Numerical simulation of the magnetization of high-temperature superconductors: 3D finite element method using a single time-step iteration

TL;DR

This paper presents a 3D finite element method for simulating high-temperature superconductor magnetization, using a single time-step approach that reduces computation time while maintaining high accuracy.

Contribution

The paper introduces a novel single time-step finite element approach for HTS magnetization simulation, incorporating demagnetisation effects and flux creep, validated against established methods.

Findings

Single time-step calculations achieve high accuracy.

Method significantly reduces simulation time.

Validated with HTS tube and cylinder models.

Abstract

We make progress towards a 3D finite-element model for the magnetization of a high temperature superconductor (HTS): We suggest a method that takes into account demagnetisation effects and flux creep, while it neglects the effects associated with currents that are not perpendicular to the local magnetic induction. We consider samples that are subjected to a uniform magnetic field varying linearly with time. Their magnetization is calculated by means of a weak formulation in the magnetostatic approximation of the Maxwell equations (A-phi formulation). An implicit method is used for the temporal resolution (Backward Euler scheme) and is solved in the open source solver GetDP. Picard iterations are used to deal with the power law conductivity of HTS. The finite element formulation is validated for an HTS tube with large pinning strength through the comparison with results obtained with other well-established methods. We show that carrying the calculations with a single time-step (as opposed to many small time-steps) produce results with excellent accuracy in a drastically reduced simulation time. The numerical method is extended to the study of the trapped magnetization of cylinders that are drilled with different arrays of columnar holes arranged parallel to the cylinder axis.