large aspect ratio. This geometry can lead to significant dissipative losses when exposed to an alternating magnetic field. Here we report experimental measurements of the ‘dynamic resistance’ of commercially available SuperPower and Fujikura CC wires in an AC perpendicular field. The onset of dynamic resistance occurs at a threshold field amplitude, which is determined by the total DC transport current and the penetration field of the conductor. We show that the field-dependence of the normalised magnetisation loss provides an unambiguous value for this threshold field at zero transport current. From this insight we then obtain an expression for the dynamic resistance in perpendicular field. This approach implies a linear relationship between dynamic resistance and applied field amplitude, and also between threshold field and transport current and this is consistent with our experimental data. The analytical expression obtained yields values that closely agree with measurements obtained across a wide range of frequencies and transport currents, and for multiple CC wires produced by different wire manufacturers and with significantly differing dimensions and critical currents. We further show that at high transport currents, the measured DC resistance includes an additional nonlinear term which is due to flux-flow resistance incurred by the DC transport current. This occurs once the field-dependent critical current of the wire falls below the DC transport current for part of each field cycle. Our results provide an effective and simple approach to calculating the dynamic resistance of a CC wire, at current and field magnitudes consistent with those expected in superconducting machines.

Measurements and Numerical Simulations of Trapped Field in a Stack of HTS Tapes

Trapped field magnets are usually constructed on the base of bulk YBCO superconductors. However, recent achievements in the production of long-size coated conductors have opened the opportunity of using a tape stack for these applications. Better thermal conductivity, mechanical stability in high fields, and high critical current densities make such systems favorable. Moreover, the tape form of the conductor allows for organizing different spatial structures and optimizing device design. Trapped field was measured on the stack of high-temperature superconducting tapes in this work. An industrially stabilized (with copper shield) tape, which was produced by SuperOx company with GdBa 2 Cu 3 O 7-x superconductor inside, was used in experiments. The stack was made of 12-mm-diameter disk-shaped tapes, and the height was 20 layers. Magnetization was carried out by an 8-T superconducting magnet on the temperature of 77 K. To calculate the trapped field of a stack, field dependence and angular field dependence of critical current were measured on these tapes. The finite-element method was used for numerical simulations. It is shown that taking into account the magnetic field orientation in different areas of the stack leads to better agreement with the experimental measured trapped field values.

Crack problem for a functionally graded thin superconducting film with field dependent critical currents

In this study, double exponential model is established to investigate the central crack problem for a functionally graded superconducting film with filed dependent critical current. The stress intensity factors (SIFs) are analytically obtained and numerically calculated. Numerical results show the effects of applied magnetic field, model parameters, and crack length on the SIFs. Among others, in the process of field descent, the crack in the superconducting film easily propagates in the mode-I form. Increasing the graded parameter of shear modulus can inhibit crack propagation. For a fixed reduced field (especially for a larger magnetic field), both the mode-I and mode-II SIFs firstly increase, then decrease with the increasing of introduced non-dimensional exponent parameter. This study should be useful for the application of superconducting devices.

Critical state model for magneto-elastic problem of thin superconducting disks

The magneto-elastic problem of a thin superconducting disk in a perpendicular magnetic field is analyzed with field-dependent critical current. We calculate numerically the body force distribution and discuss the field dependence of Jc on the magneto-elastic behavior during field ascent and descent for three critical state models: Bean, Kim, and exponential models. The results show that when considering a field dependence of Jc, the flux and remagnetization fronts have a larger moving speed towards the center of a disk relative to the Bean model. Simultaneously, the most dangerous stage of possible cracking for the disk will arrive early in the field decreasing stage. The magnetostriction loops are also presented during a full cycle of the applied field. It is interesting that the calculated magnetostriction loops for the Kim and exponential models are quite similar to the corresponding magnetostriction curves at low and high temperatures measured in the experiment.

AC loss of HTS magnet for AMR refrigerator using magnetic field formulation and edge element in cylindrical coordinates

AMR (Active Magnetic Regenerative) refrigerators require the large variation of the magnetic field and a HTS magnet can be used. The amount of AC loss is very important considering the overall efficiency of the AMR refrigerator. However, it is very hard to estimate the precise loss of the HTS magnet because the magnetic field distribution around the conductor itself depends on the coil configuration and the neighboring HTS wires interact each other through the distorted magnetic field by the screening current Therefore, the AC loss of HTS magnet should be calculated using the whole configuration of the HTS magnet with superconducting characteristic. This paper describes the AC loss of the HTS magnet by an appropriate FEM approach, which uses the non-linear characteristic of HTS conductor. The analysis model is based on the 2-D FEM model, called as 'magnetic field formulation and edge-element model', for whole coil configuration in cylindrical coordinates. The effects of transport current and stacked conductors on the AC loss are investigated considering the field-dependent critical current. The PDE model of 'Comsol multiphysics' is used for the FEM analysis with properly implemented equations for axisymmetric model.

