Density In High-temperature Superconductors Research Articles

Influence of the physical parameters on the limits of magnetic stiffness of high-Tc superconducting levitation systems

Magnetic stiffness is one of the important stability parameters of high temperature superconducting levitation systems. Till to now, great efforts have been made to understand levitation properties including flux penetration, magnetization curves, levitation force, ac susceptibilities, etc. In this paper we present a quadratic approximation method for the limit of magnetic stiffness in a high temperature superconducting levitation system based on Kim’s critical state model and Ampère law. The system is composed with a cylindrical permanent magnet (PM) and a coaxial high temperature superconductor (HTS). It is found that the limit of magnetic stiffness depends upon both the penetration history of shielding currents distribution in HTS and applied magnetic field gradients. Furthermore, the influence of the physical parameters, such as critical current density in HTS and applied magnetic field, on the limits of magnetic stiffness is investigated in detail. The obtained results display that magnetic stiffness decreases with the increasing of critical current density, since shielding currents have not penetrated into the large portion of the HTS. With the increase of applied magnetic field, the magnetic stiffness obtain a larger magnification factor. It is related to the increase of the shielding current penetration volume and the internal magnetic field in HTS.

Depairing Current at High Magnetic Fields in Vortex-Free High-Temperature Superconducting Nanowires.

Superconductors are essential in many present and future technologies, from large-scale devices for medical imaging, accelerators, or fusion experiments to ultra-low-power superconducting electronics. However, their potential applicability, and particularly that of high-temperature superconductors (HTS), is severely affected by limited performances at large magnetic fields and high temperatures, where their use is most needed. One of the main reasons for these limitations is the presence of quantized vortices, whose movements result in losses, internal noise, and reduced performances. The conventional strategy to overcome the flow of vortices is to pin them along artificial defects. Here, we theoretically and experimentally demonstrate that critical-current density in high-temperature superconductors can reach unprecedented high values at high fields and temperatures by preventing vortex entry. By tailoring the geometry, that is, reducing the width, W, of nanowire-patterned HTS films, the range of the Meissner state, for which no vortices are present, is extended up to very large applied field values, on the order of ∼1 T. Current densities on the order of the depairing current can be sustained under high fields for a wide range of temperatures. Results may be relevant both for devising new conductors carrying depairing-current values at high temperatures and large magnetic fields and for reducing flux noise in sensors and quantum systems.

Effect of temperature-dependent critical current density on the fracture behavior for a rectangular superconducting slab with a center crack

Superconducting cables made of high-temperature superconductors have great potential applications in space solar power station. Since the critical current density of high temperature superconductor is dependent of temperature and determines the distribution of the magnetic flux density, temperature change can affect the pinning force. In this paper, model-I crack problem of a long rectangular superconducting slab under thermal effect is investigated. The stress intensity factors of the slab during the field decent of pulsed field magnetization (PFM) and field cooling (FC) are calculated. Compared with that without considering thermal effect, the result shows that once the temperature of the slab rises, the variation of the stress intensity factor will have a peak during the applied magnetic field decent for the PFM. While for the FC, temperature rise causes the stress intensity factor to decrease.

How resistive must grain boundaries in polycrystalline superconductors be, to limit Jc?

Although we can use misorientation angle to distinguish the grain boundaries that can carry high critical current density in high temperature superconductors (HTS) from those that cannot, there is no established normal state property equivalent. In this paper, we explore the superconducting and normal state properties of the grains and grain boundaries of polycrystalline YBa2Cu3O7−x (YBCO) using complementary magnetisation and transport measurements, and calculate how resistive grain boundaries must be to limit in polycrystalline superconductors. The average resistivity of the grain boundaries, in our micro- and nanocrystalline YBCO are 0.12 Ωm and 8.2 Ωm, values which are much higher than that of the grains and leads to huge values of 2 × 103 and 1.6 × 105 respectively. We find that the grain boundaries in our polycrystalline YBCO are sufficiently resistive that we can expect the transport to be several tens of orders of magnitude below the potential current density of the grains in our YBCO samples, as is found experimentally. Calculations presented show that increasing values by ∼2 orders of magnitude in high fields is still possible in all state-of-the-art technological high-field superconductors. We conclude: grain boundary engineering is unlikely to improve sufficiently in randomly aligned polycrystalline YBCO, to make it technologically useful for high-field applications; in low temperature superconducting intermetallics, such as Nb3Sn, large increases in may be achieved by completely removing the grain boundaries from these materials and, as is the case for thin films of Nb, Ba(FeCo)2As2 and HTS materials, by incorporating additional artificial pinning.

