Critical State Model Research Articles

Improvement of Critical Current Density in Bi-2223 Superconductor by Ag-Doping

High-Tc superconducting polycrystalline Bi-2223 undoped sample (A0) and 5wt.% Ag-doped sample (A5) have been prepared by solid-state reaction method at 8550C with sintering time of 8 days. X-ray powder diffraction (XRD) results shown that the major phase of these samples is Bi-2223. The volume ratio of Bi-2223 phase observed to be increased from 78% for undoped sample (A0) to 95% for 5wt.% Ag-doped sample (A5). The enhancement of the onset of high-Tc superconductivity (Tc,onset = 112.5 K) in silver doping sample was observed by DC-resistivity measurements. From the AC-susceptibility measurements combined with Bean critical state model, the temperature dependent parabolic law of inter-granular or matrix critical current density (Jcm) was fitted. Some Jcm values were estimated from these parabolic laws. The results showed that 5wt% Ag-doping can make the Bi-2223 sample with nearly double critical current density.

Flux vortex dynamics in type-II superconductors

The flux-pinning landscape in type-II superconductors determines the response of the flux line lattice to changing magnetic fields. Typically, the flux vortex behaviour is hysteretic and well described within the framework of the Bean critical-state model and its extensions. However, if the changing magnetic field does not move the flux vortices from their pinning sites, their response remains linear and reversible. The vortex displacement, then, is characterised by the Campbell penetration depth, which itself is related directly to the effective size of the pinning potential. Here, we present measurements of the Campbell penetration depth (and the effective size of the pinning potential) as a function of magnetic field in a single-grain bulk GdBa2Cu3O superconductor using a pick-up coil method. Hence, the hysteretic losses, which take into account the reversible vortex movement, are established.

Simple and Fast Method for Computing Induced Currents in Superconductors Using Freely Available Solvers for Ordinary Differential Equations

The current distribution in a superconductor is commonly calculated by solving the Maxwell's equations in differential form. An alternative method based on an integral form of Maxwell's equations was proposed by E. H. Brandt. Since the integral formulation needs to be solved in the conductor volume only, this method can be easily implemented in a programming language such as MATLAB. Brandt's approach has been used by several authors over the years, but no ready-to-use implementations are available. In this article, we present a step-by-step derivation of the method for a thin strip, a rectangular bar, and a cylindrical bulk. The results are validated using a comparison with exact solutions of the critical state model and a finite element solution of the $H$-formulation.

The Influence of Nano-Sized SnO2 Doping on Physical and Magnetic Properties of the Bi2Sr2-x(SnO2)xCa1Cu1.75Na0.25Oy Superconductors

In this study, we have investigated the effect of nano-sized SnO2 (50 nm) doping on the superconducting properties of Bi-2212 ceramics. In the first stage of the the experiment, the composition Bi2Sr2-xSnxCa1Cu1.75Na0.25Oy where x = 0, 0.05, 0.1 and 0.2 is selected due to the positive effect of sodium substitution on the grain sizes of the Bi-2212. X-ray diffraction results indicate that all the samples have considerable amount of Bi-2212 phases. Scanning electron microscopy (SEM) analysis of all samples clearly shows significant grain growth due to lower crystallization temperature formed by sodium. The lowest resistivity in the nano-sized SnO2-doped samples at 150 K is obtained for the sample of x = 0.05. The M-H hysteresis loops for all the samples have been measured within ± 2 T externally applied magnetic field range at T = 15 and 25 K, respectively. The undoped and the sample with x = 0.05 SnO2 have both large M-H loops, indicating the improvement of flux pinning properties of the Bi-2212 as well as enhanced intergrain connectivity. However, the width of the hysteresis loop in samples including high (x > 0.05) SnO2 contents significantly decreased, indicating deterioration in superconducting properties of the Bi-2212 system. Additionally, the critical current densities (Jc) of all the samples at 15 K are calculated from their hysteresis loop measurements by using Bean’s critical state model. When compared with other samples, a slight increase in Jc is obtained for x = 0.05 SnO2. The results indicate that the optimal contents of sodium (x = 0.25) and nano-sized SnO2 (x = 0.05) in the Bi-2212 system are effective for achieving enhanced superconductivity properties.

