Dynamics of the Magnetic Flux Trapped in Fractal Clusters of a Normal Phase in Percolative Superconductors

The effect of the fractal clusters of a normal phase, which act as pinning centers, on the dynamics of magnetic flux in percolative type-II superconductor is considered. The main features of these clusters are studied in detail: the cluster statistics is analyzed; the fractal dimension of their boundary is estimated; the distribution of critical currents is obtained, and its peculiarities are explored. It is found that there is the range of fractal dimension where this distribution has anomalous statistical properties, specifically, its dispersion becomes infinite. It is examined how the finite resolution capacity of the cluster geometric size measurement affects the estimated value of fractal dimension. The effect of fractal properties of the normal phase clusters on the electric field arisen from magnetic flux motion is investigated for the cluster area distribution of different kinds. The voltage-current characteristics of fractal superconducting structures in the resistive state are obtained for an arbitrary fractal dimension. It is revealed that the fractality of the boundaries of the normal phase clusters intensifies the magnetic flux trapping and thereby raises the critical current of a superconductor.     

The pinning enhancement upon the magnetic flux trapping in the clusters of a normal phase with fractal boundaries

The phenomenon of magnetic flux trapping in a hard superconductor with the normal phase clusters acting as the pinning centers is considered. The critical current distribution for the clusters of an arbitrary fractal dimension is determined. The fractal character favors the magnetic flux trapping, thus increasing the critical current.     

Suppression of magnetic relaxation in a high-temperature superconductor placed near a ferromagnet

The phenomenon of the suppression of magnetic relaxation in a high-temperature superconductor (HTSC) with trapped magnetic flux has been observed when the superconducting sample approached a ferromagnet. It is suggested that the ferromagnet is magnetized in the magnetic field of the sample and, in turn, induces currents in the superconductor, which circulate in a direction opposite to that of the trapped flux current. As a result, the magnetic structure becomes stable with respect to the magnetic flux creep because oppositely directed Lorentz forces can act upon different regions of vortices.     

Depinning at the initial stage of the resistive transition in superconductors with a fractal cluster structure

The effects of the initial dissipation of the energy in a superconductor containing fractal clusters of a normal phase are considered. In the interval of currents preceding the resistive transition, an increase in the fractal dimension of clusters leads to an increase of the sample resistance and widening of the region of initial dissipation in the current-voltage characteristic. This is caused by an increase in the density of free vortices broken away from the pinning centers when the current flows. Dependences of the density of vortices on the fractal dimension of cluster boundaries are found for various values of the transport current.     

Superconductor Stability Against Quench and Its Correlation with Current Propagation and Limiting

This paper presents a numerical (finite element) analysis of superconductor stability and current propagation under random variations of critical superconductor parameters. Instead of using singular (homogeneous) values, random variations potentially are appropriate to take into account any conductor inhomogeneity that can be considered as an obstacle to current propagation. Traditional assumptions like homogeneous current distribution, critical temperature, critical current density and critical magnetic fields are not justified in general; a local disturbance (for example, release of mechanical stress energy), if not immediately distributed by solid conduction, would generate a transient increase of local conductor temperature. Local critical current density and magnetic field then will be reduced, and current distribution will change. Disturbances may arise also from transport currents that locally exceed the critical current of the superconductor. Disturbances of all kinds may increase the conductor temperature above its critical value. A local analysis of all superconductor states thus is mandatory to safely avoid a quench. As an extension of standard stability models, also flux flow resistive states are taken into account. We will try to find a possibly existing correlation between current propagation and superconductor stability. Fault current limiting is discussed as a special case of current propagation. The analysis is applied to a bundle of high-temperature superconductor (HTSC) filaments. As will be shown, temperature profiles in a superconductor do not allow a clear distinction between Ohmic resistive or flux flow resistive fault current limiting. Though frequently made in the literature, this separation is highly questionable, because Ohmic resistive and flux flow resistive states may locally coexist, side by side, but are not very stable in the superconductor volume.     

The time-decaying critical current density of a type-II superconductor and its measuring method

The paper will show that a critical current which has been thought to be defined only in the critical state of a type-II superconductor is able to measure by making use of its time-decaying behavior below onset currents of the resistive state due to flux creep. This is a kind of adiabatic process, in which the measurement of critical currents is done by waiting for a quench which takes place when the persistent current induced in a superconducting sample goes cross the time-decaying critical current and also is a method measuring life of the persistent current in the sample. According to this method, potential barrier models for flux pinning and characteristic parameters about superconductors will be determined.     

Retardation of the Magnetic Relaxation in High-Temperature Superconductors Near a Ferromagnet

The creep of a magnetic flux trapped in a bulk high-temperature superconductor has been studied. It has been found that the magnetic relaxation is retarded when the superconductor is placed near a ferromagnet. The value of the retardation effect depends on the sequence of magnetization and the approach of the superconductor to a ferromagnet. The magnetic relaxation is fully suppressed when a superconducting sample first is magnetized and then is brought close to a ferromagnet. An interpretation of this effect has been discussed. Being magnetized, a ferromagnet produces its own magnetic field. While penetrating into a disk sample through its planes, the ferromagnet field induces screening currents, which circulate oppositely to the current that arises upon trapping of the magnetic flux. As a result, the stability of the magnetic structure is sharply improved since opposite driving forces can act on different sections of the vortices.     

