Thin shell model of a coated conductor with a ferromagnetic substrate

TL;DR

This paper introduces a simplified integral model for coated conductors with magnetic substrates, enabling efficient simulation of their electromagnetic response and AC losses, using a thin shell approximation and spectral numerical methods.

Contribution

The paper develops a novel integral formulation and spectral numerical method for modeling coated conductors with magnetic substrates, simplifying previous complex models.

Findings

Model accurately predicts electromagnetic response and AC losses.

The model converges to known analytical solutions in limiting cases.

Efficient Chebyshev spectral method enhances computational performance.

Abstract

Coated conductors with magnetic substrates are thin multilayer structures; their high aspect ratio and nonlinear material properties present significant difficulties for numerical simulation. Using the high width-to-thickness ratio of coated conductors we derive an integral formulation for a model based on an infinitely thin approximation for the superconducting layer and a quasistatic thin shell approximation for the magnetic substrate. The proposed model describes electromagnetic response of a coated conductor with a magnetic substrate and is much simpler than the existing models. A single dimensionless parameter characterizes the substrate having a finite magnetic permeability and a finite thickness. An accurate and efficient Chebyshev spectral method is derived for numerical solution. The influence of a magnetic substrate on the superconducting current and AC losses is investigated. In the limiting cases our model solution tends to the known analytical solutions.