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Publication# Computation of 2-D Current Distribution in Superconductors of Arbitrary Shapes Using a New Semi-Analytical Method

Abstract

This paper presents an original semi-analytical method (SAM) for computing the 2-D 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 (Jz), the vector potential (Az), and the magnetic flux density (Bx, By), for a linear variation of over 2-D triangular elements. The derivation of these new formulas, which is also presented in this paper, is based on the analytic solution of the 2-D 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.

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Related concepts (3)

Finite element method

The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).

Current density

In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point. In SI base units, the electric current density is measured in amperes per square metre. Assume that A (SI unit: m2) is a small surface centred at a given point M and orthogonal to the motion of the charges at M.

Magnetic field

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets.