Critical Current Distribution Research Articles

Thermal Analysis and In-Field Critical Current Estimation of Conduction-Cooled REBCO Magnet Considering Nonuniform Temperature Distribution

Due to the high upper critical field and transition temperature, REBCO coated conductor show great promise for conduction-cooled magnet applications. The normal zone of high temperature conductor (HTS) spreads slowly, and the conversion of a weak spot into a hot spot is localized and quite fast. Hence, in-field critical current weak spot evaluation under the nonuniform temperature gradient is important for conduction-cooled magnet stability estimation. Cooling path design needs to take the weak spot into account. In this study, a temperature-field-angle dependent critical current estimation neural network was first trained based on a public database of HTS critical current. The equivalent thermal conductivity was applied for the interface contact between the turns. Thermal contact conditions were given to the interface between the coil and bobbin considering actual production situations, such as thermal grease. Combing the non-uniform magnetic field and thermal distribution, the critical current distribution was evaluated to track the weak part. The results of this study will be employed in the design analysis of high magnetic field conduction cooling magnets in the future.

Noncontact Evaluation of HTS Cylinder for Compact Cryogen-Free NMR

Herein, a compact cryogen-free nuclear magnetic resonance (NMR) system is developed using a stacked high-temperature superconducting (HTS) bulk system. To compensate for magnetic field uniformity, an HTS cylinder is installed inside the measurement space. The cylinder is wound with REBCO tapes placed on the surface of a copper cylinder. The uniformity of its critical current density is important for NMR signal detection. Such an operation requires an examination of the quality of the critical-current-density distribution of the cylinder. A noncontact measurement method is required for such an examination. When a magnetic field is applied, the superconductor exhibits a demagnetization effect. Moreover, if any defect exists in any part of the superconducting tape, that particular part would contain no demagnetization, thus disturbing the relevant magnetic field distribution. In this study, this phenomenon is investigated using DC and AC magnetic fields. The magnets and sensor are placed inside the HTS cylinder, and magnetic fields are applied to the HTS cylinder surface. The results confirm that the proposed method is effective and applicable for evaluating the critical-current distribution.

Electromagnetic and Thermal Analysis of HTS AC Cable using T-A Formulation

High temperature superconducting (HTS) cables have been developed into various products and attracted wide attention in industrial applications due to their high critical temperature, current density, zero resistance and overcurrent strength. Recently the triaxial YBCO cables are used in AC applications with the consideration of the flexibility and economy of materials. In this paper, the transient electromagnetic thermal characteristics of a triaxial HTS cable are analysed by the T-A formulation and the Thermal-Fluid Coupling Module of the COMSOL software under the condition of alternating current flow. Firstly, the electromagnetic T-A formulation and the basic theory of heat transfer are introduced. Transient magnetic fields, critical current distribution, and magnetization losses are discussed under T-A modelling. To evaluate the thermal behaviour of the cable under normal current conditions, liquid nitrogen laminar flow is coupled with the heat transfer module, while the heat source data are obtained from the previous T-A results.

Study on Optimization Design of Electromagnetic Loading liner

Electromagnetic loading liner is a new way to obtain a jet, which utilizes the Lorentz force to collapse the liner. To form effective jet, the jet critical forming model of electromagnetic loading is established based on the traditional jet critical forming conditions and electromagnetic loading characteristics. Through dimensional analysis, control variable method and theoretical calculation, the upper and lower critical peak current distributions are obtained. Finally, the loading current of 1mm thick liner structure is optimized by the critical peak current distribution diagram. The jet forming of the liner under the optimized current loading is calculated through theoretical simulation. The whole liner forms a jet, and the jet velocity, kinetic energy and liner utilization are much improved, which verifies the reliability of the critical current distribution diagram.