Simulation and calculation on rotation loss of high temperature superconducting bearings

High temperature superconducting (HTS) bearings are applied in flywheel energy storage and cryogenic liquid pump successfully due to self-stability and low-loss. Experiments and the current vector potential method (T-method) are generally used in the research of the rotation loss of superconducting bearings. Based on the B-H curve of the HTS deduced by the critical state model, the external magnetic field strength of the rotor system was obtained by using the finite element software. By means of numerical calculation, the rotation loss of HTS and the free decay curve were obtained. Furthermore, the friction coefficient of the designed HTS was calculated, which was 4.6 × 10−7. It was also found that the thickness of edge permanent magnet affected the magnetic field distribution on the surface of superconductors, and a more symmetrical magnetic field distribution can be generated by changing the thickness.

Irreversibility Line and Enhancement of Magnetic Flux Pinning in Sm-Doped Y123 Superconductor with CuO Nanoparticles

Y1−xSmxBa2Cu3O7−∂ (x = 0.00, 0.01, 0.02 and 0.05 wt.%) samples with Nano-CuO have been prepared by the solid-state reaction method. The effects of Sm doped in the YBCO system with Nano-CuO (40 nm) on structural, critical temperature (Tc), irreversibility line (IL), critical current density, JC and flux line pinning force are investigated. We also measured magnetization as a function of temperature (M–T) and magnetic loops (M–H) at constant temperatures of 10, 20, 30, 40, 50 and 60 K up to 10 kG. XRD measurements show that all the sintered samples have orthorhombic structure. The sample with x = 0.01 wt.% Sm substituted for Y on YBCO superconductor improves the critical temperature more than that of the pure Y123 and the other samples. For this sample, the zero field-cooled and field-cooled magnetization as a function of temperature measurements reveals the shift of IL to higher temperatures and magnetic fields. The critical current density and flux pinning force calculated using the Bean’s critical state model indicate an enhancement of Jc and Fp for the Sm-doped x = 0.01 sample compared with the sample with x = 0.02 and even the pure Y123.

Fracture analysis of superconducting composites with a sandwich structure based on electromagnetic–thermal coupled model

This paper analyzes a multilayer structure with a superconducting layer in the center and strengthening layers in the outer part. This represents a generalized structural form of multilayered high-temperature superconducting cable structures for space solar power station application. An analytical model for considering the influences of thermal–mechanical–electrical–magnetic coupling and the temperature on the stress distribution will be developed. The superposition method is used to solve the temperature distribution problem. After the temperature field is calculated, the magnetic field using a critical state model that considers the temperature effect will be developed. Finally, we analyzed the influence of material properties on the thermal and magnetically induced stress intensity factors in trapped field, zero field cooling and field cooling. Results show that the stress intensity factors induced either by thermal stress or by the Lorentz force must not be neglected. If the elastic module or the thickness of substrate layer increases, the stress intensity factor induced by thermal stress increases, while the one induced by the Lorentz force declines. Importantly, when reducing the thickness of the substrate layer, the total stress intensity factor will decrease at the early stage of heat conduction but increase at the late stage of heat conduction. This fact indicates that that thicker substrate layer is not always good from the reliability point of view.

