arXiv subjects

Benoît Vanderheyden

Publications and source records attributed to Benoît Vanderheyden.

12 recordsLinked to original sources

arXiv2026

Homogenization of HTS coils with the h, h-phi, and t-omega foil conductor model

Efficient numerical models are required for the design of systems with high temperature superconductor (HTS) coils, as fully resolved finite element simulations of individual coated conductors become computationally prohibitive. This work applies the foil conductor model (FCM) to insulated HTS coils using magnetic field conforming h-(full), h-$ϕ$, and t-$ω$ formulations. The approach replaces individual turns by a homogenized bulk and ensures physically consistent current density distributions in the coils by using additional voltage basis functions in the finite element formulations. The models are verified in 2D axisymmetric and 3D geometries with a pancake coil simulation under AC transport current excitation. All FCM formulations show excellent agreement with reference detailed simulations, with coefficients of determination above 0.99 for instantaneous AC losses. In 3D, the h-$ϕ$ and especially the t-$ω$ formulation substantially reduce the number of degrees of freedom by using the magnetic scalar potential in non-conducting regions. Scalability is demonstrated with a 3D stack of racetrack coils model with a field- and angle-dependent critical current density. For the stack of racetrack coils, while maintaining accurate loss prediction, the t-$ω$ FCM achieves a speedup factor of 22 and reduces degrees of freedom by 78 % with respect to a detailed reference model.

cs.CE↗

arXiv2026

Current patterns and loss contributions in CORT cables carrying AC current

Conductor-on-round-tube (CORT) cables are a potential solution for carrying AC power in a small cross-section. Due to the geometry of the cable and the helical arrangement of the coated conductors (CC), the current follows a non-trivial pattern inside each CC. For instance, for the case of a single-layer cable, the current flow is mostly axial along the outer face of the CCs and mostly azimuthal along their inner face. Such a current distribution, known as the Garber current pattern, affects the transport AC losses. In numerical models, commonly adopted simplifications are either based on straight conductors or infinitely thin CCs. Such approaches neglect the Garber current pattern and thus misrepresent both the detailed current flow within the CC and the resulting 3D distribution of the fields. In this work, the detailed 3D current distribution in the CCs is investigated in a one-layer CORT cable, as a function of the cable geometrical parameters such as the conductor thickness, the pitch angle, and the gap between adjacent CCs. In particular, the impact of the Garber current pattern is studied on the two largest contributions to the AC losses, namely the surface losses (associated with the penetration of the component of the magnetic field parallel to the wide faces of the superconducting layer) and the edge losses (associated with the penetration of the perpendicular component of the magnetic field occurring in the vicinity of the gaps between the CCs). The detailed distribution of the currents in the CCs is examined and its relationship with the different AC loss mechanisms is established. This study is carried out by means of an effective 2D model that uses a system of coordinates conforming with the helical structure of the cable.

cond-mat.supr-con↗

arXiv2026

Explicit Turn Resolution with Anisotropic Homogenisation for Efficient 3D Magneto-Thermal Finite-Element Simulation of Large-Scale No-Insulation HTS Magnets

No-insulation (NI) and metal-insulation (MI) high-temperature superconducting (HTS) magnets require three-dimensional (3D) models to describe the current distribution around critical current defects. In this work, we design and validate the EXTRA homogenisation method, standing for explicit turn resolution with anisotropic homogenisation method. It allows 3D magneto-thermal finite-element (FE) simulations of large-scale magnets to be performed with high accuracy at a reasonable computational cost. The method combines the anisotropic homogenisation of turn-to-turn contact layers (T2TCLs) and their neighbouring winding turns with the explicit resolution of specific T2TCLs. In particular, the inner- and outermost winding turns and adjacent contact layers are explicitly resolved to properly describe the current distribution near current leads. In addition, the method is able to simulate local $J_{\textrm{c}}$ defects for a broad range of turn-to-turn contact resistances, provided the winding turns and T2TCLs next to the defect are explicitly resolved. For efficiency, the resolved T2TCLs are modelled using the surface contact approximation. The consistency of the proposed method is first verified on a 50-turn single pancake benchmark. It is shown to reproduce AC losses and temperature distributions obtained with a turn-resolved FE reference model, for both nominal operation and during thermal runaway. The computational efficiency of the EXTRA method is demonstrated with the simulation of a stack of three 150-turn pancake coils, for which computation time is reduced by a factor of up to 13 with respect to a turn-resolved FE reference model. Finally, the results of a large-scale 3D FE simulation, currently out of reach of turn-resolved models, are provided for an insert HTS magnet with 10,000 turns. The EXTRA method is open-source and input files to reproduce all results are made available.

