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arxiv: 2605.31009 · v1 · pith:PUTPQ5RHnew · submitted 2026-05-29 · ⚛️ physics.acc-ph · cond-mat.mtrl-sci· cond-mat.supr-con· cs.CE· physics.comp-ph

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

Louis Denis , Erik Schnaubelt , Julien Dular , Mariusz Wozniak , Beno\^it Vanderheyden , Christophe Geuzaine This is my paper

Pith reviewed 2026-06-28 20:16 UTC · model grok-4.3

classification ⚛️ physics.acc-ph cond-mat.mtrl-scicond-mat.supr-concs.CEphysics.comp-ph
keywords no-insulation HTS magnetsanisotropic homogenizationfinite-element simulationmagneto-thermal modelingcurrent distributionthermal runawaypancake coilshigh-temperature superconductors
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The pith

The EXTRA method mixes explicit turns near leads and defects with anisotropic homogenization to enable accurate 3D magneto-thermal simulations of large no-insulation HTS magnets.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents the EXTRA homogenisation method for three-dimensional modeling of no-insulation high-temperature superconducting magnets. It resolves only the inner- and outermost winding turns and those next to defects explicitly while applying anisotropic homogenization to the remaining turns and turn-to-turn contact layers. This hybrid approach matches the current distributions and temperature profiles of fully resolved reference models in both nominal operation and thermal runaway. Benchmarks confirm consistency on a 50-turn pancake, while a three-pancake stack runs up to 13 times faster and a 10,000-turn insert becomes feasible.

Core claim

The EXTRA method enables 3D magneto-thermal finite-element simulations of large-scale no-insulation HTS magnets by explicitly resolving the inner- and outermost winding turns and adjacent contact layers, along with those next to defects, while applying anisotropic homogenization to all other turns and turn-to-turn contact layers. Resolved contact layers use the surface contact approximation. On a 50-turn single pancake the method reproduces AC losses and temperature distributions from a turn-resolved reference model. For a stack of three 150-turn pancakes computation time falls by a factor of up to 13. Results are shown for an insert magnet containing 10,000 turns.

What carries the argument

The EXTRA method, which selectively resolves specific turn-to-turn contact layers explicitly while applying anisotropic homogenization to the bulk of the winding and layers.

If this is right

  • Current distribution near current leads is captured accurately enough for defect studies in large magnets.
  • Thermal runaway behavior can be modeled in 3D for stacks of pancake coils at practical cost.
  • Magnets with 10,000 turns become accessible to full 3D magneto-thermal analysis.
  • Computation time reductions of roughly an order of magnitude are achieved relative to fully resolved models.
  • The surface contact approximation for resolved layers preserves accuracy while lowering mesh size.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The selective explicit resolution pattern may extend to other layered conductors where only boundary or defect regions dominate the global response.
  • The same homogenization-plus-explicit strategy could be tested on metal-insulation windings that exhibit comparable contact resistance ranges.
  • Coupling the method to time-stepping optimization routines might allow rapid evaluation of defect placement during magnet design.
  • Open availability of the input files suggests the approach can serve as a baseline for comparing alternative homogenization schemes.

Load-bearing premise

That explicitly resolving only the inner- and outermost turns and those next to defects is enough to capture the essential current distribution near leads and defects while the anisotropic homogenization of the rest remains accurate.

What would settle it

A direct comparison on a 150-turn pancake stack in which a fully turn-resolved 3D model produces current paths or local temperature rise near a defect that differ markedly from the EXTRA predictions.

Figures

Figures reproduced from arXiv: 2605.31009 by Beno\^it Vanderheyden, Christophe Geuzaine, Erik Schnaubelt, Julien Dular, Louis Denis, Mariusz Wozniak.