In situ detection of delamination and critical current degradation caused by the thermal stress in epoxy impregnated REBa2Cu3O7−δ coils

Epoxy impregnated superconducting coils have better structural integrity and thermal stability. However, for REBa2Cu3O7−δ (REBCO, RE=Rare earth) coils, the mismatch of thermal expansion coefficients between epoxy and REBCO tapes is a serious problem. In this work, the temperature distribution, stress evolution during the cooling process, critical current distribution, and delamination sites inside REBCO coils impregnated using Stycast 2850FT have been studied. We measured the temperature distribution and the hoop strain in the penultimate turn of impregnated coils during the cooling process and analyzed the thermal stress evolution. No damage was observed for coils with the ratio between outer and inner diameter Ro/Ri<1.93. The delamination behavior occurred in coils with Ro/Ri>2.37, where the coils even exhibited a two-stage delamination. The delamination mechanism of REBCO coils was proposed from three aspects: the mechanical analysis, the critical current degradation, and the microscopic analysis. In this work, we found that the actual delamination behavior may appear earlier than the steady-state temperature, and temperature distribution will push the radial stress peak toward the inner radius of the coil, making the inner turn more susceptible to delamination. Multiple delamination locations were accurately predicted and confirmed. The measured compressive hoop strain first increased from −4212 με to −4684 με with the increase in Ro/Ri and then decreased to −3835 με obviously due to delamination. This work reveals in detail the delamination mechanism in impregnated REBCO coils, which is of great significance for the development of damage-free coils.

Research on Data-Driven Approaches for Life Prediction of YBCO Tapes Under Overcurrent

Superconducting power devices have many advantages. In recent years, prototypes of various superconducting power devices based on high-temperature superconducting wires have been successfully developed, and some prototypes have also been tested on the power grid, which has accelerated the development of superconducting power technology. However, the reliability of superconducting devices under overcurrent has not yet been supported by research, which is part of the important reason that restricts large-scale promotion of them. In this article, the critical current degradation and life distribution characteristics of yttrium barium copper oxide (YBCO) tapes under overcurrent were analyzed. The overcurrent test adopted a sinusoidal alternating current with an amplitude of 480 A (4–5 times the critical current) and a frequency of 50 Hz. The duration of each overcurrent was 0.44 s. The critical current of the sample was measured in liquid nitrogen using the 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup> V·m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> criterion. The results show that there is an approximately exponential relationship between the critical current degradation rate of YBCO tapes and the number of overcurrent cycles. The life of YBCO tapes under overcurrent can be considered to obey the two-parameter Weibull distribution. Two different remaining useful life of YBCO tape prediction models based on data-driven methods were built. It is verified through cross-checking that the relative prediction errors of the two methods are 8.4% and 5.3%, respectively. And the validity of the models was verified through uncertainty analysis and the comparison with two traditional statistical methods.

HTS Cross-Shaped Strand With Copper Former: Improvement of HTS Quasi-Isotropic Strand for Better Twisting Characteristics

Twisting strain is a main reason that leads to the degradation of the critical current of high temperature superconducting (HTS) quasi-isotropic strand (Q-IS) under torsional loads. In this article, an HTS cross-shaped strand (C-SS) is proposed in order to improve the twisting characteristics of Q-IS. We first simulate and measure the critical current of Q-IS and C-SS under self-field at 77 K. Subsequently, the arrangement direction of REBCO tapes in Q-IS and C-SS that can minimize the twisting strain is analyzed and obtained. Finally, the twisting strain distribution and twisting characteristics of Q-IS and C-SS under different torsional loads are analyzed numerically and experimentally. The results show that the critical current of C-SS is slightly less than that of Q-IS without torsional load. However, the critical current density and magnetic field distribution of C-SS show better isotropic properties than that of Q-IS. When torsional loads are exerted on both strands, C-SS presents better twisting characteristics than Q-IS and its normalized critical current degrades slower than that of Q-IS.

