Spectral solution of axisymmetric magnetization problems for thin superconducting shells

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.