Figure 1
Figure 1. Figure 1: Reference model visualised on a conceptual pancake coil geometry. Top view (left) and coil cross [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Principle of the proposed EXTRA homogenisation method on a conceptual HTS magnet cross [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Homogenisation of the radial electric resistivity of the T2TCLs illustrated with the EXTRA [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Visualisation of the normal vector ⃗n on the reference (left) and EXTRA homogenised (right) meshes. The normal vector is defined as a piecewise constant vector along the discretised winding mesh, and it does not vary along the z-direction. The reference mesh is shown with dashed lines next to the homogenised mesh with solid lines. The transition layer between neighbouring effective turns of different thick… view at source ↗
Figure 5
Figure 5. Figure 5: Source current Isrc during the sudden discharge test and central axial magnetic flux density Bz computed with the reference and EXTRA homogenised (N e t = 50 and N e t = 10) models, with Rcl,t = 10−6 Ω m2 . The right figure focuses on the quasi-exponential decay during the discharge. Both figures share the same legend. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Evolution of total AC losses (sum of winding [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Conceptual visualisation, as a top view, of the current entering the pancake coil in the reference [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Turn-to-turn current distribution (integrated per turn) as a function of winding turn index (left) [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Maximal temperature rise, total AC loss, central axial flux density and total voltage evolution, for [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Location of studied Jc defects (left) in the 50-turn pancake coil, with defects A and B respectively between turn coordinates 24.8 and 25.2, and turn coordinates 46.4 and 46.6. Two different defects (A in the center of the coil, B near its edge) are simulated to verify the generality of the proposed approach. Conceptual visualisation, as a top view, of the current bypassing the Jc defect (right) in a stea… view at source ↗
Figure 11
Figure 11. Figure 11: Evolution of maximal temperature rise (left) and total AC losses (right) during ramp-up computed [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Turn-to-turn current distribution (integrated per turn) as a function of winding turn index (left) [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Evolution of maximal temperature rise (left) and total AC losses (right) during ramp-up computed [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Maximal temperature rise evolution (left) during the slow-ramping runaway experiment for the [PITH_FULL_IMAGE:figures/full_fig_p017_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Maximal temperature rise (left) and total AC losses (right) during operation of the magnet, with [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Maximal temperature rise (left) and total AC losses (right) during operation of the magnet, [PITH_FULL_IMAGE:figures/full_fig_p020_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Clipped view of the FE mesh of the EXTRA homogenised model with [PITH_FULL_IMAGE:figures/full_fig_p021_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Maximal temperature (top left), AC losses (top right), central field (bottom left) and voltage [PITH_FULL_IMAGE:figures/full_fig_p023_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Clipped views of the total magnetic flux density (sum of 15T background field and self-field) [PITH_FULL_IMAGE:figures/full_fig_p023_19.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper introduces the EXTRA method, which combines anisotropic homogenization of interior turn-to-turn contact layers (T2TCLs) and winding turns with explicit resolution of inner/outermost turns, adjacent layers, and defect-adjacent regions (using surface-contact approximation for resolved T2TCLs). It claims this enables accurate 3D magneto-thermal FE simulations of large NI HTS magnets at reduced cost. Validation on a 50-turn pancake reproduces AC losses and temperature distributions from a turn-resolved reference for nominal operation and thermal runaway. Efficiency is shown on a 450-turn stack (up to 13x speedup), with a demonstration on a 10,000-turn insert magnet.

Significance. If the accuracy of the homogenization holds when scaling beyond the validated regime, the method would enable 3D simulations of defect behavior and thermal runaway in magnets with thousands of turns that are currently intractable with turn-resolved models. The open-source release and provision of input files for all results are positive for reproducibility.

major comments (2)
  1. [large-scale demonstration / 10,000-turn insert magnet] The central accuracy claim for the 10,000-turn demonstration rests on unverified extrapolation: the 50-turn benchmark provides a reference solution, but the 10k-turn case has none, so any growth of homogenization error with stack height, coupling to thermal runaway, or effects on lead-current paths cannot be quantified (see abstract description of the large-scale simulation).
  2. [method description / resolved T2TCLs] The surface-contact approximation for explicitly resolved T2TCLs is presented as an efficiency choice, but its modeling error is only assessed within the 50-turn benchmark; no separate convergence or sensitivity test is reported for the 450-turn or 10k-turn cases where it could affect overall current distribution.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive review and detailed comments. We address each major comment point by point below, with proposed revisions where the manuscript can be strengthened.

read point-by-point responses

  1. Referee: [large-scale demonstration / 10,000-turn insert magnet] The central accuracy claim for the 10,000-turn demonstration rests on unverified extrapolation: the 50-turn benchmark provides a reference solution, but the 10k-turn case has none, so any growth of homogenization error with stack height, coupling to thermal runaway, or effects on lead-current paths cannot be quantified (see abstract description of the large-scale simulation).

