Electric field induced by magnetic flux motion in superconductor containing fractal clusters of a normal phase

The influence 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 voltage–current characteristics of such a superconductor are obtained taking into account the effect of fractal properties of cluster boundaries on the magnetic flux trapping. It is revealed that the fractality reduces the electric field arising from magnetic flux motion and thereby raises the critical current of a superconductor.     

Resistive state of superconducting structures with fractal clusters of a normal phase

The effect of morphologic factors on magnetic flux trapping and critical currents in a superconducting structure, which presents a type II percolation superconductor with pinning centers, is considered. The role of pinning centers is played by fractal clusters of the normal phase. The properties of these clusters are analyzed in detail: their statistics is studied, the distribution of critical currents of depinning is found, and the depen-dences of the main statistical parameters on the fractal dimension are obtained. The effect of fractal clusters of the normal phase on the electric field caused by the motion of the magnetic flux after the vortices have been broken away from pinning centers is considered. The current-voltage characteristics of superconducting structures in a resistive state are obtained for an arbitrary fractal dimension. It is found that the fractality of the boundaries of normal-phase clusters forces magnetic flux trapping, thereby increasing the critical current.     

Current-voltage characteristics of a foamed Bi1.8Pb0.3Sr2Ca2Cu3O x high-temperature superconductor with fractal cluster structure

The influence of the structure of foamed polycrystalline bismuth-based superconductors on their critical currents and current-voltage characteristics is studied. It is found that superconducting foams have a fractal structure, and the fractal dimension of the boundary between the normal and superconducting phases is estimated. The magnetic and transport properties of superconducting foams are investigated, and the current-voltage characteristics are obtained in a wide range of currents. The effect of percolation phenomena on vortex pinning in a foamed superconductor is considered. The current-voltage characteristics of the superconducting foams at the beginning of the resistive transition are found to be in good agreement with a model in which a magnetic flux is assumed to be trapped in the fractal clusters of a normal phase.     

Resistive states of the composite superconductors at magnetic flux creep

The effect of magnetic flux creep on the formation of resistive states of the composite superconductors has been studied taking into account their self-heating. The obtained results have been compared with the calculations carried out using the existing thermal stabilization theory, which is based on the model of a stepwise transition from the superconducting to normal state. It has been shown that, over a wide range of the superconductor temperature, this model leads to overrated effective electric resistances of the composite. As a result of its stable self-heating, the notions on the critical current, which determine the maximum transport current and on the resistive transition temperature, the higher of which in the transport current begins dividing between the superconductor and matrix, a loss a physical sense at magnetic flux creep, are used in the existing thermal stabilization theory. As a result, the limits of the theory of thermal stabilization of the composite superconductors can be extended if the theory has been used to describe stable sates at currents, which are higher than the conditionally defined critical current of the composite.     

On aggregate structures in a rod-like haematite particle suspension by means of Brownian dynamics simulations

We have investigated aggregation phenomena in a suspension composed of rod-like haematite particles by means of Brownian dynamics simulations. The magnetic moment of the haematite particles lies normal to the particle axis direction and therefore the present Brownian dynamics method takes into account the spin rotational Brownian motion about the particle axis. We have investigated the influence of the magnetic particle–field and particle–particle interactions, the shear rate and the volumetric fraction of particles on the particle aggregation phenomena. Snapshots of aggregate structures are used for a qualitative discussion and the cluster size distribution, radial distribution function and the orientational correlation functions of the direction of particle axis and magnetic moment are the focus for a quantitative discussion. The significant formation of raft-like clusters is found to occur at a magnetic particle–particle interaction strength much larger than that required for a magnetic spherical particle suspension. This is because the rotational Brownian motion has a significant influence on the formation of clusters in a suspension of rod-like particles with a large aspect ratio. An applied magnetic field enhances the formation of raft-like clusters. A shear flow does not have a significant influence on the internal structure of the clusters, but influences the cluster size distribution of the raft-like clusters.     

Formation of an ensemble of nanoclusters under rapid deposition of atoms on a surface

The results of an experimental study of the formation of nanometer-size Au clusters on NaCl(100) and HOPG(0001) surfaces under pulsed laser deposition are presented. No clusters of small sizes (d ≤ 1 nm) have been found in the cluster size distribution. The distribution itself at d < 5 nm has the form of a percolation distribution. It has been established that the perimeter of clusters with sizes d < 5 nm has a fractal structure. The fractal dimension of clusters is different for NaCl(100) and HOPG(0001) surfaces with different symmetries; it decreases with increasing cluster size from D _f ≈ 1.2–1.4 at d ≈ 1.5 nm to D _f ≈ 1 at d ≈ 5 nm. A physical mechanism of nanocluster formation is suggested. Under pulsed laser deposition, the attainable densities of adatoms are close to the percolation threshold in the region of thermodynamically unstable states and many-particle correlation regions are formed in a spatially inhomogeneous adsorbate. Clusters are formed on the surface from many-particle correlation regions in several diffusion jumps. The suggested mechanism allows the fractal dimension of the clusters forming on surfaces with different symmetries, its dependence on cluster size, and the cluster size distribution functions to be calculated.     

