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

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.

References in corpus (3)

• Magnetic shielding properties of high-temperature superconducting tubes subjected to axial fields
• "Unusual" critical states in type-II superconductors
• Bulk high-Tc superconductors with drilled holes: how to arrange the holes to maximize the trapped magnetic flux ?

Cited by in corpus (8)

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• Fast and efficient critical state modelling of field-cooled bulk high-temperature superconductors using a backward computation method
• 3D magnetization currents, magnetization loop, and saturation field in superconducting rectangular prisms
• Fully-staggered-array bulk Re-Ba-Cu-O short-period undulator: large-scale 3D electromagnetic modelling and design optimization using A-V and H-formulation methods
• Pulsed-field magnetization of drilled bulk high-temperature superconductors: flux front propagation in the volume and on the surface
• Modification of the trapped field in bulk high-temperature superconductors as a result of the drilling of a pattern of artificial columnar holes