    Authors: We agree that no turn-resolved reference exists for the 10,000-turn case, as such a simulation remains computationally intractable. The EXTRA method explicitly resolves all regions governing lead currents and defect bypass (inner/outermost turns, adjacent T2TCLs, and defect neighborhoods), while homogenization is restricted to interior volumes whose local error was bounded in the 50-turn benchmark. The 450-turn stack provides an intermediate check that global quantities remain consistent. We will revise the abstract and conclusion to state that the 10,000-turn result demonstrates computational reach and qualitative behavior rather than claiming quantified accuracy beyond the validated regime. revision: yes

  2. Referee: [method description / resolved T2TCLs] The surface-contact approximation for explicitly resolved T2TCLs is presented as an efficiency choice, but its modeling error is only assessed within the 50-turn benchmark; no separate convergence or sensitivity test is reported for the 450-turn or 10k-turn cases where it could affect overall current distribution.

    Authors: The surface-contact approximation error was quantified only against the 50-turn reference. Because the number of explicitly resolved T2TCLs stays small and localized (near leads and defects) even at larger scales, the local modeling discrepancy is not expected to propagate differently. Nevertheless, we accept that an explicit sensitivity study on the larger geometries would be valuable. We will add a short paragraph in the methods or results section discussing the expected invariance of the approximation error with stack size, supported by the existing benchmark data. revision: partial

standing simulated objections not resolved
  • A direct turn-resolved reference solution for the 10,000-turn magnet cannot be generated with present computational resources, so the magnitude of any scale-dependent homogenization error cannot be measured.

Circularity Check

0 steps flagged

No circularity: method validated against independent turn-resolved references

full rationale

The EXTRA method is a numerical homogenization technique whose accuracy is checked by direct comparison to separate turn-resolved FE models on the 50-turn benchmark (reproducing AC losses and temperature distributions). The 10k-turn demonstration is presented as an application without any fitted parameter or self-citation chain that reduces the claimed accuracy back to the target data by construction. All load-bearing steps rely on external reference solutions rather than internal redefinition or renaming.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based on the abstract only, the claim rests on standard finite-element assumptions plus the domain assumption that selective explicit resolution plus anisotropic averaging captures the essential physics. No new physical entities are introduced and no parameters appear to be fitted to the target results.

axioms (2)
  • standard math Finite-element discretization and coupling of magneto-thermal equations are valid for this geometry
    The entire simulation framework relies on standard FE methods.
  • domain assumption Anisotropic homogenization of turn-to-turn contact layers and neighboring turns accurately represents averaged behavior away from leads and defects
    This is the core efficiency assumption stated in the abstract.

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Reference graph

Works this paper leans on

69 extracted references · 67 canonical work pages · 1 internal anchor

  1. [1]

    High-temperature superconductors and their large-scale applications,

    T. A. Coombs et al., “High-temperature superconductors and their large-scale applications,” Nat. Rev. Electr. Eng., vol. 1, no. 12, pp. 788–801, Dec. 2024.doi: 10.1038/s44287-024-00112-y

    work page doi:10.1038/s44287-024-00112-y 2024

  2. [2]

    Reel-to-reel critical current measurement of coated conductors,

    S. Furtner, R. Nemetschek, R. Semerad, G. Sigl, and W. Prusseit, “Reel-to-reel critical current measurement of coated conductors,”Supercond. Sci. Technol., vol. 17, no. 5, S281, Mar. 2004.doi:10.1088/0953-2048/17/5/037

    work page doi:10.1088/0953-2048/17/5/037 2004

  3. [3]