Scaling rules for critical current density in anisotropic biaxial superconductors

Recent researches highlight the additional anisotropic crystallographic axis within the superconducting plane of high temperature superconductors (HTS), demonstrating the superconducting anisotropy of HTS is better understood in the biaxial frame than the previous uniaxial coordinates within the superconducting layer. To quantitatively evaluate the anisotropy of flux pinning and critical current density in HTS, we extend the scaling rule for single-vortex collective pinning in uniaxial superconductors to account for flux-bundle collective pinning in biaxial superconductors. The scaling results show that in a system of random uncorrected point defects, the field dependence of the critical current density is described by a unified function with the scaled magnetic field of the isotropic superconductor. The obtained angular dependence of the critical current density depicts the main features of experimental observations, considering possible corrections due to the strong-pinning interaction.

A magneto-mechanical fully coupled model for giant magnetostriction in high temperature superconductor

This paper presents a fully coupled model to account for the flux pinning induced giant magnetostriction in type-II superconductors under alternating magnetic field The superconductor E-J constitutive law is characterized by power law where the critical current density is assumed to depend exponentially on the flux density. The governing equations of the two-field problem (i.e., the interactions of elastic and magnetic effects) are formulated in a two-dimensional model. The magnetostriction curves and magnetization loops are calculated over a wide range of parameters. The effects of applied magnetic field frequency f and amplitude B0 and critical current density on magnetostriction and magnetization are discussed. Results show that the critical current density of high temperature superconductor (HTS) YBCO has a significant effect on the magnetization and magnetostriction. The pinning-induced magnetostriction which has been observed in experiment can be qualitatively simulated by this model.

Numerical Studies of Axial and Radial Magnetic Forces Between High Temperature Superconductors and a Magnetic Rotor

The magnetic bearing is considered as one of the most prospective applications of high temperature superconductors (HTSs) which can realize stable levitation in a magnetic field generated by permanent magnet devices or coils. The exploration of this kind of HTS bearing through numerical investigation is usually made by assuming the induced current circulates only within the ab-plane and thus simplifying the actual three-dimensional problem to a two-dimensional one. In this paper, on the basis of the three-dimensional model of the HTS bulk established before, we further introduce the developed finite-element software to calculate the magnetic field generated by a magnetic rotor which is composed of permanent magnet (PM) rings and ferromagnet (FM) shims, and in this way, we can investigate the magnetic forces (radial force and axial force) of a simplified HTS bearing model, i.e., two symmetric HTS bulks and a magnetic rotor, at a three-dimensional level. The investigations performed in this paper lead to the observations: the favorable configuration to construct the HTS bearing is that the axial height of each HTS element should be equivalent to the axial heights of PM ring plus FM shim; the increase of the radial thickness of PM ring will improve both the radial force and the axial force considerably, but its margin decreases; the enhancement of critical current density of HTSs due to the decrease of operating temperature can result in a higher increase of both the radial and axial force with a lower nominal gap between the HTSs and the magnetic rotor.

