Modelling the penetration of magnetic flux in thin superconducting films with shell transformations

Abstract

Purpose Finite element (FE) models are considered for the penetration of magnetic flux in type-II superconductor films. A shell transformation allows boundary conditions to be applied at infinity with no truncation approximation. This paper aims to determine the accuracy and efficiency of shell transformation techniques in such non-linear eddy current problems. Design/methodology/approach A three-dimensional H – ϕ formulation is considered, where the reaction field is calculated in the presence of a uniform applied field. The shell transformation is used in the far-field region, and the uniform applied field is introduced through surface terms, so as to avoid infinite energy terms. The resulting field distributions are compared against known solutions for different geometries (thin disks and thin strips in the critical state, square thin films). The influence of the shape, size and mesh quality of the far-field regions are discussed. Findings The formulation is shown to provide accurate results for a number of film geometries and shell transformation shapes. The size of the far-field region has to be chosen in such a way to properly capture the asymptotic decay of the fields, and a practical procedure to determine this size is provided. Originality/value The importance of the size of the far-field region in a shell transformation and its proximity to the conducting domains are both highlighted. This paper also provides a numerical way to apply a constant magnetic field in a given region, while the source, on which only the far-field behaviour of the applied field depends, is excluded from the model.