Temperature- and field-dependent critical currents in [(Bi,Pb)2Sr2Ca2Cu3Ox]0.07(La0.7Sr0.3MnO3)0.03 thick films grown on LaAlO3 substrates

La0.7Sr0.3MnO3 (LSMO) nanoparticles were embedded in (Bi,Pb)2Sr2Ca2Cu3Ox (Bi2223) thick films, which were grown by simple melting-quenching-annealing (MQA) method on (001)-oriented LaAlO3 (LAO) substrates. The nominal composition of the composite-like hybrid system was (Bi2223)1−x(LSMO)x with x = 0.03. The constituent elements, Bi2223 and LSMO, were prepared separately by standard solid state reaction and Pechini's method, respectively. The analysis of the X-ray diffraction patterns suggested a polycrystalline growth mode of the thick films on the LAO substrates. From electric transport measurements, the superconducting onset temperature and the superconducting critical temperature (ρ = 0) ended up being 105 and 62 K, respectively. The flux pinning energy U was determined using the Anderson-Kim model. The value of U was compared with those obtained for similar samples with concentrations x = 0.01 and x = 0.05. Current-voltage characteristics were recorded at different temperatures in order to analyze the behavior of the superconducting current (Ic) of the films. A dramatic drop of Ic was observed at ∼20 K. This seems to be linked to the presence of flux creep acting as dissipation factors attributed to LSMO nanoparticles. Isothermal magnetization loops recorded at T < Tc and T > Tc showed clear diamagnetic and ferromagnetic signals, which verify the multifunctional character of the system. Based on the isothermal M(H)-loops recorded at 5, 20, and 40 K and taking Kim's model into account, the dependence of superconducting current density (Jc), and the volume pinning force (Fp) on the magnetic field were calculated. The dependence Jc(B) at 5 K showed an exponential-type behavior, which is described by an empirical equation. This empirical equation considers the maximum value of Fp, which may be scaled with the Kramer's expression for Fp. From this scaling procedure, diverse exponents, associated with different pinning mechanisms, were determined. The drastic fall of Jc(B) at T > 20 K is discussed by considering the decreasing of the lower critical field (Hc1), penetration field (Hp), irreversible magnetic field (Hirr), and magnetization maximum (Mmax) with increasing in the LSMO particle content.

Magneto-elastic behaviour of thin type-II superconducting strip with field-dependent critical current

The magneto-elastic behavior of thin superconducting strip in perpendicular magnetic field with field-dependent critical current is studied. We calculate numerically the body force, strain, displacement, and thickness changes in the strip for the Bean model and Kim model during the field ascent and descent. The differences in magnetostriction between the Bean model and the Kim model are analyzed. The magnetostriction during one full cycle of the applied field for both models is presented. The results show that magnetostriction loops are different in these models, and at low temperatures Kim model is in better agreement with experiment than Bean model.

10.1007/s11454-008-1002-9

The magnetic field dependences of critical current are numerically constructed for a long Josephson junction with a shunt-or resistor-type microscopic inhomogeneities and compared to the critical curve of a junction with exponentially varying width. The numerical results show that it is adequate to replace the distributed inhomogeneity of a long Josephson junction by an inhomogeneity localized at one of its ends, which has certain technological advantages. It is also shown that the critical curves of junctions with exponentially varying width and inhomogeneities localized at the ends are unaffected by the mixed fluxon-antifluxon distributions of the magnetic flow. This fact may explain the improvement of the spectra of microwave radiation noted in the literature.

Role of the Grain Oxidation in Improving the In-Field Behavior of ${\rm MgB}_{2}$Ex-Situ Tapes

The grain size and the grain boundaries play an important role in determining the pinning properties and the current carrying capability of MgB2. Here we present an experimental study on the effect of grain oxidation on the superconducting properties of MgB2 ex-situ Powder-in-Tube (PIT) tapes. We fabricated Fe-sheathed monofilamentary tapes using a variety of powders synthesized in inert (IA) or oxidizing (OA) atmosphere. In order to understand the role of magnesium oxide (MgO) we studied the effect of the presence of the oxidation layer on the field dependence of the critical current density. To this purpose, we developed a process for the powder synthesis and tube filling and sealing in controlled atmosphere to reduce the oxygen contamination; with this process the connectivity of the grains in the final tapes proved to be increased. Then, we introduced a controlled oxidation step. We will show how the presence of the MgO layer enhances the critical current field dependence. High energy X-ray diffraction measurements were performed on the samples, and the grain size of the unsintered and sintered powders in the tapes was measured by means of Scanning Electron Microscopy (SEM). The pinning force was studied, and different mechanisms were found for the samples prepared in IA and OA. The different behavior shown by the two different typologies of tapes was correlated with the presence or absence of the MgO layer.