Field Dependence Of Critical Current Density Research Articles

Large-scale vibrating coil magnetometer for the magnetic characterization of bulk superconductors

This work presents the design and validation of a vibrating coil magnetometer for the characterization of the field dependence of the critical current density of centimeter-sized bulk superconductors as an alternative to the destructive methods typically used. The magnetometer is also shown to be capable of measuring the magnetic moment in an applied field of up to 5 T for diverse magnetic materials, such as soft and hard ferromagnets and high-temperature superconducting pellets. The vibrating coil magnetometer was first optimized using finite element simulations and calibrated using a commercial vibrating sample magnetometer. The vibrating coil magnetometer was benchmarked with hysteresis measurements of a Nd2Fe14B disk made with a commercial hysteresisgraph, showing good agreement between the different setups. The magnetic hysteresis of a YBa2Cu3O7−x superconducting pellet was measured at 77 K, showing a penetration field of 1 T and an irreversibility field of 4 T. The field dependent critical current density of the superconductor was then inferred from the magnetic hysteresis measurements and extrapolated at low fields. Finally, the resulting critical current density was used to successfully reproduce the measured magnetization curve of the pellet at 2 T with finite element simulations.

Superconducting Magnetic Energy Storage for Pulsed Power Magnet Applications

As part of the exploration of energy efficient and versatile power sources for future pulsed field magnets of the National High Magnetic Field Laboratory-Pulsed Field Facility (NHMFL-PFF) at Los Alamos National Laboratory (LANL), the feasibility of superconducting magnetic energy storage (SMES) for pulsed-field magnets and other pulsed power loads is examined. Basic SMES parameters needed to power one of the coil groups of the large 100 T magnet were determined. A circuit topology for the power transfer between the SMES and the magnet was devised, and the basic performance of the topology was simulated to reproduce the pulse shape currently used in the 100 T magnet. The Finite element analysis (FEA) method was used to calculate the magnetic field distribution of several preferred coil configurations for effective SMES design. Magnetic field distribution and the field dependent critical current density of commercial high temperature superconducting (HTS) tapes were used to understand the conductor/cable requirements for the SMES.

Effect of thickness on the superconducting properties of the thin films of FeTe0.55Se0.45 deposited on YSZ substrates using Pulsed laser deposition (PLD) technique

We report the successful fabrication of thin films of thickness ∼26 nm, 59 nm, 76 nm, and 158 nm of the composition FeTe0.55Se0.45 on the (100)-oriented Yttria-stabilized zirconia (YSZ) substrate using the pulsed laser deposition (PLD) technique. The effect of thickness on the structure and superconducting properties of the thin films has been investigated. X-ray diffraction study reveals the growth of thin films along the c-axis. The temperature-dependent resistivity measurements confirm superconductivity in all the fabricated thin films, and the highest ∼ 16.2 K has been observed for the thin film of thickness ∼59 nm, which is higher than the corresponding value of the polycrystalline target sample. The superconducting parameters such as upper critical magnetic field coherence length thermally activated energy (TAE) U0, and vortex phase state have been measured by magnetotransport measurements near in the different applied magnetic fields up to 12 T. The TAE values determined from the conventional and modified thermally activated flux flow (TAFF) models are discussed and compared. A crossover from 2-dimensional (2D) vortex to 3-dimensional (3D) vortex behaviour has been observed. The vortex phase diagrams are used to observe the transition from the vortex liquid to the vortex glass state in the grown thin films. Moreover, magnetoresistance (MR) measurements show non-saturating linear magnetoresistance (LMR) in the high field region, indicating the presence of the possible topological state in the grown thin films. The values of magnetic field dependent transport critical current density, have been evaluated from the current-voltage (I-V) curves. Furthermore, the normalised pinning force density has been used to characterize the pinning processes using the Dew Hughes’ scaling rule which reveals that the grown thin films contain δl-surface pinning centers.

