Spectral solution of axisymmetric magnetization problems for thin superconducting shells

TL;DR

This paper presents a spectral numerical method for axisymmetric magnetization problems in thin superconducting shells, offering high accuracy and serving as benchmarks for more general cases.

Contribution

It introduces a novel spectral approach using Chebyshev polynomials and the method of lines for axisymmetric thin-shell superconducting magnetization modeling.

Findings

The method achieves high accuracy in axisymmetric magnetization simulations.

It can handle both open and closed shells, including complex geometries like spheres.

Solutions can serve as benchmarks for non-axisymmetric problems.

Abstract

Existing numerical methods for modeling magnetization in thin type-II superconducting films have mostly been developed for flat films. This work introduces an efficient spectral method for axisymmetric magnetization problems involving non-flat films. The method is based on the integral thin-shell current-density formulation of the problem, employs Chebyshev polynomial expansions for spatial discretization, and uses the method of lines for time integration. It applies to both open and closed axisymmetric shells and is so accurate that the solutions obtained can serve as benchmarks for numerical methods for general, not necessarily axisymmetric, thin-shell magnetization problems. As one of the examples, we consider magnetic shielding by a superconducting sphere.