    Stability of DC transport in HTS conductor with local critical current reduction,

    F. Gömöry and J. Šouc, “Stability of DC transport in HTS conductor with local critical current reduction,”Supercond. Sci. Technol., vol. 34, no. 2, p. 025005, Jan. 2021.doi: 10.1088/1361-6668/abc73e

    work page doi:10.1088/1361-6668/abc73e 2021

  4. [4]

    Analysis of current and heat transfer in locations with reduced critical current in coated conductor tape,

    F. Gömöry and J. Šouc, “Analysis of current and heat transfer in locations with reduced critical current in coated conductor tape,”Supercond. Sci. Technol., vol. 37, no. 9, p. 095017, Aug. 2024.doi:10.1088/1361-6668/ad6484

    work page doi:10.1088/1361-6668/ad6484 2024

  5. [5]

    Influence of critical current defect on operation, quench detection and protection of a conduction-cooled pancake rebco coil,

    M. Wozniak et al., “Influence of Critical Current Defect on Operation, Quench Detection and Protection of a Conduction-Cooled Pancake REBCO Coil,”IEEE Trans. Appl. Supercond., vol. 35, no. 5, pp. 1–6, Aug. 2025.doi:10.1109/TASC.2025.3532246

    work page doi:10.1109/tasc.2025.3532246 2025

  6. [6]

    Quench Detection and Protection for High-Temperature Superconductor Accelerator Magnets,

    M. Marchevsky, “Quench Detection and Protection for High-Temperature Superconductor Accelerator Magnets,”Instruments, vol. 5, no. 3, p. 27, Sep. 2021.doi: 10.3390/instruments5030027

    work page doi:10.3390/instruments5030027 2021

  7. [7]

    HTS Pancake Coils Without Turn-to-Turn Insulation,

    S. Hahn, D. K. Park, J. Bascunan, and Y. Iwasa, “HTS Pancake Coils Without Turn-to-Turn Insulation,”IEEE Trans. Appl. Supercond., vol. 21, no. 3, pp. 1592–1595, Jun. 2011.doi: 10.1109/TASC.2010.2093492

    work page doi:10.1109/tasc.2010.2093492 2011

  8. [8]

    Current Status of and Challenges for No-Insulation HTS Winding Technique,

    S. Hahn, “Current Status of and Challenges for No-Insulation HTS Winding Technique,” TEION KOGAKU, vol. 53, no. 1, pp. 2–9, Mar. 2018.doi:10.2221/jcsj.53.2

    work page doi:10.2221/jcsj.53.2 2018

  9. [9]

    Basic mechanism of self-healing from thermal runaway for uninsulated REBCO pancake coils,

    Y. Yanagisawa et al., “Basic mechanism of self-healing from thermal runaway for uninsulated REBCO pancake coils,”Physica C: Superconductivity, vol. 499, pp. 40–44, Apr. 2014.doi: 10.1016/j.physc.2014.02.002

    work page doi:10.1016/j.physc.2014.02.002 2014

  10. [10]

    A (RE)BCO Pancake Winding With Metal-as-Insulation,

    T. Lécrevisse and Y. Iwasa, “A (RE)BCO Pancake Winding With Metal-as-Insulation,”IEEE Trans. Appl. Supercond., vol. 26, no. 3, pp. 1–5, Apr. 2016.doi: 10.1109/TASC.2016.2522638

    work page doi:10.1109/tasc.2016.2522638 2016

  11. [11]

    Filled Thermoplastic Based Coating for Tailored Contact Resistance in HTS Coils,

    M. Crescenti et al., “Filled Thermoplastic Based Coating for Tailored Contact Resistance in HTS Coils,”IEEE Trans. Appl. Supercond., vol. 36, no. 5, pp. 1–5, Aug. 2026.doi: 10.1109/TASC.2026.3656161

    work page doi:10.1109/tasc.2026.3656161 2026

  12. [12]