On the Temperature- and Magnetic Field–Dependent Critical Current Density of Compressed Hydrogen Sulphide

On the Temperature- and Magnetic Field–Dependent Critical Current Density of Compressed Hydrogen Sulphide

Investigation of high-energy ultrasonication of RE 2BaCuO5 (RE = Y, Gd) on the growth and superconducting properties of REBa2Cu3O7−δ top-seeded melt textured bulks

Recently, an improvement in the flux pinning performance of REBa2Cu3O7−δ (REBCO) bulk was achieved employing high energy ultrasonic irradiation (up to 300 W and 60 min) prior to the infiltration-growth process. Here, we demonstrate that a higher ultrasonic power and shorter duration treatment (450 W for 30 min) of the RE 2BaCuO5 (RE211, RE= Y, Gd) powder produces individual, nanometer-sized and surface damaged RE211 particles (RE211Ultra). We study the growth of YBCO and GdBCO systems via the top-seeded melt-growth method, with the addition of 30 mol% of RE211Ultra, which were pre-treated by high-energy ultrasonication and compared with the conventional method. Isothermal growth experiments clarified that the addition of RE211Ultra particles enables faster and more effective crystal growth via an improved peritectic reaction due to their size in the nanometer range and presence of sharp edges, which are crucial for growing large, single grain bulks of REBCO. Microstructural investigations by scanning electron microscopy indicated the presence of two differently sized RE211 inclusions within the bulk GdBCO and YBCO superconductors. All samples showed an onset of superconductivity at ∼92 K or above. Utilizing the effective growth temperature window and the addition of RE211Ultra, single grain bulks of GdBCO and YBCO were fabricated by the slow-cooling method. The field dependent critical current density (J c) of the bulk samples using RE211Ultra were found to exhibit superior performance over the standard GdBCO/YBCO samples due to significant changes of sample growth and of their microstructures. Here, we discuss various factors affecting the addition of RE211Ultra on the development of the microstructure, growth of bulk, single grain materials and further, the superconducting properties of different REBCO superconductors.

A modified model to estimate the screening current-induced magnetic field of a REBCO magnet

Experiments have shown that the actual value of the magnetic field in a magnet wound by rare-earth (RE) Ba2Cu3O7−x tape during operation is less than its design value due to the effect of the screening current-induced magnetic field (SCMF). Several simulation methods have been used to calculate the SCMF. In this paper, a modified model is proposed to estimate the SCMF of a magnet based on the previous simple model. The inductance correction and field-dependent critical current density are considered in the modified model. Two parameters, the reversal and Nagaoka coefficients, are introduced in the model. The former is used to track the location of the minimum SCMF value in the charging process and the latter is applied to correct the induction of the magnet. The numerical results indicate that the SCMF estimated by the modified model is in agreement with those from experiments and the finite element method. Moreover, the effects of electromagnetic and geometrical parameters on the reversal and Nagaoka coefficients are also investigated. Finally, the model is extended to estimate the SCMF of a no-insulation magnet.

Fast solution of the superconducting dynamo benchmark problem

A model of high-temperature superconducting dynamos, a promising type of flux pump capable of wireless injection of a large DC current into a superconducting circuit, has recently been chosen as an applied superconductivity benchmark problem and solved using ten different numerical methods (Ainslie et al 2020 Supercond. Sci. Technol. 33 105009). Using expansions in Chebyshev polynomials for approximation in space and the method of lines for integration in time we derive a simple and accurate numerical method which is much faster. The proposed numerical method was applied also to problems with transport current and a field-dependent sheet critical current density.

A New Microscopic Approach To Deal with the Temperature- and Applied Magnetic Field–Dependent Critical Current Densities of Superconductors