A–V formulation for numerical modelling of superconductor magnetization in true 3D geometry

We present the numerical procedure suitable for computing the distribution of electrical currents in a superconductor with geometry extending in all three spatial dimensions when it is exposed to a magnetic field changing in time. Its main advantage is that it solves the problem in terms of vector potential, of the magnetic field. Such an A-formulation is usually the default option for magnetic field calculations in commercial finite element codes. We have used it in the past when a two-dimensional (2D) approximation was found to be sufficient to predict AC losses of single wires, cables, and coils with circular turns. Incorporation of superconductor properties based on the critical state model is straightforward in 2D because the flow of current is restricted to one direction only. The main challenge in extending the method to three dimensions is to cope with the situation when currents could flow in any direction. We have found that assuming that the local current density in a superconductor is always parallel to the local electrical field, and that its modulus is limited by the critical current density, provides sufficient input for accomplishing a new working equation, linking the vector of current density to the time derivative of the magnetic vector potential. Our method successfully passed testing on the benchmark problem of superconducting cube magnetization. It is also used to interpret the magnetization measured on two cylindrical superconducting objects in the transverse field: one was a tube made from bulk BSCCO and the other a REBCO coated conductor tape helically wound on a non-metallic tube. Computed magnetization loops in both cases show good agreement with experiments and confirm the validity of the method.

Hydrostatic Pressure Effect on the Pinning Mechanism of α‐BiPd Noncentrosymmetric Superconductors

Temperature and field dependence of magnetic measurements under hydrostatic pressure are carried out on a noncentrosymmetric superconductor α‐BiPd up to ≈1 GPa, and a 3D (temperature—magnetic field—pressure) phase diagram is reported for the first time. The experimental results are analyzed using various theoretical approaches, such as the Ginzburg–Landau formula, Bean's critical state model, Dew–Hughes model, and collective pinning theory, and several superconducting parameters are also estimated. Critical temperature, critical current density, and pinning force are decreased with the application of both pressure and magnetic field. It is observed that pressure diminishes the superconductivity moderately and changes the mean free path, which leads to crossover from the δTc pinning mechanism to δl type in α‐BiPd.

A state-dependent constitutive model for methane hydrate-bearing sediments inside the stability region

The presence of methane hydrate in soil pores alters the stress–strain and volumetric behaviour of soil. The extent of this alteration is affected by initial temperature and pore pressure when hydrate is formed inside the thermodynamically stable region. In this paper, a state-dependent critical state model is developed for methane hydrate-bearing sediments (MHBS) within the theoretical framework of bounding surface plasticity. A phase parameter is newly introduced into the constitutive model to account for the coupled effects of temperature and pore pressure on the mechanical behaviour of MHBS. This unique feature of the proposed model enables it to capture the behaviour of MHBS inside the methane hydrate stability region. A non-associated flow rule is adopted and a modified dilatancy expression is proposed considering the degree of hydrate saturation, phase parameter and stress state of MHBS. To verify the new model, computed results are compared to measured results of drained triaxial tests on MHBS with different morphologies and at different effective confining stresses, degrees of hydrate saturation and phase states inside the stability region. The comparison reveals that the model is capable of capturing the key features such as the evident strain-softening behaviour due to hydrate degradation and the change in stress–strain and volumetric behaviour of MHBS at different initial conditions inside the stability region.

Energy losses in magnetic contactless bearings on the base of high-Tc superconducting tapes

High-temperature superconducting tapes are very promising for application in rotary magnetic bearings owing to its excellent magnetic and transport properties as well as possibility to easy create magneto-levitation systems of various geometry. One of problem arising in the rotation superconducting bearings is the presence of the energy loss resulting from the magnetization hysteresis due to inhomogeneity of magnetic field from permanent magnets. In this report we present results theoretical studies of rotation losses in the model superconducting bearing based on commercial high temperature superconducting (HTS) tape. The bearing stator has a cylindrical shape and is made of a multilayer HTSC tape. The bearing rotor is made of permanent magnets located at the same radius relative to the axis of rotation. As a result of numerical calculations carried out in the framework of the critical state model, the rotor geometry was established, at which the value of energy losses was minimal.