Magnetic-flux creep at the initial stage of resistive transition in superconductors with fractal clusters of normal phase

The effect of magnetic-flux creep on an electric field induced in a percolating superconductor containing fractal clusters of normal phase is considered. Current voltage characteristics of these superconductors are obtained taking into account the effect of fractal dimensionality of cluster boundaries on nonlinearity of CVC at low transport currents. It has been found that fractality of clusters of the normal phase suppresses magnetic-flux creep at the initial stage of resistive transition, thus increasing the current-carrying ability of the superconductor.     

Flux-Pinning-Induced Stress and Deformation Analyses of a Long Rectangular Superconducting Bicrystal

The flux-pinning-induced stress and deformation of a long rectangular superconducting bicrystal with an arbitrary aspect ratio are analyzed based on the critical-state model and the finite element numerical method. The flux and current distributions in the superconductor with a low-angle grain boundary (GB) are obtained based on a constant GB critical current density assumption. The distributions of the stresses within the superconductor are obtained for different magnetization stages. The deformation and especially the shape distortion in the irreversible magnetostriction of the superconductor are analyzed. In addition, the relation between the maximum stress on the grain boundary and the ratio of the GB critical current density to the grain critical current density is discussed when the applied magnetic field is reduced to zero.     

Effect of External Nonuniform Magnetic Field on Flux Creep Process in Superconductor

The effect of an external nonuniform magnetic field on the flux creep rate in a high-temperature superconductor with trapped magnetic flux was studied. The magnetic relaxation was suppressed when the superconductor was put into a field of permanent magnets or when it approached a ferromagnet. The effect arises when the field sources (being magnetized, the ferromagnet produces its own field) are placed near the superconductor surface, where the flux line ends are located. For these cases, we carried out the calculations of vortex and current density distributions, which demonstrate that reverse currents flow in the near-surface regions of the sample. This verifies the hypothesis suggested earlier about the influence of counter Lorentz forces retarding the creep of the vortices. In the interpretation of the results, we also take into consideration the magnetic force acting on the vortex ends in the external nonuniform magnetic field that allows us to explain the experimental results, in which the current structure in the sample is unipolar.     

Vortex dynamics at the initial stage of resistive transition in superconductors with fractal cluster structure

The effect of fractal normal-phase clusters on vortex dynamics in a percolative superconductor is considered. The superconductor contains percolative superconducting cluster carrying a transport current and clusters of a normal phase, acting as pinning centers. A prototype of such a structure is YBCO film, containing clusters of columnar defects, as well as the BSCCO/Ag sheathed tape, which is of practical interest for wire fabrication. Transition of the superconductor into a resistive state corresponds to the percolation transition from a pinned vortex state to a resistive state when the vortices are free to move. The dependencies of the free vortex density on the fractal dimension of the cluster boundary as well as the resistance on the transport current are obtained. It is revealed that a mixed state of the vortex glass type is realized in the superconducting system involved. The current-voltage characteristics of superconductors containing fractal clusters are obtained and their features are studied.     

Computation of screening currents in superconducting persistent current devices

The penetration of screening currents induced in a hollow superconducting cylinder exposed to a transverse magnetic field is calculated two-dimensionally using a numerical model which simulates the superconductor by a system of parallel wires. Assuming the critical state model and taking account of the dependence of critical current density on magnetic field, the penetration depth and local current density is computed.     

Gibbs free-energy barrier against irreversible magnetic flux entry into a superconductor

We have calculated the Gibbs free-energy barrier against irreversible magnetic flux entry into a superconductor for a long cylinder with elliptical cross section which approximates a long, flat strip. Our model is simplified to the two-dimensional case by assuming magnetic flux to enter in the form of a long, narrow, normal domain parallel to the axis of the cylinder. The following four contributions to the Gibbs free energy have been taken into account: (1) loss of condensation energy and gain of magnetic field energy inside the superconductor, (2) magnetic field energy outside the superconductor, (3) energy of interaction of the domain with an applied magnetic field, and (4) energy of interaction with an applied electrical transport current. Because of the Gibbs free-energy barrier, the critical magnetic field for entry of magnetic flux can be enhanced considerably above that calculated using Silsbee's rule. This enhancement is found to be proportional to the square root of the width of the superconducting cylinder. Important consequences of this are the enhancement of the critical current in a superconducting strip in zero magnetic field at which electrical resistance starts to appear and a corresponding modification of Silsbee's rule. We have demonstrated these effects experimentally through measurements of the onset of the current-induced resistive state in a series of superconducting indium strips of different widths and thicknesses. The experimental results confirm the theoretical predictions. The Gibbs free-energy-barrier effect described here can be interpreted as a novel flux-pinning mechanism, which might be called edge pinning.Work performed in part in the Ames Laboratory and in part in the Argonne National Laboratory of the U.S. Atomic Energy Commission.     