New attractive-force concept for Cooper pairs and theoretical evaluation of critical temperature and critical-current density in high-temperature superconductors

We propose a new attractive interaction between pairs of holes that results in Cooper pairs and a linear temperature dependence of the spin-energy gap derived from Fermi statistics. This interaction is a Lorentz force between two moving holes with equal velocity. This force is analogous to the attractive electromagnetic force between parallel current-carrying leads; local currents exist at a CuO2 surface. Combining the spin-energy gap and the proposed attractive force, we derive a critical temperature equation that gives the dependence of critical temperature on doping. This equation contains electric charge, coherence, Debye temperature, hole concentration, and forbidden band gap. It does not contain numerical or fitting parameters. By comparing the values obtained by this equation with experimental results, we find that the proposed theory agrees with the results for doping dependence. Furthermore, we use the spin-energy gap to obtain results for the temperature dependence of critical current density.

Effect of magnetic particle additions on flux pinning in bulk Y-Ba-Cu-O superconductors

Abstract In order to increase the critical current density of high temperature superconductors, it is commonly employed to disperse nonsuperconducting particles as flux pinning centers into the superconductive matrix. For Y-Ba-Cu-O bulk superconductors Y2BaCuO5 (Y211) phase particles are known to be effective pinning centers. It has been proposed that magnetic particles are more efficient pinning centers, since they will have a stronger positive interaction with quantized fluxoids. A combined addition of Y211 and magnetic metal fine powders has been reported to be effective in improving flux pinning performances. Therefore, in this study we aimed at improving the pinning forces of Y-Ba-Cu-O bulk superconductors by introducing the Fe-Al-Si-based alloys that are ferromagnetic. We also studied the effect of the addition of γ-hematite, which is non-magnetic, in order to compare the contribution to the flux pinning enhancement. For comparative study, we measured the trapped field in single-domain bulk superconductors and found that a small addition of Fe-Al-Si based ferromagnetic powders and γ-hematite improved field trapping ability.

On the Relation Between the Nonlinear Surface Impedance and the Superfluid Current Density in High-Temperature Superconductors

The nonlinear surface impedance is related to a local description of the nonlinear superfluid current density that depends on the condensate velocity, by use of the definition of surface impedance as the ratio between the electric field and magnetic field at the conductor surface. To obtain this relation, we follow a rigorous approach based on the time-domain nonlinear London equations and the two-fluid model. The formulation is compared with harmonic balance simulations of an equivalent transmission line circuit that models a plane wave propagating across a vacuum-superconductor boundary, and shows very good agreement for the resulting surface impedance as a function of current density at the surface.

High-Speed Method for Analyzing Shielding Current Density in High-Temperature Superconductor

A fast method is proposed for calculating the shielding current density in a high-temperature superconductor. When the power law is assumed as the constitutive relation linking the shielding current density and the electric field, the initial-boundary-value problem for the shielding current density cannot be always solved with the Runge-Kutta method. This is the case even when an adaptive step-size control algorithm is incorporated. In order to overcome this difficulty, the constitutive relation is modified for a large value of the shielding current density. By using this method, a numerical code is developed for calculating the shielding current density. The results of computations show that the proposed method is much faster than the conventional implicit one for a large-scale problem.

A Criterion for Determining Stabilizer Thickness of YBCO Coated Conductors Based on Coil Protection

The purpose of this study is to propose a criterion for determining stabilizer thickness of YBCO coated conductors. The permissible disturbance energy density in high-temperature superconductors (HTSs) is two or three orders of magnitude greater than that in low-temperature superconductors (LTSs). On the other hand, to enhance the reliability and safety of HTS coils, an establishment of a protection scheme assuming a quench caused by a failure in power supply, cooling system or similar problem is also required for HTS coil systems. Quenching produces excessive temperature or voltage in the coil winding; overheating may cause the conductor to meltdown, or high voltage may punch a hole in the winding. To avoid these types of damages in YBCO coils, a suitable stabilizer thickness must be determined for the sophisticated structure of YBCO coated conductors, which are composed of highly textured thin-film on a flat flexible substrate. Therefore, we investigate the appropriate structure for YBCO coated conductors from the perspective of energy dumping (i.e., quench protection). Based on the protection scheme that the stored magnetic energy in the coils is dumped by an external dump resistance prepared as a quench protection, we derive a function that examines the heat balance of a quenching YBCO coil in an adiabatic condition and propose a criterion using the function to determine an appropriate stabilizer thickness for YBCO coated conductors.