physics.acc-ph↗

arXiv2025

Simultaneous Multi-Scale Homogeneous H-Phi Thin-Shell Model for Efficient Simulations of Stacked HTS Coils

The simulation of large-scale high-temperature superconducting (HTS) magnets is a computational challenge due to the multiple spatial scales involved, from the magnet to the detailed turn-to-turn geometry. To reduce the computational cost associated with finite-element (FE) simulations of insulated HTS coils, the simultaneous multi-scale homogeneous (SMSH) method can be considered. It combines a macroscopic-scale homogenized magnet model with multiple single-tape models and solves both scales monolithically. In this work, the SMSH method is reformulated using the $h$-$ϕ$ thin-shell (TS) approximation, where analyzed tapes are collapsed into thin surfaces, simplifying mesh generation. Moreover, the magnetic field is expressed as the gradient of the magnetic scalar potential outside the analyzed tapes. The discretized field is then described with nodal functions, further reducing the size of the FE problem compared to standard $h$ formulations. The proposed $h$-$ϕ$ SMSH-TS method is verified against state-of-the-art homogenization methods on a 2-D benchmark problem of stacks of HTS tapes. The results show good agreement in terms of AC losses, turn voltage and local current density, with a significant reduction in simulation time compared to reference models. All models are open-source.

physics.acc-ph↗

arXiv2025

Acceleration of Multi-Scale LTS Magnet Simulations with Neural Network Surrogate Models

While the prediction of AC losses during transients is critical for designing large-scale low-temperature superconducting (LTS) magnets, brute-force finite-element (FE) simulation of their detailed geometry down to the length scale of the conductors is a computational challenge. Multi-scale methods, balancing between a coarse approximation of the fields at the scale of the magnet and a detailed description at the scale of the conductors, are promising approaches to reduce the computational load while keeping a sufficient accuracy. In this work, we introduce a neural network approach to accelerate multi-scale magneto-thermal simulations of LTS magnets by replacing costly single-turn FE models with neural network surrogates. The neural network architecture is presented and discussed, together with an automated procedure for generating simulation data for its training. The resulting accelerated multi-scale model is used to simulate current ramp-up procedures for the IBA S2C2 magnet. The surrogate-based multi-scale model is compared with a conventional multi-scale model based on a composite wire-in-channel FE model. The surrogate model is shown to reproduce single-turn filament hysteresis, inter-filament coupling, and eddy losses, while the computational time of the multi-scale method is reduced by a factor of 800.

physics.acc-ph↗

arXiv2025

Impact of border defects on the magnetic flux penetration in superconducting films

Defects in superconducting systems are ubiquitous and nearly unavoidable. They can vary in nature, geometry, and size, ranging from microscopic-size defects such as dislocations, grain boundaries, twin planes, and oxygen vacancies, to macroscopic-size defects such as segregations, indentations, contamination, cracks, or voids. Irrespective of their type, defects perturb the otherwise laminar flow of electric current, forcing it to deviate from its path. In the best-case scenario, the associated perturbation can be damped within a distance of the order of the size of the defect if the rigidity of the superconducting state, characterized by the creep exponent $n$, is low. In most cases, however, this perturbation spans macroscopic distances covering the entire superconducting sample and thus dramatically influences the response of the system. In this work, we review the current state of theoretical understanding and experimental evidence on the modification of magnetic flux patterns in superconductors by border defects, including the influence of their geometry, temperature, and applied magnetic field. We scrutinize and contrast the picture emerging from a continuous media standpoint, i.e. ignoring the granularity imposed by the vortex quantization, with that provided by a phenomenological approach dictated by the vortex dynamics. In addition, we discuss the influence of border indentations on the nucleation of thermomagnetic instabilities. Assessing the impact of surface and border defects is of utmost importance for all superconducting technologies, including superconducting resonators, superconducting single-photon detectors, superconducting radio-frequency cavities and accelerators, superconducting cables, superconducting metamaterials, superconducting diodes, and many others.

