Electric field formulation for thin film magnetization problems

TL;DR

This paper introduces a variational formulation for thin film magnetization in superconductors, enabling accurate numerical computation of electric fields and magnetization, especially near the critical state model.

Contribution

It develops a novel variational approach that allows precise numerical analysis of thin film superconductors across different current-voltage power laws.

Findings

Accurate computation of electric field and magnetization in thin films.

Effective approximation of the critical state model at high power values.

Numerical simulations for various film geometries and inhomogeneities.

Abstract

We derive a variational formulation for thin film magnetization problems in type-II superconductors written in terms of two variables, the electric field and the magnetization function. A numerical method, based on this formulation, makes it possible to accurately compute all variables of interest, including the electric field, for any value of the power in the power law current-voltage relation characterizing the superconducting material. For high power values we obtain a good approximation to the critical state model solution. Numerical simulation results are presented for simply and multiply connected films, and also for an inhomogeneous film.