The giant dispersion of critical currents in a superconductor with fractal clusters of a normal phase

The influence of fractal clusters of a normal phase on the dynamics of a magnetic flux trapped in a percolation superconductor is considered. The critical depinning current distribution and the current-voltage characteristics of fractal superconducting structures in the resistive state are determined for an arbitrary fractal dimension of the cluster boundaries. The interval of fractal dimensions is found in which the dispersion of critical currents exhibits unlimited growth. It is established that the fractality of clusters favors a decrease of the electric field arising during the magnetic flux motion, thus increasing the critical current value. The region featuring the giant dispersion of critical currents can be expected to provide for the maximum current-carrying capacity of a superconductor.     

Microwave response of superconducting thin films in magnetic fields

We calculate the complex conductivity of a superconducting thin film in a tilted magnetic field. Use is made of the time-dependent Ginzburg-Landau equations to deal with the dynamical behavior of the order parameter associated with the vortex motion in response to the microwave. The reactive part of the conductivity at zero frequency vanishes identically due to the vortex motion and the conductivity resembles that in the flux-flow regime of the type-II superconductor, unless the dc magnetic field is parallel to the film surface with high precision.     

Model calculations of the time-dependent flux-flow voltage in a thin-film type I superconductor

The temporal structure of the flux-flow voltage is calculated in the current-induced dissipative state of a thin-film type I superconductor. The instantaneous voltage generated by multiquantum flux tubes moving through a superconducting specimen depends upon both the instantaneous velocity and a geometry-dependent function of the position of the flux tube relative to the measuring circuit. The flux-tube velocity is strongly affected by the transport-current distribution, by the short-range edge-pinning effect, and by the repulsive interaction of simultaneously moving flux tubes. For a measuring circuit with leads kept far from the specimen surface, both nonuniform contributions due to the flux-flow velocity and the geometry-dependent function simultaneously cause the instantaneous voltage to peak when flux tubes nucleate and annihilate at the sample edges. Our model calculations reproduce reasonably well the experimental results obtained from signal averaging measurements.     

Thermal state of superconducting films on wide substrates

The stationary thermal state of a long superconducting film on a wide substrate is analyzed analytically. Expressions describing voltage-current characteristics and temperature-current dependence of the film are derived for the flux creep, flux flow and normal regimes. It is shown how the flux creep influences the conditions of the thermal stability. In particular, it is found that the bistability of the thermal state can appear in this regime. Under the boiling crisis, the temperature-current dependence for a film differs markedly from that for a wire and is characterized by a smooth temperature increase with the current. A “mixed” regime is analyzed where the flux flow and normal states exist simultaneously with the boundary between them parallel to the film axis.     

Dissipation in current-carrying high-T c superconducting ceramics in applied magnetic field

The dissipation mechanism in high-T _csuperconducting ceramics was studied by analyzing the magnetic field dependence of the transport critical current and the form of the current-voltage characteristics. It was found that the actual magnetic field dependence of the transport critical current is significantly slower than that predicted by the weak-link-quenching model. The low-voltage-level current-voltage characteristics were described in terms of thermally activated flux creep at grain boundaries, taking into account collective pinning of intergranular Josephson vortices. For the investigated samples, a low-field, high-temperature mean pinning energy barrier of a few tens of meV was determined.     

Dissipation in current-carrying high-Tcsuperconducting ceramics in applied magnetic field

The dissipation mechanism in high-T _csuperconducting ceramics was studied by analyzing the magnetic field dependence of the transport critical current and the form of the current-voltage characteristics. It was found that the actual magnetic field dependence of the transport critical current is significantly slower than that predicted by the weak-link-quenching model. The low-voltage-level current-voltage characteristics were described in terms of thermally activated flux creep at grain boundaries, taking into account collective pinning of intergranular Josephson vortices. For the investigated samples, a low-field, high-temperature mean pinning energy barrier of a few tens of meV was determined.     

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.     

Nonlinear current-voltage characteristics of normal-superconducting boundaries

The voltage drop at a normal-superconducting boundary is considered in the case when the current flowing across the boundary is of the order of the critical current of the superconductor. The finite supercurrent decreases the distance the electric field penetrates into the superconductor, and leads to a nonlinear current-voltage characteristic. Explicit calculations are carried out for a dirty superconductor close to the transition temperature.Supported in part by National Science Foundation Grant DMR 78-21068.     

Effect of Critical Current Density and Critical Temperature on ac Susceptibility

Based on the flux creep equation, the effect of critical current density and critical temperature on ac susceptibility is investigated numerically in a superconducting slab immersed in an ac magnetic field. The current density dependence of the flux creep activation barrier is employed as the logarithmic law. The fundamental ac susceptibilities of the slab as a function of temperature for the same ac field have been derived in a unified picture. The results show that ac susceptibility in flux creep regime is affected by critical current density and critical temperature.     

The Thermomagnetic Instability in Superconducting Films with Adjacent Metal Layer

Dendritic flux avalanches is a frequently encountered consequence of the thermomagnetic instability in type-II superconducting films. The avalanches, which are potentially harmful for superconductor-based devices, can be suppressed by an adjacent normal metal layer, even when the two layers are not in thermal contact. The suppression of the avalanches in this case is due to so-called magnetic braking, caused by eddy currents generated in the metal layer by propagating magnetic flux. We develop a theory of magnetic braking by analyzing coupled electrodynamics and heat flow in a superconductor-normal metal bilayer. The equations are solved by linearization and by numerical simulation of the avalanche dynamics. We find that in an uncoated superconductor, even a uniform thermomagnetic instability can develop into a dendritic flux avalanche. The mechanism is that a small non-uniformity caused by the electromagnetic non-locality induces a flux-flow hot spot at a random position. The hot spot quickly develops into a finger, which at high speeds penetrates into the superconductor, forming a branching structure. Magnetic braking slows the avalanches, and if the normal metal conductivity is sufficiently high, it can suppress the formation of the dendritic structure. During avalanches, the braking by the normal metal layer prevents the temperature from exceeding the transition temperature of the superconductor. Analytical criteria for the instability threshold are developed using the linear stability analysis. The criteria are found to match quantitatively the instability onsets obtained in simulations.     