Experimental determination of the temperature dependence of the superfluid electron density in high-temperature superconductors

It is established that the temperature dependence of the effective density of superfluid electrons for Cu(1) lattice sites calculated within the framework of the Bardeen-Cooper-Schriffer (BCS) theory is at variance with the experimental data obtained using Mossbauer spectroscopy for YBa2Cu3O7, YBa2Cu4O8, Tl2Ba2Ca2Cu3O10, Bi2Sr2Ca2Cu3O10, and HgBa2Ca2Cu3O8 compounds. At the same time, the experimental data for Cu(2) lattice sites are in satisfactory agreement with BCS results.

Numerical simulation of inductive measurement of critical current density in HTS: high-performance method for solving shielding current equations

A numerical code has been developed for analyzing the time evolution of the shielding current density in the high-temperature superconductor (HTS) bulk. In the code, the shielding current equations are discretized by means of the element-free Galerkin method and the resulting nonlinear system is solved by use of the pseudo Newton method with a variable relaxation factor. By means of the code, the shielding current density is calculated in cases where the ac current flows in a coil placed just above the HTS. The voltage induced in the coil is evaluated as a function of time and its spectral analysis is performed. The results of computations show a qualitative agreement with Mawatari's experimental results.

Scaling of the superfluid density in high-temperature superconductors

A scaling relation Nc≃4.4σdcTc has been observed parallel and perpendicular to the copper–oxygen planes in the high-temperature superconductors; Nc is the spectral weight and σdc is the dc conductivity just above the critical temperature Tc. In addition, Nb and Pb also fall close to this scaling line. The application of the Ferrell–Glover–Tinkham sum rule to the BCS optical properties of Nb above and below Tc yields Nc≃8.1σdcTc when the normal-state scattering rate is much greater than the superconducting energy gap (1/τ>2Δ, the “dirty” limit). This result suggests that the high-temperature superconductors may be in the dirty limit. The superconductivity perpendicular to the planes is explained by the Josephson effect, which again yields Nc≃8.1σdcTc in the BCS formalism. The similar forms for the scaling relation in these two directions suggests that in some regime the dirty limit and the Josephson effect may be viewed as equivalent.

Scaling of the superfluid density in high-temperature superconductors

A scaling relation ${N}_{c}\ensuremath{\simeq}4.4{\ensuremath{\sigma}}_{\mathit{dc}}{T}_{c}$ has been observed in the copper-oxide superconductors, where ${N}_{c}$ is the spectral weight associated with the formation of the superconducting condensate ${\ensuremath{\rho}}_{s}=8{N}_{c}$, ${T}_{c}$ is the critical temperature, and ${\ensuremath{\sigma}}_{\mathit{dc}}$ is the normal-state dc conductivity close to ${T}_{c}$. This scaling relation is examined within the context of a clean and dirty-limit BCS superconductor. These limits are well established for an isotropic BCS gap $2\ensuremath{\Delta}$ and a normal-state scattering rate $1∕\ensuremath{\tau}$; in the clean limit $1∕\ensuremath{\tau}⪡2\ensuremath{\Delta}$, and in the dirty limit $1∕\ensuremath{\tau}>2\ensuremath{\Delta}$. The dirty limit may also be defined operationally as the regime where ${\ensuremath{\rho}}_{s}$ varies with $1∕\ensuremath{\tau}$. It is shown that the scaling relation ${N}_{c}$ or ${\ensuremath{\rho}}_{s}\ensuremath{\propto}{\ensuremath{\sigma}}_{\mathit{dc}}{T}_{c}$, which follows directly from the Ferell-Glover-Tinkham sum rule, is the hallmark of a BCS system in the dirty-limit. While the gap in the copper-oxide superconductors is considered to be $d$ wave with nodes and a gap maximum ${\ensuremath{\Delta}}_{0}$, if $1∕\ensuremath{\tau}>2{\ensuremath{\Delta}}_{0}$ then the dirty-limit case is preserved. The scaling relation implies that the copper-oxide superconductors are likely to be in the dirty limit and, as a result, that the energy scale associated with the formation of the condensate scales linearly with ${T}_{c}$. The $a\text{\ensuremath{-}}b$ planes and the $c$ axis also follow the same scaling relation. It is observed that the scaling behavior for the dirty limit and the Josephson effect (assuming a BCS formalism) are essentially identical, suggesting that in some regime these two pictures may be viewed as equivalent.