Beyond the effective length: How to analyze magnetic interference patterns of thin-film planar Josephson junctions with finite lateral dimensions

The magnetic-field-dependent critical current ${I}_{\text{c}}(B)$ of a Josephson junction is determined by the screening currents in its electrodes. In macroscopic junctions, a local vector potential drives the currents; however, in thin-film planar junctions, with electrodes of finite size and various shapes, they are governed by nonlocal electrodynamics. This complicates the extraction of parameters such as the geometry of the effective junction area, the effective junction length, and the critical current density distribution from the ${I}_{\text{c}}(B)$ interference patterns. Here, we provide a method to tackle this problem by simulating the phase differences that drive the shielding currents and use those to find ${I}_{\text{c}}(B)$. To this end, we extend the technique proposed by Clem [Phys. Rev. B 81, 144515 (2010)] to find ${I}_{\text{c}}(B)$ for Josephson junctions separating a superconducting strip of length $L$ and width $W$ with rectangular, ellipsoid, and rhomboid geometries. We find the periodicity of the interference pattern ($\mathrm{\ensuremath{\Delta}}B$) to have geometry-independent limits for $L\ensuremath{\gg}W$ and $L\ensuremath{\ll}W$. By fabricating elliptically shaped superconductor--normal-metal--superconductor junctions with various aspect ratios, we experimentally verify the $L/W$ dependence of $\mathrm{\ensuremath{\Delta}}B$. Finally, we incorporate these results to correctly extract the distribution of critical currents in the junction by the Fourier analysis of ${I}_{\text{c}}(B)$, which makes these results essential for the correct analysis of topological channels in thin-film planar Josephson junctions.

Modeling of HTS high-current stacked conductors with defective tapes in different locations

The numerical modeling of HTS stacked conductors was performed with different quantities and locations of defective tapes. The effects of various defective tapes on the overall critical currents, current distributions, and AC losses were studied. Results show the more defective tapes and the higher defect grades were, the larger degradations of critical currents would be. If the quantity of defective tapes was 10, compared with the non-defect case, the AC loss increased by 62% in Scenario A (defective tapes increasing from outside to inside), increased by 24% in Scenario B (defective tapes increasing from inside to outside), and increased by 48% in Scenario C (defective tapes increasing from top to bottom). Therefore, to overcome the issues on current-carrying capability and AC loss, adding reasonable redundancy and safety allowance for HTS tapes, overall critical currents and cryogenic systems is necessary. Overall, this article presents novel analysis and results, which are useful for the future designs of HTS high-current stacked conductors/cables.

Study on field-based superconducting cable for magnetic energy storage devices

During the design of superconducting magnets, the Ic(B) curve is widely used to evaluate the critical current density distribution in the magnet, safety factor is determined by the lowest value of critical current density and operating current. However, other parts of the magnets will work in over-safe state, which leads to a huge waste of superconducting properties as well as budget problem. This article presents a Field-based cable to improve the utilizing rate of superconducting magnets in SMES system. The quantity of HTS tapes are determined by the magnetic field distribution. By this approach, the cost of HTS materials can be potentially reduced. Firstly, the main motivation as well as the entire design method are introduced. Then, a typical no-insulation coil is designed and fabricated based on Field-based stacked cable to validate the feasibility of this method. Both charging/discharging test and the magnetic field test are carried out to explore the working mechanism of this coil. The unique working performance on time constant and field distribution are analyzed in detail.