Superconducting current stability in composite superconductors

The maximum transport current in multifilament composite superconductors has been studied. The experimentally obtained values of transport current exceed the normal phase minimum propagation current substantially. The current-voltage characteristics of the investigated samples have been studied. It is shown that the relatively high value of the maximum transport current is attributed, under the given experimental conditions, to the behaviour of the current-voltage characteristic in the region of low values of the electric field. The theory and experiment are in good agreement.     

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.     

Effect of Flux Jump on Current Density Distributions in Type-II Superconductors

The effect of flux jump on the current density distributions is studied in type-II superconducting slab. The magnetothermal diffusion equations based on the Kim model in the regime of flux creep are presented to estimate the effect of flux jump on the distributions of current density inside the slab and the changes of surface current density in the flux jump process. Numerical results show that the current density distributions are dependent on the flux jump. It is intended that the flux jump analysis presented be useful to researchers interested in flux jump instability characteristics.     

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     

Continuous vortex cutting in type II superconductors with longitudinal current

The consequences of stipulating translational symmetry for a type II superconductor to which longitudinal electric current and longitudinal magnetic field are applied are investigated. The magnetic flux lines must cut each other continuously in order to generate an electric field in this symmetry. We describe the steady state by two interpenetrating vortex lattices moving into and out of the sample. We find for the slab and cylinder geometries that cutting, crossjoining, and subsequent straightening of the flux lines reduce the electric field, as compared with the normal conducting state, by a factor which is of the order of one over the total number of flux lines in the cylinder. We conclude that the much larger voltages observed in cylinders of several millimeters diameter can be explained only by a breakdown of translational symmetry. With translational ¥mmetry, the voltage initially increases as the third power of the current. The resulting vortex configuration is force-free. The transverse flux component increases and the longitudinal component decreases from the axis to the surface, leading to a paramagnetic moment. The drift or oscillation velocity of the flux lines is reduced by the same factor as the electric field. We predict low-frequency oscillations of the vortices near the surface of thin superconducting wires.     

Flux flow and resonant modes in multi-junction Josephson stacks

Magnetic field dependent current-voltage characteristics of stackled Nb/(Al−AlO_x/Nb)_n long Josephson junctions are investigated experimentally. The thickness of their common superconducting electrodes provides the magnetic coupling between the junctions. For stacks of n=7 Josephson junctions the current-voltage characteristics display collective flux-flow behaviour of Josephson vortices. In the interior layers Josephson vortices move simultaneously under the influence of the bias current. The flux-flow behaviour is modulated by a complicated structure of cavity-like resonances which show broad range of characteristic frequencies. The measurements can be qualitatively explained by the Kleiner model for the resonances in stacks. Mutual locking of junctions in the stack is indicated by pronounced cavity resonances with large voltage spacing.     

Electric field induced by collective vortex creep in superconductors with fractal clusters of normal phase

The influence of the collective creep of magnetic flux on the electric field induced in a superconducting composite with fractal cluster structure is considered. Current–voltage (I–V) characteristics of these superconductors are determined with allowance for the influence of the fractal dimensionality of boundaries of the normal phase clusters and the height of pinning barriers on the nonlinearity of I–V characteristics at small transport currents. A relationship is established between the collective pinning and vortex glass state that is formed in superconductors with a fractal cluster structure. It is shown that the intensity of an electric field induced in the case of collective creep is smaller than that for Anderson–Kim creep.     

Combined time-resolved magnetooptical and electrical flux detection in thin-film superconductors

The dynamic behavior of the current-induced dissipative flux-flow state in a thin-film type I superconductor was studied by simultaneous stroboscopic magnetooptical flux detection and direct recording of the time-resolved flux-flow voltage. Employing high-resolution magnetooptical flux detection with a high-speed stroboscope, it was possible to visualize globally individual multiquantum flux tubes during their rapid motion across the superconducting Pb film, yielding spatial and temporal resolution of better than 1 μm and 0.1 μsec, respectively. Simultaneously, the temporal structure of the flux-flow voltage was recorded using a highly sensitive signal-averaging procedure, thereby yielding a voltage resolution of about 30 nV at a time resolution of 10 nsec (corresponding to a recording bandwidth of 25 MHz). The recorded temporal voltage structures agreed well with the voltages expected from the velocity profiles of all flux tubes existing simultaneously obtained from the magnetooptical data. The experiments are the first to demonstrate full agreement between both independent flux-detection measurements, clearly confirming the existing theory.     

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.     

Inverse Flux Creep in Ring-Shaped Superconductors

Anomalous flux creep is depicted in ring-shaped superconductors, where the vortex movement goes to the inner edge of the sample. The current dissipation phenomenon is inverted and an induction of the current is achieved. Thus, an increase in the current circulating by the superconductor is obtained. The experimental technique consists in the utilization of a closed magnetic circuit for the current induction and a magnet ring with the field opposite to the vortex trapped in the superconducting wall.