Computation of the Nonlinear Magnetic Response of a Three Dimensional Anisotropic Superconductor

TL;DR

This paper introduces a perturbation method leveraging the small skin depth relative to sample size to efficiently compute the nonlinear magnetic response of anisotropic 3D superconductors, reducing computational effort.

Contribution

A novel perturbation approach that exploits small skin depth to simplify the calculation of magnetic moments in anisotropic superconductors.

Findings

Method reduces computational complexity.

Applicable to various numerical algorithms.

Effective for anisotropic, unconventional superconductors.

Abstract

Many problems in computational magnetics involve computation of fields which decay within a skin depth $\delta$, much smaller than the sample size $d$. We discuss here a novel perturbation method which exploits the smallness of $\epsilon \equiv \delta / d$ and the asymptotic behavior of the solution in the exterior and interior of a sample. To illustrate this procedure we consider the computation of the magnetic dipole and quadrupole moments of an anisotropic, unconventional, three dimensional superconductor. The method significantly reduces the required numerical work and can be implemented in different numerical algorithms.