    The normal-zone propagation properties of the non-insulated HTS coil in cryocooled operation,

    S. Kim, A. Saitou, J. Joo, and T. Kadota, “The normal-zone propagation properties of the non-insulated HTS coil in cryocooled operation,”Physica C: Superconductivity and its Applications, vol. 471, no. 21-22, pp. 1428–1431, Nov. 2011.doi: 10.1016/j.physc.2011.05.209

    work page doi:10.1016/j.physc.2011.05.209 2011

  13. [13]

    Ramping turn-to-turn loss and magnetization loss of a No-Insulation (RE)Ba2Cu3Ox high temperature superconductor pancake coil,

    Y. Wang, H. Song, W. Yuan, Z. Jin, and Z. Hong, “Ramping turn-to-turn loss and magnetization loss of a No-Insulation (RE)Ba2Cu3Ox high temperature superconductor pancake coil,”J. Appl. Phys., vol. 121, no. 11, p. 113903, Mar. 2017.doi: 10.1063/1.4978593

    work page doi:10.1063/1.4978593 2017

  14. [14]

    45.5-Tesla direct-current magnetic field generated with a high-temperature superconducting magnet,

    S. Hahn et al., “45.5-tesla direct-current magnetic field generated with a high-temperature superconducting magnet,”Nature, vol. 570, no. 7762, pp. 496–499, Jun. 2019.doi: 10.1038/s41586-019-1293-1

    work page doi:10.1038/s41586-019-1293-1 2019

  15. [15]

    Quench and self-protecting behaviour of an intra-layer no-insulation (LNI) REBCO coil at 31.4 T,

    Y. Suetomi et al., “Quench and self-protecting behaviour of an intra-layer no-insulation (LNI) REBCO coil at 31.4 T,”Supercond. Sci. Technol., vol. 34, no. 6, p. 064003, Apr. 2021.doi: 10.1088/1361-6668/abf54e

    work page doi:10.1088/1361-6668/abf54e 2021

  16. [16]

    Degradation Characteristics of a 20 T REBCO Insert Magnet After a 4.2 K Standalone Test,

    L. Shao et al., “Degradation Characteristics of a 20 T REBCO Insert Magnet After a 4.2 K Standalone Test,”IEEE Trans. Appl. Supercond., vol. 33, no. 5, pp. 1–6, Aug. 2023.doi: 10.1109/TASC.2023.3254483

    work page doi:10.1109/tasc.2023.3254483 2023

  17. [17]

    Turn-to-turn contact characteristics for an equivalent circuit model of no-insulation ReBCO pancake coil,

    X. Wang et al., “Turn-to-turn contact characteristics for an equivalent circuit model of no-insulation ReBCO pancake coil,”Supercond. Sci. Technol., vol. 26, no. 3, p. 035012, Jan. 2013.doi:10.1088/0953-2048/26/3/035012

    work page doi:10.1088/0953-2048/26/3/035012 2013

  18. [18]

    An equivalent circuit grid model for no-insulation HTS pancake coils,

    Y. Wang, H. Song, D. Xu, Z. Y. Li, Z. Jin, and Z. Hong, “An equivalent circuit grid model for no-insulation HTS pancake coils,”Supercond. Sci. Technol., vol. 28, no. 4, p. 045017, Mar. 2015.doi:10.1088/0953-2048/28/4/045017 27 May 2026 EXTRA homogenisation method for 3D FE simulation of NI coils L. Denis et al

    work page doi:10.1088/0953-2048/28/4/045017 2015

  19. [19]

    Analyses of transient behaviors of no-insulation REBCO pancake coils during sudden discharging and overcurrent,

    T. Wang et al., “Analyses of Transient Behaviors of No-Insulation REBCO Pancake Coils During Sudden Discharging and Overcurrent,”IEEE Trans. Appl. Supercond., vol. 25, no. 3, pp. 1–9, Jun. 2015.doi:10.1109/TASC.2015.2393058

    work page doi:10.1109/tasc.2015.2393058 2015

  20. [20]

    Finite-element modelling of no-insulation HTS coils using rotated anisotropic resistivity,

