Numerically implemented perturbation method for the nonlinear magnetic moment of an anisotropic superconductor

TL;DR

This paper introduces a numerical perturbation method to efficiently compute the magnetic moment of anisotropic superconductors by solving nonlinear Maxwell-London equations, reducing computational effort significantly.

Contribution

The paper presents a novel numerical perturbative approach for calculating magnetic moments in anisotropic superconductors, incorporating nonlinear current relations and boundary conditions.

Findings

Method reduces computational work compared to previous approaches.

Successfully applied to an oblate spheroid sample.

Provides a framework for similar problems in other fields.

Abstract

We present a method to compute the magnetic moment of a bulk, finite-size, three-dimensional, anisotropic superconductor. Our numerically implemented perturbative procedure is based on a solution of the nonlinear Maxwell- London equations, where we include the nonlinear relation between current and gauge invariant velocity. The method exploits the small ratio of penetration depth to sample size. We show how to treat the open boundary conditions over an infinite domain and the continuity requirement at the interface. We demonstrate how our method substantially reduces the computational work required and discuss its implementation to an oblate spheroid. The numerical solution is obtained from a finite difference method. We briefly discuss the relevance of this work to similar problems in other fields.