Based on the formalism of the Bethe-Salpeter equation, we present here a new approach to deal with the temperature (T)- and the applied magnetic field (H)-dependent critical current densities (jcs) of superconductors (SCs). Saliently, it employs (i) the premise that the chemical potential μ (T, H) subsumes most of the factors to which the widely varying empirical values of jc (T, H) of an SC are conventionally attributed, (ii) the basic equation that defines jc as a product of the electronic charge, the number density of superconducting electrons (ns) and their critical velocity (vc), (iii) a recently derived equation for ns (T, H), and (iv) the empirical values of jc (T, H)—which it is meant to explain—as inputs into one of its equations which, paradoxical though it may seem, is shown to have the virtue of shedding light on several parameters related to jc (T, H), such as μ, ns, vc, m*, nL, and λm, where m* is the effective mass of an electron, nL the number of occupied Landau levels, and λm the magnetic interaction parameter. Remarkably, the approach is found to lead to two branches of μ-dependent solutions with distinctly different values of the parameters corresponding to the same value of jc (T, H). This is reminiscent of the behavior of the chemical potential in SCs with a low density of charge carriers that was reported by Marel [Physica C 165, 35 (1990)] and described as anomalous. Finally, we show that our approach suggests the exciting possibility of fabricating an SC that has a bespoke value of jc at suitably chosen values of T and H. For the sake of concreteness, we employ here some of the available empirical data on the jc (T, H) values of Bi-2212.

Finite Element Method Based Estimation of Critical Current Density of NbTi

The purpose of this article is to estimate the magnetic field dependent critical current density scaling relation of NbTi used in a superconducting wire. The estimation problem is set using a finite element method based forward model solving the critical current of a wire in external magnetic fields. A sensitivity analysis is carried out to reveal the uncertainties in the process. It is shown that the methods provide accurate predictions of critical currents in a wire, but there are uncertainties related to the zero-field critical current density of the material.

Numerical Simulation of Superconducting Generator Based on the T–A Formulation

Due to the excellent electromagnetic properties of superconductor materials, superconducting generators have higher efficiency, lower weight and volume than traditional rotating machines. However, it is difficult to simulate the electromagnetic behavior in the superconducting generator due to the nonlinear $E - J$ relationship. A numerical model based on the $T - A$ formulation and moving mesh method is adopted to simulate the superconducting rotating machine, and the electromagnetic and mechanical behaviors of the superconducting rotating machine are investigated. The fully superconducting generator investigated in this article is radial type, which consists of field windings and armature windings made from YBa2Cu3O $_{7 - \delta}$ (YBCO) superconducting race-track coils. The anisotropic field-dependent critical current density and the $E - J$ power law relationship are considered in our model. The “virtual tape” model is introduced to calculate the induced current in the $T - A$ formulation. The numerical results are obtained by the finite element method. The electromagnetic results calculated by our model are compared with results from the $H - A$ formulation. The ac losses and stress distributions in superconducting coils are presented based on the $T - A$ formulation. The results show that the body force and stress are periodic, and the stress will concentrate on the boundary of the coil. The magnetic field in the rotor is larger than that in the stator, and the field windings suffer greater body force and stress than the armature windings. This model has acceptable relative error with the $H - A$ model for the time saved following $T - A$ approach and relevance to mechanical calculations. Thus, this model can aid the design of superconducting rotating machines.

Sn addition effects on CaKFe4As4 superconductors

The effects of adding low-melting point metals (Pb, Sn, In and Ge) to polycrystalline CaKFe4As4 (CaK1144) superconductors were investigated. We found that Sn is the most stable with CaK1144 among these low-melting point metals. Synthesis conditions as well as the doping quantity of Sn were optimized, and phase stability, microstructures and superconducting properties were investigated. At the optimized sintering temperature of 700 °C, Sn was effectively solidified in grain boundaries (GBs) of the CaK1144 bulk samples and secondary phase formations were not serious in optimized samples. As the Sn amount increased, filling of Sn in the GBs increased up to 30 wt% with homogeneous dispersion. The magnetic field dependence of critical-current density (Jc) was significantly enhanced by 30 wt% Sn addition and decreased with further increase of Sn addition. The filling up of 1144 grain boundaries by the optimal amount of Sn enhanced the Jc from 11.7 kA cm−2 to 21.7 kA cm−2 in a self-field and at 4.2 K. Sn addition was effective both to suppress the impurity phases as well as increase Jc of CaK1144.