Cylindrical cavity expansion analysis of dilatant sand considering granule breakage

Most cavity expansion problems in sand have not considered the effects of dilatancy, granule breakage and overconsolidation ratio, and all the current researches have simplified the solution process, which can not accurately reflect the mechanical response of the soil around the cavity. The critical state model considering the breakage and dilatancy characteristics of sand was adopted to convert the drained cylindrical cavity expansion problem described by the traditional Euler into the one by Lagrangian description; combined with relevant flow rule and based on the definition of generalized average principal stress and deviatoric stress, four first-order ordinary differential equations were obtained without any simplification. Finally, the semi-analytical exact solution of the cylindrical cavity expansion problem in sand was calculated by using Matlab programming. The impact of soil overconsolidation ratio (OCR) on the cavity expansion results were analyzed by a calculation example. The results indicate that the granule breakage has a greater influence on the dilatancy behavior of sand compared with OCR and the combined effect of the two causes the soil to show different dilatancy characteristics during cavity expansion; in addition, normally consolidated and lightly/moderately overconsolidated soil has been characterized by strain hardening during cavity expansion, while the heavily overconsolidated soil has experienced a complicated stage of strain hardening-strain softening-strain hardening.

Transparency of Planar Interfaces in Superconductors: A Critical-State Analysis

The problem of determining the transparency of current flow through a planar interface connecting two superconducting parts, being bulks, tapes, or films, is analyzed within the critical-state model. An exact relation between the magnetic moment of a sample containing such an interface and its transparency is derived for rectangular specimens in fully developed Bean critical states. The result can serve as theoretical basis for using standard magnetometry to measure the quality of joints, grain boundaries, and other weak links between superconducting parts.

Influence of gamma irradiation exposure on structural, electrical and magnetic properties of Bi-2223 with Nb2O5 addition

The effects of gamma irradiation on the phase analysis, electrical and magnetic characteristics of Bi-2223 superconductors with Nb2O5 addition were systematically examined. The pristine and Nb-added Bi-2223 superconducting bulk samples were produced by the solid state reaction procedure using high purity oxide powders. The samples were exposed to 1, 5, and 10 kGy gamma ray. The effects of γ-irradiation on the phase analysis, electrical and physical properties of the samples were studied before and after irradiation. The phase formation and the lattice parameters of the samples were characterized by X-ray diffraction (XRD). The superconducting transition temperatures of the samples were determined from the resistance–temperature curve using the four point probe method. The current carrying capacities of all samples were estimated from the magnetization curve using the Bean critical state model.

Constitutive model for predicting stress-strain behavior of fine-grained sediments using shear-wave velocity

The mechanical response of a sediment to an applied stress is significantly affected by variations of material properties, state conditions, and stress states. These stress state and conditions are utilized to infer input parameters for advanced soil constitutive models. Parameters such as void ratio and effective stresses have been readily inferred from shear-wave velocities under low-strain conditions. Thus, this research aimed to develop a shear-wave velocity-based constitutive model within a critical state soil mechanics framework to predict the undrained triaxial behavior of fine-grained sediments. Laboratory tests were performed for sediment samples ranging from silt-predominant to clay-predominant sediments. As result, a new two-term power function was developed that determined mean effective stress as a function of shear-wave velocity. By virtue of this new power function, the Original Cam Clay and Modified Cam Clay critical state models were adapted to estimate the stress-strain behavior and stress paths under undrained conditions, in terms of shear velocity. In addition, correlations were developed using the state and material properties to predict the input model parameters. The developed correlations allow broad application of the proposed framework to different sediment types in which clay and silt are the dominant deposits.

Tunnelling-induced surface settlement: on the choice of soil constitutive model

Increasing tunnel excavations in dense urban areas faces the issue of accurately predicting tunnelling-induced surface settlement. The quality of those predictions closely depends on the choice of soil constitutive model. In this context, some widely used soil models in engineering practice not only fail to reproduce some characteristics of soil behaviour on the constitutive level but also lead to shallower settlement. This article studies the influence of the choice of the soil model on tunnelling-induced displacements through a case study. Three different soil models are used to simulate soil behaviour, namely the hardening soil model, the modified cam clay model and a proposed enhanced critical state model incorporating deviatoric and volumetric hardening. The proposed model is first validated on different triaxial tests and its features are especially highlighted for overconsolidated soils. This model is then compared to the other two models on tunnelling simulations. The results show great predicted settlement sensitivity to the choice of soil model. The proposed model engenders deeper settlement and, consequently, enables a more conservative design. Furthermore, parametric studies demonstrate significant disparities in the predicted displacements by the different soil models depending on the initial conditions and the stress relaxation ratio.