Time-domain analysis of shielding current density in high-temperature Superconductor

The numerical code has been developed for the time-domain analysis of the shielding current density in the high-temperature superconductor (HTS). By means of the code, the shielding current density is calculated in cases where the ac current flows in a 1-turn coil placed just above the HTS. The voltage induced in the coil is evaluated as a function of time and its spectral analysis is performed. The results of computations show that, above a certain limit of the coil current, the third-harmonic voltage is suddenly excited and it grows more rapidly than any other harmonic voltage. It is also found that, if the dc magnetic field as well as the coil field is applied, the square root of the third-harmonic voltage is proportional to the coil current.

Quasiparticle density of state in d-wave superconducting superlattice systems

The effect of the superlattice structure along the c-axis on the single particle density of high temperature superconductors is investigated by considering superlattice systems that consists of metals/insulators and d-wave superconductors (NS/IS superlattices). It is shown that the position of quasiparticle peak is sensitive to how one models the c-axis tunneling. For the NS superlattice, the position of the quasiparticle peak can be considerably smaller than the gap value, while for the IS superlattice, the quasiparticle peak always remains at the bulk value so that the whole system behaves like a single superconductor. Furthermore, in the presence of a small current, the density of state at zero energy becomes non-zero for the NS superlattice while it sticks to zero for the IS superlattice. This results in different behaviors in the specific heat measurements, providing a possible way to differentiate between these two models.

Interpretation of the critical current in Bi 2Sr 2Ca 2Cu 3O x tape conductors as parallel weak-link and strong-link paths

To better understand the dominant mechanisms that limit the critical current density in high temperature superconductors, the dependence of the critical current density on magnetic field and temperature of Bi 2Sr 2Ca 2Cu 3O x tapes is measured in magnetic fields up to 8 T and temperatures between 4.2 and 100 K. The results were modeled by describing the current in the tape as two parallel current paths. The critical current density of one path is limited by weak links and that of the other path by intragranular flux pinning. The temperature dependence of the parameters used in the model indicates that the weak link contribution vanishes at a temperature of 86 K. This is an indication that the weak link behavior is dominated by a remnant Bi 2Sr 2CaCu 2O x phase. At higher temperatures the critical current density of the tape is limited by intragranular pinning.

Homogeneity area of Bi2Sr2CaCu2O8 - based solid solutions with substitution of alkaline earth elements by Nd and La

ABSTRACTCreation of precipitates in bulk matrix to act as pinning centres is a prospective way to improve critical current density in high temperature superconductors. It is possible to generate such precipitates via partial decomposition of the supersaturated solid solution derived from a superconducting phase. To control this process one should go by a knowledge of stability field for these solutions. The objective of present work was determination of the homogeneity area of Bi2Sr2Ca1−xRxCu2O8+d and Bi2Sr2−xCaRxCu2O8+d (R = Nd, La). Semi-quantitative XRD analysis was used to evaluate phase composition of specimens quenched from various temperatures. It was found that solubility limits of Nd and La in Bi-2212 for cases of alkaline earth element substitution by rare earth elements with smaller ionic radii (substitution Ca by Nd; Sr by Nd and La) were the same (values of x are about 0.8). These limits are determined by fraction of Cu+ ions in lattice site attributed to Cu2+. In case of substitution of Ca by La stability area of 2212 was found to be much narrower (values of x about 0.3) compared to other substitutions. One ca n deduce this fact from the difference of Ca2+ and La3+ ionic radii.