Selective triggering of magnetic flux avalanches by an edge indentation

We numerically investigate the effect of an edge indentation on the threshold field of thermomagnetic instabilities in superconducting films subjected to a ramping magnetic field, applied perpendicular to the plane of the film. In particular, we are able to address the question on whether edge indentations promote magnetic flux avalanches. For the magnetic field-independent critical current density model, the triggering of the first magnetic flux avalanche systematically occurs at the edge indentation. In contrast to that, for the more realistic field-dependent critical current density model the first flux avalanche can take place either at or away from the indentation. This selective triggering of magnetic flux avalanches is shown to result from two effects. Namely, (i) the variation of the threshold magnetic field for the first flux avalanche triggered at the indentation and (ii) the reduction of the critical current density by large local magnetic fields at the tip of the indentation which translates in a lower power density dissipated near the tip. We demonstrate that this interplay can be tuned by varying the indentation size, ramp rate of applied field ${\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{H}}_{a}$, and working temperature ${T}_{0}$. We build up a phase diagram in the ${\ensuremath{\mu}}_{0}{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{H}}_{a}\ensuremath{-}{T}_{0}$ plane with well-defined boundaries separating three distinct regimes of thermomagnetic instability.

Anisotropic field dependence of the electronic transport in superconducting FeSe thin films

Electronic transport measurements were carried out on c-axis oriented epitaxial FeSe thin films in static magnetic fields up to 14 T parallel to the crystallographic c-axis and parallel to the ab-plane. The temperature dependence of the upper critical fields and was determined from the field dependence of the resistivity. While was orbitally limited, the larger was paramagnetically limited. The anisotropy was decreasing with decreasing temperature and revealed a pseudoisotropic behaviour towards zero temperature. This temperature dependence is indicative of the multiband character of FeSe. From measurements of the temperature- and field-dependent critical current densities the effective depinning or irreversibility field was obtained, and its angular dependence yielded the effective mass anisotropy . The temperature dependence of , which was different from that of , can be considered as another signature of multiband FeSe.

An Improved Self-Consistent Model and Its Application to Estimate the Critical Current of REBCO Magnet

There is a growing interest in using HTS magnet to improve the performance of the electric devices such as motor/generator, NMR/MRI and EDS train. For the HTS magnet, the critical current is of importance since it determines the current-carrying capacity, i.e., the ability to generate magnetic field. So, it is imperative to estimate the critical current of HTS magnet. However, the numerical modelling of the magnet is not straightforward due to the field-dependent critical current density, a large number of turns and the ultra-high aspect ratio, e.g., of REBCO (REBa2Cu3Ox, where RE = Rare Earth) coated conductor. To make the estimation of the critical current accessible, this paper aims at developing an improved self-consistent model. First, the analytical expressions of the self-field of a generalized racetrack magnet are derived from the Biot-Savart's law. Secondly, the self-consistent model is introduced and validated by comparing the estimated critical current of a racetrack REBCO magnet with the measured one. Thirdly, based on the homogenized technique, the efficiency of self-consistent model is significantly improved with accuracy preserved. Lastly, we estimate the critical current of a generalized racetrack REBCO magnet for EDS train use with the improved self-consistent model.

A Fermi Energy-Incorporated Framework for Dealing with the Temperature- and Magnetic Field-Dependent Critical Current Densities of Superconductors and Its Application to Bi-2212

It is well known that the critical current density of a superconductor depends on its size, shape, nature of doping and the manner of preparation. It is suggested here that the collective effect of such differences for different samples of the same superconductor is to endow them with different values of the Fermi energy—a single property to which may be attributed the observed variation in their critical current densities. The study reported here extends our earlier work concerned with the generalized BCS equations [Malik, G.P. (2010) Physica B, 405, 3475-3481; Malik, G.P. (2013) WJCMP, 3,103-110]. We develop here for the first time a framework of microscopic equations that incorporates all of the following parameters of a superconductor: temperature, momentum of Cooper pairs, Fermi energy, applied magnetic field and critical current density. As an application of this framework, we address the different values of critical current densities of Bi-2212 for non-zero values of temperature and applied magnetic field that have been reported in the literature.