Effect of heat capacity and conductivity of NbTi normal matrix of a composite superconductor on the stability to magnetic flux jumps

The stability against magnetic flux jumps has experimentally been studied in the external magnetic field for three samples from NbTi composite superconductors, one monofilamentary and two multifilamentary. A comparison between the experiment and theory of thermomagnetic stability of composite superconductors has been carried out. We have determined threshold values of the rates of the external magnetic fields, starting from which heat capacity and conductivity of the normal composite matrix become determining stabilizing factors. For the first time, the increasing dependence of field of first magnetic flux jump on the rate of the rise in the external magnetic field has been experimentally registered in the superconducting wire for MRI. The reason for this effect is the shunting effect of a high pure copper matrix and the low volume fraction of a superconductor in the composite (~10%).     

Magnetic relaxation in superconductors with varying creep behavior

The relaxation of an electromagnetic field inside low-and high-temperature superconductors in the case when the magnetic flux occupies the cross section incompletely is studied theoretically in the self-similar approximation. On the macroscopic level, creep is described by phenomenological equations for exponential and power I-V characteristics. A relation between the nonlinearity of the I-V curves and the magnetic relaxation process is found. The range of low electric fields is shown to be of considerable importance for the relaxation in high-temperature superconductors. In this range, the equations for exponential and power I-V curves may differ substantially from those at high fields. Complete analytical solutions are contrasted with a numerical solution to the problem.     

Some numerical calculations on high field superconductivity

Numerical calculations are presented for the field dependence of critical currents in high field superconductors. The computations are done under two simplifying assumptions, namely that the fluxoids are pinned strongly enough so that flux creep and flux flow does not have to be taken into account, and that spin orbital interaction can be neglected. Only the zero temperature limit is considered. Furthermore, a diagram is calculated with the help of which the following three fields can be read off easily for a given sample: the supercooling and superheating critical field and the field for which the energies in the normal and superconducting state are equal.     

SIMULATION ON LOCAL FLUX CREEP IN TYPE-Ⅱ SUPERCONDUCTORS

Using C programming language, we have simulated the flux creep process in nonideal type-Ⅱ superconductors. Global and local magnetization curves are calculated and the logarithmic time dependence of local magnetic induction B under a constant external field is examined. The effects of nonuniform pinning potential and self-organized criticality (SOC) model on the simulations are discussed. The results show that the main feature of flux creep is the relaxation effect. The form of hysteresis loops is dependent on the magnetic field sweep rate. SOC can account for the occurrence of fluctuation to a certain extent and nonuniform pinning potential can enhance the fluctuation.     

Why an ac magnetic field shifts the irreversibility line in type-II superconductors

We show that for a thin superconducting strip placed in a transverse dc magnetic field--the typical geometry of experiments with high-T(c) superconductors--the application of a weak ac magnetic field perpendicular to the dc field generates a dc voltage in the strip. This voltage leads to the decay of the critical currents circulating in the strip, and eventually the equilibrium state of the superconductor is established. This relaxation is not due to thermally activated flux creep but to the "walking" motion of vortices in the two-dimensional critical state of the strip with in-plane ac field. Our theory explains the shaking effect that was used for detecting phase transitions of the vortex lattice in superconductors.     

A finite fractal cluster theory of 1/f noise in percolation systems near metal-insulator transition

The problem of 1/f noise in thin metal films and metal-insulator composites in the scaling fractal regime near percolation threshold is considered. The correspondence between a percolation transition and a second order phase transition is extended from the point of view of electronic polarization and electrical fluctuations. The charge fluctuations on finite fractal clusters are argued to be analogous to spontaneous order parameter fluctuations in phase transitions, being correlated upto percolation correlation length. The charge relaxation times are shown to be related to the cluster sizes having distribution function of the formg()^–b , whereb is connected to Euclidean and fractal dimensionalities and critical exponents. This produces the 1/f noise spectrum. Below percolation threshold, the nodes-links-blobs picture is invoked such that the blobs represent metallic conductances of the finite clusters and the links are tunnelling conductances between them through narrowest barrier regions. Above threshold, the finite cluster network is visualized as connected to the infinite cluster through narrowest tunnelling regions. The correlated spontaneous charge fluctuation on finite fractal clusters is held responsible for conductance fluctuation on either side of the metal-insulator transition via tunnelling processes. Finally, the scaling behaviour of noise magnitude near percolation threshold is explained.     

