Homogenization of HTS coils with the h, h-phi, and t-omega foil conductor model
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917375854510080 |
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| author | Paakkunainen, Elias Denis, Louis Vanderheyden, Benoît Geuzaine, Christophe Rasilo, Paavo Schöps, Sebastian |
| author_facet | Paakkunainen, Elias Denis, Louis Vanderheyden, Benoît Geuzaine, Christophe Rasilo, Paavo Schöps, Sebastian |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_00154 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Homogenization of HTS coils with the h, h-phi, and t-omega foil conductor model Paakkunainen, Elias Denis, Louis Vanderheyden, Benoît Geuzaine, Christophe Rasilo, Paavo Schöps, Sebastian Computational Engineering, Finance, and Science 78M10, 35Q61 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. |
| title | Homogenization of HTS coils with the h, h-phi, and t-omega foil conductor model |
| topic | Computational Engineering, Finance, and Science 78M10, 35Q61 |
| url | https://arxiv.org/abs/2604.00154 |