Vortex Dynamics at the Initial Stage of Resistive Transition in Superconductors with Fractal Cluster Structure

No Heading The effect of fractal normal-phase clusters on vortex dynamics in a percolative superconductor is considered. The superconductor contains percolative superconducting cluster carrying a transport current and clusters of a normal phase, acting as pinning centers. A prototype of such a structure is YBCO film, containing clusters of columnar defects, as well as the BSCCO/Ag sheathed tape, which is of practical interest for wire fabrication. Transition of the superconductor into a resistive state corresponds to the percolation transition from a pinned vortex state to a resistive state when the vortices are free to move. The dependencies of the free vortex density on the fractal dimension of the cluster boundary as well as the resistance on the transport current are obtained. It is revealed that a mixed state of the vortex glass type is realized in the superconducting system involved. The current-voltage characteristics of superconductors containing fractal clusters are obtained and their features are studied.PACS numbers: 74.81.–g, 74.25.Fy     

The state of vortex glass induced by creep of vortices in percolation superconductors

The influence of magnetic flux creep on the dynamics of vortices in percolation superconductors containing fractal clusters of the normal phase has been considered. Dependences of the resistance of these superconductors on the transport current are obtained for different fractal dimensions of cluster boundaries. It is established that the vortex-glass state is implemented in percolation superconductors with a fractal cluster structure under collective creep of vortices.     

Correlations Between Magnetic Flux and Levitation Force of HTS Bulk Above a Permanent Magnet Guideway

In order to clarify the correlations between magnetic flux and levitation force of the high-temperature superconducting (HTS) bulk, we measured the magnetic flux density on bottom and top surfaces of a bulk superconductor while vertically moving above a permanent magnet guideway (PMG). The levitation force of the bulk superconductor was measured simultaneously. In this study, the HTS bulk was moved down and up for three times between field-cooling position and working position above the PMG, followed by a relaxation measurement of 300 s at the minimum height position. During the whole processes, the magnetic flux density and levitation force of the bulk superconductor were recorded and collected by a multipoint magnetic field measurement platform and a self-developed maglev measurement system, respectively. The magnetic flux density on the bottom surface reflected the induced field in the superconductor bulk, while on the top, it reveals the penetrated magnetic flux. The results show that the magnetic flux density and levitation force of the bulk superconductor are in direct correlation from the viewpoint of inner supercurrent. In general, this work is instructive for understanding the connection of the magnetic flux density, the inner current density and the levitation behavior of HTS bulk employed in a maglev system. Meanwhile, this magnetic flux density measurement method has enriched present experimental evaluation methods of maglev system.     

Local Magnetic Measurements of Trapped Flux Through a Permanent Current Path in Graphite

Temperature- and field-dependent measurements of the electrical resistance of different natural graphite samples suggest the existence of superconductivity at room temperature in some regions of the samples. To verify whether dissipationless electrical currents are responsible for the trapped magnetic flux inferred from electrical resistance measurements, we localized them using magnetic force microscopy on a natural graphite sample in remanent state after applying a magnetic field. The obtained evidence indicates that at room temperature a permanent current flows at the border of the trapped flux region. The current path vanishes at the same transition temperature \(T_c\approx 370\) K as the one obtained from electrical resistance measurements on the same sample. This sudden decrease in the phase is different from what is expected for a ferromagnetic material. Time-dependent measurements of the signal show the typical behavior of flux creep of a permanent current flowing in a superconductor. The overall results support the existence of room-temperature superconductivity at certain regions in the graphite structure and indicate that magnetic force microscopy is suitable to localize them. Magnetic coupling is excluded as origin of the observed phase signal.     

Properties of the distorted flux-line lattice near a planar surface

The magnetic field, current density, and energy of an arbitrary array of curved or straight flux lines in a type II superconductor with a planar surface are calculated from the London theory. The general expressions and their expansion with respect to displacements from the equilibrium flux-line positions are given. The elastic energy of the distorted flux-line lattice near a planar surface is presented and discussed. The equilibrium configuration becomes unstable to the growth of helical perturbations if a current exceeding a critical value is applied parallel to the external magnetic field.     

Statistics of normal-phase clusters and magnetic-flux trapping in films of high-T c superconductors

The morphological properties of YBCO superconducting films and their relationship to magnetic and transport phenomena are considered. A geometric probability analysis of the principal statistical characteristics of normal-phase clusters is performed, and their influence on the dynamics of trapped magnetic flux under the action of a pulsed transport current is revealed. The superconducting film is treated as a percolation system. It is found that the critical currents have a statistical distribution, which is specified by the morphology of the material being studied. The critical current for passage of the film into the resistive state is found. Pis’ma Zh. Tekh. Fiz. 25, 30–36 (June 26, 1999)     

The structure and manipulation of vortex states in a superconducting square with 2×2 blind holes

We consider a mesoscopic square superconductor with 2×2 blind holes in the presence of a homogeneous magnetic field. Under suitable conditions a diagonal L=2 state is realized and the system reduces to double degenerate states with different flux configurations, which can be considered as logic states. We show the possibility of manipulation of these states by circulating currents in a loop near the superconductor.