Numerical estimation of AC losses in Bi2212/Ag wire and coil

The multi-filamentary Bi2Sr2CaCu2O8-x (Bi2212) round wire is the candidate for high field magnets, which is macroscopically isotropic and has large critical current in high field. AC losses generated in coils by ac transport current and magnetic field will lead to the rise of local temperature and consumption of liquid helium. However, the simulations of AC losses in coils are limited by the complicated geometry. This paper presents a homogenization model for computing the current density distributions, field distributions and AC losses in coils wound by multifilament Bi2212/Ag round wire. Based on two-dimensional axisymmetric H-formulation (H is the magnetic filed), the field dependent critical current density and the nonlinear relation between the electric filed E and the current density J are used to describe the macroscopic behavior of the superconductor. To validate the homogenization model, the AC loss is compared with the result of origin model which has the actual filament configuration of round wire. The homogenization model is powerful to estimate the AC losses of cables and coils made by Bi2212/Ag round wire.

The effect of pressure and doping on the critical current density in nickel doped BaFe2As2

Single crystals of Ba(Fe1−xNix)2As2 have been produced for systematic magnetic measurements of the critical current density (Jc) over a range of dopings from x = 0.025 to 0.066 and a range of temperatures from 2 K. Analysis of the field dependent critical current density, Jc, shows strong evidence pointing to a flux pinning mechanism dominated by local variation in the mean free path for all dopings. The values of Jc measured indicate a peak at approximately x = 0.049 on the pseudobinary phase diagram, close to a proposed quantum critical point at x = 0.05. Pressure dependent measurements of this sample show anomalous behaviour including a negative pressure relationship and a peak in Jc around 0.65 GPa.

Electro-mechanical behavior in arrays of superconducting tapes

Numerical simulations of the electro-mechanical behavior in arrays of superconducting tapes are presented in this paper. The superconducting properties of tapes are influenced not only by the local magnetic field but also the mechanical strain. The mechanical strain will reduce the critical current density and lead to the degradation of superconductivity. Due to the nonlinear E−J behavior, it is difficult to analytically obtain the two-dimensional current and magnetic field distributions. We use the magnetic energy minimization method based on the field-dependent critical current density to determine the distributions of the current and magnetic field in arrays of rare-earth-barium-copper-oxide (REBCO) tapes. Next, the finite element method is employed to calculate the mechanical strain and stress distributions, and the anisotropic mechanical properties of the REBCO tapes are adopted. The numerical method is verified with the analytical solution for a one-dimensional single tape with transport current. The strain and stress distributions in superconducting tapes are calculated for different transport current/external magnetic field conditions. The relationship between the stress and the number of tapes in the arrays is discussed, and the effect of the distance between adjacent tapes on the stress is also investigated. The results may be beneficial to the design of superconductor magnets.

Mechanical improvement of metal reinforcement rings for a finite ring-shaped superconducting bulk

As a key technique, reinforcement of type-II superconducting bulks with metal rings can efficiently improve their mechanical properties to enhance the maximum trapped field. In this paper, we study the magnetostrictive and fracture behaviors of a finite superconducting ring bulk reinforced by three typical reinforcing structures composed of metal rings during the magnetizing process by means of the minimization of magnetic energy and the finite element method. After a field-dependent critical current density is adopted, the magnetostriction, pinning-induced stress, and crack tip stress intensity factor are calculated considering the demagnetization effects. The results show that the mechanical properties of the ring bulk are strongly dependent on the reinforcing structure and the material and geometrical parameters of the metal rings. Introducing the metal ring can significantly reduce the hoop stress, and the reduction effect by internal reinforcement is much improved relative to external reinforcement. By comparison, bilateral reinforcement seems to be the best candidate structure. Only when the metal rings have particular Young’s modulus and radial thickness will they contribute to improve the mechanical properties the most. In addition, if an edge crack is pre-existing in the ring bulk, the presence of metal rings can effectively avoid crack propagation since it reduces the crack tip stress intensity factor by nearly one order of magnitude.

Demagnetization induced peak effect for a FeSeTe granular superconductor in ac magnetic field

The possible evidence of a peak effect in the temperature dependent magnetization and in the field dependent critical current density has been found for a FeSeTe superconducting granular sample in presence of an ac field. The existence of the peak effect has been confirmed by the numerical calculation of the inter- and intragranular magnetizations in presence of a demagnetization field with components at the third harmonic frequency generated by the sample magnetization. This suggests that the peak effect could be related to the flux dynamics inside the sample through the demagnetization field third harmonic.