Study of Y1Ba2Cu3O7−δ+CuO Nanocomposite as a Resistive Current Limiter

The influence of CuO nanoscale inclusions as the second component of the composites on the transport properties of superconducting polycrystals YBa2Cu3O7 was studied. Samples of YBa2Cu3O[Formula: see text] with different content of CuO nanoparticles were synthesized. The analysis of magnetic properties was carried out within the framework of the extended critical state model. It was found that the addition of 20[Formula: see text]wt.% CuO nanoparticles leads to an increase in the critical current density at [Formula: see text][Formula: see text]K. A further increase to 30[Formula: see text]wt.% reduces the critical current density. The results of the experimental studies of a switching superconducting fault current limiter in AC voltage networks based on high-temperature superconductors (HTSC) of the 2nd generation are given in this work. The testing equipment contains a series-connected HTSC module and a high-speed current switch with a break time of 9[Formula: see text]ms. The high efficiency of the samples made from the YBa2Cu3O[Formula: see text] + CuO nanocomposite material as an active element of a resistive current limiter is shown.

The Influence of CuO Dopant Nanoparticles, Prepared via the Arc Plasma Synthesis Method, on the Critical Current of YBa2Cu3O7 –δ Composites

Abstract—YBa2Cu3O7 – δ–CuO composites with CuO particle contents of 0.5, 1.0, 2.0, 5.0, 10, 15, 20, and 24% were produced via arc plasma synthesis. Their magnetic properties were analyzed in the context of the expanded critical state model. In comparison with a reference sample, the critical current intragranular density increased in composites with CuO concentrations of 0.5, 1, 20, and 24%. The mechanisms of the influence of nanodopants on the change in the critical current density at various volume contents of nano-CuO were proposed as well.

Observation of Two-Level Critical State in the Superconducting FeTe Thin Films**Supported by the National Key Research and Development Program of China under Grant Nos 2016YFA0301002 and 2017YFA0303000, and the National Natural Science Foundation of China under Grant No 11827805.

FeTe, a non-superconducting parent compound in the iron-chalcogenide family, becomes superconducting after annealing in oxygen. Under the presence of magnetism, spin-orbit coupling, inhomogeneity and lattice distortion, the nature of its superconductivity is not well understood. Here we combine the mutual inductance technique with magneto transport to study the magnetization and superconductivity of FeTe thin films. It is found that the films with the highest TC show non-saturating superfluid density and a strong magnetic hysteresis distinct from that in a homogeneous superconductor. Such a hysteresis can be well explained by a two-level critical state model and suggests the importance of granularity to superconductivity in this compound.

Transport properties and high upper critical field of a Fe(Se,Te) iron based superconductor

A Fe(Se,Te) iron based crystal has been studied using dc magnetic measurements as a function of temperature (T ) and magnetic field (H ). Firstly, the field dependence of the critical current density J c has been extracted from the superconducting hysteresis loops m (H ) at different temperatures within the Bean critical state model in order to obtain information about the transport properties of the sample. The knowledge of the critical current density values as a function of the field for temperatures near T c allow us to determine the values and the behavior of the irreversibility field H irr as a function of the temperature. On the other hand, by means of zero field cooling m (T ) measurements at different magnetic fields, the upper critical field H c2 has been evaluated as a function of the temperature. Both irreversibility field and upper critical field have been fitted by the equation H (T ) = H (0)(1 − T /T * )n allowing us to obtain the values of the related parameters which are in good agreement with those found in literature for the IBS systems.