cond-mat.supr-con↗

arXiv2025

Magnetic Field Conforming Formulations for Foil Windings

We extend the foil winding homogenization method to magnetic field conforming formulations. We first propose a full magnetic field foil winding formulation by analogy with magnetic flux density conforming formulations. We then introduce the magnetic scalar potential in non-conducting regions to improve the efficiency of the model. This leads to a significant reduction in the number of degrees of freedom, particularly in 3-D applications. The proposed models are verified on two frequency-domain benchmark problems: a 2-D axisymmetric problem and a 3-D problem. They reproduce results obtained with magnetic flux density conforming formulations and with resolved conductor models that explicitly discretize all turns. Moreover, the models are applied in the transient simulation of a high-temperature superconducting coil. In all investigated configurations, the proposed models provide reliable results while considerably reducing the size of the numerical problem to be solved.

cs.CE↗

arXiv2024

AC Loss Computation in Large-Scale Low-Temperature Superconducting Magnets: Multi-Scale and Semi-Analytical Procedures

In this paper, we introduce two complementary approaches for the accurate prediction of AC losses in large-scale low-temperature superconducting (LTS) magnets. These methods account for the temperature rise within the LTS coil and its impact on AC losses. The first approach is multi-scale and relies on the coupling between a macroscopic homogenized model of the LTS coil and a mesoscopic model of a single conductor for loss prediction. The second approach is semi-analytical and is based on analytical approximations for the hysteresis losses, which are validated against a single filament model. The second approach offers a faster computation suitable for initial design considerations, while the multi-scale method is shown to provide more accurate results. We apply both methods to the prediction of AC losses generated in the LTS coil inside the IBA S2C2 synchrocyclotron during its ramp-up procedure. Additionally, we discuss the convergence properties of the multi-scale approach and demonstrate the good agreement between the numerical results and experimental data.

physics.acc-ph↗

arXiv2024

Helicoidal Transformation Method for Finite Element Models of Twisted Superconductors

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 h-phi-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 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.

physics.acc-ph↗

arXiv2023

Magneto-Thermal Thin Shell Approximation for 3D Finite Element Analysis of No-Insulation Coils

For finite element (FE) analysis of no-insulation (NI) high-temperature superconducting (HTS) pancake coils, the high aspect ratio of the turn-to-turn contact layer (T2TCL) leads to meshing difficulties which result in either poor quality mesh elements resulting in a decrease of the solution accuracy or a high number of degrees of freedom. We proposed to mitigate this issue by collapsing the T2TCL volume into a surface and using a so-called thin shell approximation (TSA). Previously, two TSA have been introduced, one to solve the heat equation and the other for an $\vec{H}-ϕ$ magnetodynamic formulation. In this work, we propose to combine the magnetodynamic and thermal TSA to create a coupled magneto-thermal TSA for three-dimensional FE analysis. Particular attention is paid to the detailed derivation of the coupling terms. In the context of NI HTS pancake coils, the TSA represents the electric and thermal contact resistance of the T2TCL. For the HTS coated conductor (CC) itself, an anisotropic homogenization is used which represents its multi-layered structure. In axial and azimuthal direction, it resolves the current sharing between the HTS and other layers of the CC. The coupled TSA formulation is verified against a reference model with volumetric T2TCL. The coupled TSA is shown to significantly reduce the solution time as well as the manual effort required for high-quality meshes of the T2TCL. The implementation is open-source and a reference implementation is made publicly available.

physics.acc-ph↗

arXiv2023

Finite Element Models for Magnetic Shields Made of Stacked Superconducting Tape Annuli

Stacks of high-temperature superconducting tape annuli can be used as magnetic shields operating efficiently for both axial and transverse fields. However, due to their layered geometry and hybrid electrical and magnetic properties, implementing models of such structures is not straightforward. In this work, we propose two different modelling approaches with the finite element method: layered and homogenized. We compare their accuracy and numerical efficiency for three different formulations (h-phi, h-phi-b, and a-j), in both axial (2D-axisymmetric) and transverse (3D) configurations. We show that both approaches lead to comparable performance in the axial case, but that the homogenized model is considerably harder to use in the transverse case.

physics.acc-ph↗

arXiv2022

What Formulation Should One Choose for Modeling a 3D HTS Motor Pole with Ferromagnetic Materials?

We discuss the relevance of several finite-element formulations for nonlinear systems containing high-temperature superconductors (HTS) and ferromagnetic materials (FM), in the context of a 3D motor pole model. The formulations are evaluated in terms of their numerical robustness and efficiency. We propose a coupled h-phi-a-formulation as an optimal choice, modeling the problem with an a-formulation in the FM and an h-phi-formulation in the remaining domains. While maintaining a low number of degrees of freedom, the h-phi-a-formulation guarantees a robust resolution and strongly reduces the number of iterations required for handling the nonlinearities of HTS and FM compared to standard formulations.

physics.acc-ph↗