Computer modelling of type II superconductors in applications

Abstract

A numerical method for solving for the current and field distributions inside devices containing type II superconductors is described. The two-dimensional solution technique accommodates the effects of surrounding media including iron and can handle systems with an arbitrary number of type II superconductors and conventional materials. The technique is based on the finite element method, the method of moments and the critical state model. The impetus behind this work is the study of rotating electrical machines which contain superconducting artefacts placed alongside magnetic materials and current sources. In this paper, a reluctance machine consisting of an iron rotor flanked with two HTS pieces is chosen to demonstrate the method.

A finite-element analysis of critical-state models for type-II superconductivity in 3D

“…The same authors also presented a finite element analysis of the current densityelectric field variational formulation (see Elliott et al (2005)). Also see Barnes et al (1999) for engineering application of the Bean model to modelling electrical machine containing superconductors. In all these articles the problems are considered in 2D.…”

A Hierarchy of Models for Type-II Superconductors

“…The colour indicates the current density (blue coming out of the paper, red moving into the paper), while the contour lines indicate the direction of the magnetic field. (Numerical solution due to G. Barnes [6,5].) An example of the numerical solution of the two-dimensional Bean critical-state model (equations (205)-(206) coupled with Maxwell's equations) describing the magnetic field and electric current in a cross-section of the superconducting cylinder (assuming the cylinder has a large aspect ratio) is shown in Figure 1b [5].…”

“…(Numerical solution due to G. Barnes [6,5].) An example of the numerical solution of the two-dimensional Bean critical-state model (equations (205)-(206) coupled with Maxwell's equations) describing the magnetic field and electric current in a cross-section of the superconducting cylinder (assuming the cylinder has a large aspect ratio) is shown in Figure 1b [5]. This can be used to determine the torque on the superconducting rotor, and hence the power of the motor [6,5].…”

A macroscopic model for an intermediate state between type-I and type-II superconductivity

“…The model imposes that a current either flows at the critical level J c or does not flow at all. Many authors have studied this model [14][15][16][17][18][19]. Unfortunately, Bean's critical-state model is not fully applicable to superconductors with smooth current-voltage characteristics.…”