Finite element simulation and structure optimization of HTS solenoid

When the current passing through a high temperature superconducting (HTS) coil that exceeds a critical value, the properties of the materials which make up the coil will fail, generating large amounts of heat and even causing serious accidents. Aiming at the above safety problem, this paper took three solenoid magnets with different structures as the object, and conducted a simulation study on their electromagnetic performance through finite element method (FEM). The magnetic field intensity H was taken as the dependent variable of the control equations of the physical field. With the aid of the partial differential equation (PDE) interface of the simulation software used, the control equations were easily constructed. The pancake coil wound by many turns of ribbon conductors was abstracted as a bulk-like conductor with the same cross-sectional area. The main idea of this equivalent replacement is to simplify the internal structure of the device without affecting its electromagnetic behavior, which can accelerate the convergence speed of the simulation process and reduce the CPU burden. Models of solenoid magnets with rectangular, trapezoidal and inverted trapezoidal cross sections were established by stacking many pancake coils. The simulation results corresponding to these models show that the solenoid magnet with trapezoidal cross-section has the largest critical current and most uniform density distribution. Such advantages not only reduce the risk of superconducting material failure due to overheating at both ends, but also fully exploit the current carrying capacity of the coil in the middle area of the solenoid.

Study of Quench Behavior of No-Insulation REBCO Pancake Considering Complex Critical Current Density Distribution

This study analyzes the quench behavior of No-insulation (NI) REBCO pancake. An quench analysis simulation model considering the complex critical current density distribution was developed and validated experimentally. The developed model includes an equivalent circuit model, a thermal model, a magnetic model, and a magnet critical current estimation model. The simulation model is based on a co-simulation using MATLAB and COMSOL, considering the balance of accuracy and computation time. The lumped parameter of the NI magnet was used to solve the governing equations of the equivalent circuit module and thermal module in MATLAB. To accurately calculate the non-uniform electromagnetic field distribution over the coil, a magnetic finite element method was used in COMSOL. A neural network was used to predict the temperature-field-angle dependent magnet critical current. Considering the numerical convergence at different over-current phases, adaptive simulation was used to reduce the total simulation time. The quench behavior was analyzed using the proposed model, and the results were verified experimentally. The simulation results showed that when the azimuthal current is greater than the magnet critical current, it will gradually saturate and approach the magnet critical current, and then decrease at a similar speed. The rate of decrease is equal to the rate of decrease of the magnet critical current. Through the analyses, the corresponding sudden-discharging behavior was simulated and analyzed. The proposed model can be used to perform the post-quench and sudden discharging analyses of pancake coil and has promising applications in multi-pancake post-quench studies.

Results of ITER TF Coil Double Pancake Heat Treatment in Japan

In Japan, 9 ITER TF coils were manufactured for the ITER project. Each TF coil consists of seven Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn conductor double pancakes (DPs). In DP manufacturing, heat treatment is one of the most important processes, because the insertion of a heat treated conductor into the radial plate groove (i.e., transfer) is complicated owing to the elongation of the conductor under heat treatment. A critical current distribution over the DP may also occur owing to the temperature distribution and disturbance in the heat treatment process. To address these issues, this study developed a procedure wherein the conductor length elongation caused by heat treatment is precisely considered, and transfer can be successfully achieved for all the DPs. In addition, strand witness samples were simultaneously heat treated with the DPs, and their critical current (I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ) was measured. Subsequently, it was confirmed that the average I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> is equivalent to those in the strand acceptance test while the standard deviation of I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> for the witness samples is approximately 4% larger than that for the strand acceptance test. It was also confirmed that the disturbance of the heat treatment was negligible. Related results are described herein.

Signatures of Majorana bound states and parity effects in two-dimensional chiral p -wave Josephson junctions

We characterize topological features of Josephson junctions formed by coupled mesoscopic chiral $p$-wave superconducting islands. Through analytic and numerical studies of the low-lying BdG (Bogoliubov-de Gennes) spectrum, we identify localized MBS (Majorana bound states) nucleated in Josephson vortices by the application of a perpendicular magnetic field. Additionally, we demonstrate the existence of an extended MBS that is delocalized around the outer perimeter of the coupled islands, which has measurable consequences on the Josephson supercurrent and phase dynamics of the junction. In particular, we predict a change in the critical current diffraction pattern in which the odd integer-flux nodes are lifted in a fermion parity-dependent fashion. We model the competing stochastic effects of thermal noise and macroscopic quantum tunneling within the RCSJ framework and show the emergence of a bimodal critical current distribution. We demonstrate that increasing the parity transition rate suppresses the bimodal nature of the distribution, thus strongly emphasizing the non-trivial parity dependent nature of the many-body ground state. Finally, we consider a trijunction geometry with three islands and discuss possible schemes to braid Majorana bound states by moving the Josephson vortices to which they are bound.

The calculation and measurement of electromagnetic energy flows for investigation of critical current estimation for high-temperature superconducting coil by means of pick-up coils

For practical operations of high-temperature superconducting (HTS) devices, we have proposed a monitoring and diagnosing system to detect the degradations of superconducting properties before normal transitions occur locally in the HTS winding. The proposed system estimates the distributions of critical current indirectly from measurement results of the active power components of the Poynting vector around the monitoring HTS devices conducting ac currents by means of pick-up coils pairs mounted surrounding the HTS devices. For this purpose, it is necessary to solve the inverse problem. In order to estimate the critical current distribution, therefore, it is first necessary to be able to calculate the measurement signal distribution from the critical current distribution of the monitoring coil. This paper first proposes the calculation method of signal distributions measured by our system, next reports the results of the experiments and analysis, which were carried out to verify the validity of the calculation method. A pancake coil wound with Bi-2223 multifilamentary tape exposed to a uniform AC magnetic field was assumed as a monitoring coil in the experiments and analyses. The good agreement between the measured signals obtained from the experiments and the numerical analysis demonstrates the effectiveness of the proposed calculation method of measured signals.

Emission from Josephson junctions with Gaussian distribution of critical currents

The model which allows to obtain the spectrum of emission of systems of Josephson junctions with the inhomogeneous distributions of critical currents along junctions is developed. With the use of this model we study electrical properties of systems in which junctions have the Gaussian distributions of critical currents. In particular, IV-characteristics and power of emission from inhomogeneous junctions with dimensions smaller than the Josephson depth of penetration of magnetic field have been investigated. We showed that for such junctions the dependence of emitted power on voltage (i.e. the spectrum of emission) had maxima at voltages corresponded to Fiske steps in the whole range of voltages, though in the IV-characteristics particularities (nuclei of zero-field steps) were not seen and they could be revealed only in derivatives of these curves. The comparison of our results with similar results which we obtained earlier for long junctions allows to suppose that the investigated mechanism of the formation of zero-field steps is general and it is valid for both long and short junctions. We investigated the averaged on random realizations height of some maximum of emitted power at different values of the Gaussian standard deviation of critical currents and found the square dependence of this height on the dimensionless parameter which characterizes the standard deviation. This result was in agreement with the theory of zero-field steps. We also considered electrical properties and power of emission from the stack of two long interacting with each other Josephson junctions in magnetic field. Each of the junctions had small (about 10-3 %) Gaussian distribution of critical currents. We found that if magnetic field was absent then there were only normal modes in the system (namely, the in-phase mode and the anti-phase mode). Zero-field steps were formed at voltages corresponded to the split even Fiske step. There were only normal modes in the system also when the relation of magnetic field to the value of the magnetic field at which the critical current becomes zero was more than 0.6. When this relation was smaller, other modes existed as well. We supposed that some normal modes could be destroyed because due to magnetic field standing waves were formed at both odd and even Fiske steps, so some modes could be locked with standing waves.

Rapid Analytical Calculation of Magnetic Field and Critical Current Distributions in HTS Magnets

For the design of superconducting magnets, the magnetic field and critical current distributions are usually calculated based on finite element software such as COMSOL, ANSYS, etc. These software are necessary for accurate structure modeling and field calculation, but they occupy large memory space and comsume long simulation time. Furthermore, they are not easy to use. To achieve an easy-to-implement solution for rapid magnet field and critical current calculations, this paper investigates three types of analytical calculating methods, and builds an autonomously-operated calculating application program (APP) for the uses in various superconducting magnets.

