Current Distribution In Superconductor Research Articles

Finite Element Simulation of Temperature and Current Distribution in a Superconductor, and a Cell Model for Flux Flow Resistivity—Interim Results

A critical problem arises when current distribution in a high-temperature superconductor and its stability against quench shall be predicted: is it correct to assume homogeneous temperature distribution in superconductors, in general or only in LHe-cooled devices? The finite element analysis presented in this paper shows that during the very first instants following a disturbance, like single Dirac or periodic heat pulses, or large fault currents, temperature distribution in a BSCCO 2223 conductor is highly inhomogeneous. This is because disturbances, of transient or continuous, isolated or extended types in conductor volumes, create hot spots of comparatively long life cycle. As a consequence, separation between Ohmic and flux flow current limiter types, or decisions on the mechanism that initialises current sharing, cannot be made definitely. A semi-empirical cell model is presented in this paper to estimate flux flow resistivity in multi-filamentary superconductors in a successive approximation approach. Weak links are modelled, as nano- and microscopic surface irregularities and corresponding resistances, in analogy to thermal transport. Though the model requests input of a large amount of data (dimensions, porosities, field-dependent quantities) that still have to be verified experimentally, it is by its flexibility superior to ideas relying on, for example, imagination of separate, non-interacting chains of strong and weak links switched in parallel. In particular, and in contrast to the standard expression to calculate flux flow resistivity, the cell model suggests to replace solid conduction by an effective resistivity, a method that is more appropriate for multi-filamentary conductors. The paper also discusses integration time steps in numerical simulations that have to be selected in conformity with several characteristic times of current and thermal transport.

Sheet current model for inductances extraction and Josephson junctions devices simulation

Sheet current model for microelectronic superconductor structures, based on Maxwell and London equations, is presented. In this model, magnetic field is three-dimensional but resulting integro-differential equations for current density potential are two-dimensional. These equations are solved using finite element method and matrix of self and mutual inductances is calculated as well as current distribution in superconductors. Then, current distribution can be used for calculation of boundary conditions for Josephson junctions equations. In particular we apply this approach for calculations of bias and control line currents for flux flow oscillator simulation problem. The program and results of calculations are presented.

Computation of 2-D current distribution in superconductors of arbitrary shapes using a new semi-analytical method

This paper presents an original semi-analytical method (SAM) for computing the 2D current distribution in conductors and superconductors of arbitrary shape, discretized in triangular elements. The method is a generalization of the one introduced by Brandt in 1996, and relies on new and compact analytical relationships between the current density (J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> ), the vector potential (A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> ), and the magnetic flux density (B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> ,By), for a linear variation of J over 2D triangular elements. The derivation of these new formulas, which is also presented in this paper, is based on the analytic solution of the 2D potential integral. The results obtained with the SAM were validated successfully using COMSOL Multiphysics, a commercial package based on the finite-element method. Very good agreement was found between the two methods. The new formulas are also expected to be of great interest in the resolution of inverse problems.

Anomalous statistical properties of the critical current distribution in superconductor containing fractal clusters of a normal phase

Statistical properties of the critical current distribution in superconductor with fractal clusters of a normal phase are considered. It is found that there is the range of fractal dimensions in which the variance and expectation for this distribution increases infinitely. Simple technique of avoiding such a divergence by the use of truncated distributions is proposed. It is suggested that the most current-carrying capability of a superconductor can be achieved by modifying the cluster area distribution in such a way that the regime of giant variance of critical currents will be realized.

Mode of magnetic flux penetration into high Tc superconductors with various cross-sectional shape and their AC loss characteristics

The current distribution in superconductors with various cross-sectional shapes is calculated numerically by the finite element method. The total loss in flat tapes carrying their transport current in the perpendicular magnetic field is increased by the interaction between the self and the perpendicular magnetic field. Though BSCCO round wires are often preferred to flat tapes, numerical results suggest that they are not always advantageous from the viewpoint of AC loss reduction. In YBCO coated conductors, the transport loss decreases with increasing aspect ratio of their cross-section. But, it remains much larger than the Norris's value for strip in small current region because of the finite aspect ratio of the region where magnetic flux penetrates. Importance of the critical current density near the tape edge is pointed out, because most of the loss is generated near the tape edge where the current density is large.

Analysis of current distribution in a large superconductor

An imbalanced current distribution which is often observed in cable-in-conduit (CIC) superconductors composed of multistaged, triplet type sub-cables, can deteriorate the performance of the coils. It is, hence very important to analyze the current distribution in a superconductor and find out methods to realize a homogeneous current distribution in the conductor. We apply magnetic flux conservation in a loop contoured by electric center lines of filaments in two arbitrary strands located on adjacent layers in a coaxial multilayer superconductor, and thereby analyze the current distribution in the conductor. A generalized formula governing the current distribution can be described as explicit functions of the superconductor construction parameters, such as twist pitch, twist direction and radius of individual layer. We numerically analyze a homogeneous current distribution as a function of the twist pitches of layers, using the fundamental formula. Moreover, it is demonstrated that we can control current distribution in the coaxial superconductor.

超伝導導体内の電流分布解析

An imbalanced current distribution which is often observed in cable-in-conduit (CIC) superconductors composed of multistaged, triplet type sub-cables, can deteriorate the performance of the coils. It is, hence very important to analyze the current distribution in a superconductor and find out methods to realize a homogeneous current distribution in the conductor. We apply magnetic flux conservation in a loop contoured by electric center lines of filaments in two arbitrary strands located on adjacent layers in a coaxial multilayer superconductor, and thereby analyze the current distribution in the conductor. A generalized formula governing the current distribution can be described as explicit functions of the superconductor construction parameters, such as twist pitch, twist direction and radius of individual layer. We numerically analyze a homogeneous current distribution as a function of the twist pitches of layers, using the fundamental formula. Moreover, it is demonstrated that we can control current distribution in the coaxial superconductor.