Kinetic Simulation of Fractal Aggregation on Liquid Surfaces

A modified fractal growth model based on the deposition, diffusion, and aggregation (DDA) with cluster rotation is presented to simulate two-dimensional fractal aggregation on liquid surfaces. The mobility (including diffusion and rotation) of clusters is related to its mass, which is given by D_m=D₀ s^-γ_D and θ_m=θ₀s^-γ_θ, respectively. We concentrate on revealing the details of the influence of deposition flux F, cluster diffusion factor γ_D and cluster rotation factor γ_θ on the dynamics of fractal aggregation on liquid surfaces. It is shown that the morphologies of clusters and values of cluster density and fractal dimension depend dramatically on the deposition flux and migration factors of clusters.     

a.c. susceptibility of a YBCO single crystal in an extended frequency range interpreted by numerical solution of the continuity equation for the magnetic field

Summary a.c. susceptibility measurements on a YBCO single crystal in an extended range of frequency and applied magnetic fields are presented. The dissipation phenomena shown by these measurements are interpreted inside the framework of the thermally activated flux motion theory developed for low-temperature superconductors in early '60. For this purpose the continuity equation for the magnetic field inside the sample is solved numerically, avoiding to usea priori the standard approximations of this theory: thermally activated flux creep and thermally assisted flux flow. The whole set of a.c. susceptibility measurements, performed in a wide range of the parameters, can be fitted with good agreement between the experimental and theoretical data. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

On the Fractal dimension and correlations in percolation theory

We discuss the fractal dimension of the infinite cluster at the percolation threshold. Using sealing theory and renormalization group we present an explicit expression for the two-point correlation function within percolation clusters. The fractal dimension is given by direct integration of this function.See especially Ref. 1 for a discussion of the general aspects of percolation.     

Nonlinear properties of multiphase high-temperature superconductors of the Bi–Sr–Ca–Cu–O system in the temperature range of the superconducting transition

The nonlinear characteristics of high-temperature superconductors of the Bi–Sr–Ca–Cu–O system have been experimentally investigated in the temperature range of the superconducting transition under the influence of a harmonic alternating magnetic field. The effect of the generation of odd harmonics in the signal of response to a harmonic alternating magnetic field for multiphase high-temperature superconductors containing regions with different values of the critical temperature in their bulk has been observed for the first time. The mechanism of harmonic generation in a superconductor in the resistive state, which is associated with the switch effect, i.e., with the redistribution of eddy current density between the local regions of the superconductor, has been considered.     

Thermal electrodynamic mechanisms of a rise of current-voltage characteristic (IVC) of technical superconductors at magnetic flux creep

The processes of the formation of the macroscopic states of a superconducting tape induced by the transport current at magnetic flux creep have been studied. It has been shown that there are characteristic values of electric field intensity that are affected by a rate of current injection, properties of a superconductor, cooling conditions, and properties of a stabilizing matrix. These values are the basis of thermal electrodynamic mechanism, which determines the slope of a rise of IVC of technical superconductors. The conditions of formation of current instabilities have been studied taking into account a nonuniform temperature distribution over the cross section of a technical superconductor. The conditions of the existence of the IVC of technical superconductors have been formulated. These conditions allow for the stable heating of a superconductor as high as the critical temperature. The results of the carried out studies should be taken into account when measuring the IVC of superconducting materials and determining their critical parameters and the current of instability occurrence.     

The influence of inhomogeneous properties of a system on the percolation process in two-dimensional space

The percolation process in a two-dimensional inhomogeneous lattice is studied by the Monte Carlo method. The inhomogeneous lattice is simulated by a random distribution of inhomogeneities differing in size and number. The influence of inhomogeneities on the parameters (critical concentration, average number of sites in finite clusters, percolation probability, critical exponents, and fractal dimension of an infinite cluster) characterizing the percolation in the system is analyzed. It is demonstrated that all these parameters essentially depend on the linear size of inhomogeneities and their relative area.     

Computer simulations of two-phase flow with surface tension in the percolation cluster

Percolation clusters with varying occupation probability were constructed. Viscous fingering (VF) in the percolation cluster, based on the assumption that throat radii are Rayleigh distributed, is investigated by means of a successive over-relaxation technique. The fractal dimension and the sweep efficiency of VF in the percolation cluster when surface tension is considered are larger than when surface tension is neglected. The fractal dimension of VF will increase as the percolation probability increases or the viscous ratio decreases. VF's fractal dimension of porous media in the limit viscous ratio → ∞ is found to be identical with the DLA. The topology and the geometry of the porous medium have a strong effect on the displacement processes and the structure of the VF.