Prediction of Critical Currents in Superconducting Windings Using Wire Data and Field Modeling

This paper reports on the integration of publicly available HTS conductor electromagnetic performance data into a magnetic Finite Element model for determining the critical current distribution along a section of conductor in a spatially fluctuating magnetic field. The simulation results from this model are shown to be in close agreement to experimentally obtained results. Typically monitoring for quench is done by measuring the volt-drop along a section of conductor to be protected and determining when the volt-drop reaches a predetermined level. This work shows that under spatially varying magnetic field conditions, small areas of the voltage monitored section of conductor could have already surpassed the critical current level for that section of conductor and hence stand a high probability of being a site for quench. Under these conditions, it is proposed to use the maximum electric field developed along the conductor as a criterion for determining the critical current. This work points to the need for developing a quench detection technique that can be applied to much smaller sections of conductor, particularly in geometries that are expected to experience the largest variations of magnetic field such as that in a rotating electric machine.

Electromagnetic Analysis of HTS DC Cables Based on Critical State Model

High-temperature superconducting (HTS) DC cables have the advantages of low transmission loss, high current density and large transmission capacity, which have gained more and more attentions in recent years. The typical structures of HTS DC cables include unipolar and bipolar coaxial that doubles the cable's transmission capacity. Based on the critical state model, this article analyses and contrasts the critical current density distributions and degradations due to magnetic field in the HTS tapes of the unipolar and coaxial bipolar DC cables. The influences of the bipolar cables with different voltage levels are also compared. The results show that the critical current density degradations due to magnetic field are almost the same in both unipolar and coaxial bipolar structures, which are mainly caused by the self-field. For the bipolar cables, the current density distribution in the outer layer HTS tapes changes with the voltage level. To evaluate the influence of the axial magnetic field, a 3-D model of the unipolar cable is established with a helical wound pitch of the HTS tapes. The results show that the axial magnetic field is relatively low and the critical current density would not degrade if the helical angle of the HTS tapes is reasonably small.

Critical Current Distributions of Recent Bi-2212 Round Wires

Bi-2212 is the only high-field, high-temperature superconductor (HTS) capable of reaching a critical current density $J_{\text{c}}$(16 T, 4.2 K) of 6500 $\mathrm{A\cdot mm^{-2}}$ in the highly desirable round wire (RW) form. However, state-of-the-art Bi-2212 conductors still have a critical current density ($J_{\text{c}}$) to depairing current density ($J_{\text{d}}$) ratio around 20 to 30 times lower than that of state-of-the-art $\mathrm{Nb-Ti}$ or REBCO. Previously, we have shown that recent improvements in Bi-2212 RW $J_{\text{c}}$ are due to improved connectivity associated with optimization of the heat treatment process, and most recently due to a transition to a finer and more uniform powder manufactured by Engi-Mat. One quantitative measure of connectivity may be the critical current ($I_{\text{c}}$) distribution, since the local $I_{\text{c}}$ in a wire can vary along the length due to variable vortex-microstructure interactions and to factors such as filament shape variations, grain-to-grain connectivity variations and blocking secondary phase distributions. Here we compare $\sim$ 0.1 m length $I_{\text{c}}$ distributions of Bi-2212 RWs with recent state-of-the-art very high-$J_{\text{c}}$ Engi-Mat powder and lower $J_{\text{c}}$ and older Nexans granulate powder. We do find that the $I_{\text{c}}$ spread for Bi-2212 wires is about twice the relative standard of high-$J_{\text{c}}$ $\mathrm{Nb-Ti}$ well below $H_{\text{irr}}$. We do not yet see any obvious contribution of the Bi-2212 anisotropy to the $I_{\text{c}}$ distribution and are rather encouraged that these Bi-2212 round wires show relative $I_{\text{c}}$ distributions not too far from high-$J_{\text{c}}$ $\mathrm{Nb-Ti}$ wires.