Helicoidal Transformation Method for Finite Element Models of Twisted Superconductors

Computational modeling; Geometry; Magnetic fields; Superconducting magnets; Superconductivity; Three-dimensional displays; Wires; Cartesian coordinate system; Computational modelling; External fields; External magnetic field; Finite element modelling (FEM); Helicoidal structure; Magnetic-field; Three-dimensional display; Transformation methods; Transport currents; Electronic, Optical and Magnetic Materials; Condensed Matter Physics; Electrical and Electronic Engineering

Abstract :

[en] This paper deals with the modelling of superconducting and resistive wires with a helicoidal symmetry, subjected to an external field and a transport current. Helicoidal structures are three-dimensional, and therefore yield computationally intensive simulations in a Cartesian coordinate system. We show in this paper that by working instead with a helicoidal system of coordinates, the problem to solve can be made two-dimensional, drastically reducing the computational cost. We first introduce the state-of-the-art approach and apply it on the <inline-formula><tex-math notation="LaTeX">$h$</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">$\phi$</tex-math></inline-formula>-formulation with helicoidally symmetric boundary conditions (e.g., axial external magnetic field, with or without transport current), with an emphasis on the function space discretization. Then, we extend the approach to general boundary conditions (e.g., transverse external magnetic field) and we present numerical results with linear materials. In particular, we discuss the frequency-dependent losses in composite wires made of superconducting filaments embedded in a resistive matrix. Finally, we provide outlook to the application of the generalized model with nonlinear materials.

Disciplines :

Electrical & electronics engineering
Energy
Materials science & engineering

Author, co-author :

Dular, Julien ; Université de Liège - ULiège > Montefiore Institute of Electrical Engineering and Computer Science

Henrotte, François ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Applied and Computational Electromagnetics (ACE)

Nicolet, Andre ; AMU - Aix-Marseille University [FR]

Wozniak, Mariusz ; CERN - Centre Européen de Recherche Nucléaire [CH]

Vanderheyden, Benoît ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Electronique et microsystèmes

Geuzaine, Christophe ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Applied and Computational Electromagnetics (ACE)

Language :

English

Title :

Helicoidal Transformation Method for Finite Element Models of Twisted Superconductors

Publication date :

2024

Journal title :

IEEE Transactions on Applied Superconductivity

ISSN :

1051-8223

Publisher :

Institute of Electrical and Electronics Engineers Inc.

Volume :

Issue :

Pages :

1-15

Peer reviewed :

Peer Reviewed verified by ORBi

Tags :

CÉCI : Consortium des Équipements de Calcul Intensif

Additional URL :

http://xplorestaging.ieee.org/ielx8/77/10586813/10564211.pdf?arnumber=10564211

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique

Available on ORBi :

since 30 July 2024

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