    R. C. Mataira, M. D. Ainslie, R. A. Badcock, and C. W. Bumby, “Finite-element modelling of no-insulation HTS coils using rotated anisotropic resistivity,”Supercond. Sci. Technol., vol. 33, no. 8, 08LT01, Jun. 2020.doi:10.1088/1361-6668/ab9688

    work page doi:10.1088/1361-6668/ab9688 2020

  21. [21]

    From Modelling to Application: Exploring Quench Tolerance in High-Field HTS Magnets,

    E.-K. C. Brewerton et al., “From Modelling to Application: Exploring Quench Tolerance in High-Field HTS Magnets,”IEEE Trans. Appl. Supercond., vol. 36, no. 3, pp. 1–6, May 2026. doi:10.1109/TASC.2025.3635639

    work page doi:10.1109/tasc.2025.3635639 2026

  22. [22]

    Fast and accurate electromagnetic modeling of non-insulated and metal-insulated REBCO magnets,

    E. Pardo and P. Fazilleau, “Fast and accurate electromagnetic modeling of non-insulated and metal-insulated REBCO magnets,”Supercond. Sci. Technol., vol. 37, no. 3, p. 035016, Feb. 2024.doi:10.1088/1361-6668/ad1c6f

    work page doi:10.1088/1361-6668/ad1c6f 2024

  23. [23]

    Screening currents increase thermal quench propagation speed in ultra-high-field REBCO magnets,

    E. Pardo, A. Dadhich, N. Jerance, and P. Fazilleau, “Screening currents increase thermal quench propagation speed in ultra-high-field REBCO magnets,”Results in Engineering, vol. 29, p. 108933, Mar. 2026.doi:10.1016/j.rineng.2025.108933

    work page doi:10.1016/j.rineng.2025.108933 2026

  24. [24]

    Magnetization loss of no-insulation coil for an electrodynamic suspension system,

    X. Wang et al., “Magnetization loss of no-insulation coil for an electrodynamic suspension system,”Supercond. Sci. Technol., vol. 34, no. 6, p. 065007, May 2021.doi: 10.1088/1361-6668/abe18c

    work page doi:10.1088/1361-6668/abe18c 2021

  25. [25]

    Numerical Study on Thermal Stability of No-Insulation Coils Using a Three-Dimensional Finite-Element Model,

    W. Zhao, Y. Lu, D. Zhou, C. Bai, Q. Li, and C. Cai, “Numerical Study on Thermal Stability of No-Insulation Coils Using a Three-Dimensional Finite-Element Model,”IEEE Trans. Appl. Supercond., vol. 32, no. 5, pp. 1–10, Aug. 2022.doi:10.1109/TASC.2022.3175749

    work page doi:10.1109/tasc.2022.3175749 2022

  26. [26]

    Electromag- netic simulation of no-insulation coils using h-ϕthin shell approxima- tion,

    E. Schnaubelt, M. Wozniak, S. Schöps, and A. Verweij, “Electromagnetic Simulation of No-Insulation Coils Using H – Phi Thin Shell Approximation,”IEEE Trans. Appl. Supercond., vol. 33, no. 5, pp. 1–6, Aug. 2023.doi:10.1109/TASC.2023.3258905

    work page doi:10.1109/tasc.2023.3258905 2023

  27. [27]

    Thermal thin shell approx- imation towards finite element quench simulation,

    E. Schnaubelt, M. Wozniak, and S. Schöps, “Thermal thin shell approximation towards finite element quench simulation,”Supercond. Sci. Technol., vol. 36, no. 4, p. 044004, Mar. 2023. doi:10.1088/1361-6668/acbeea

    work page doi:10.1088/1361-6668/acbeea 2023

  28. [28]

    Magneto-thermal thin shell approximation for 3D finite element analysis of no-insulation coils,

    E. Schnaubelt et al., “Magneto-Thermal Thin Shell Approximation for 3D Finite Element Analysis of No-Insulation Coils,”IEEE Trans. Appl. Supercond., vol. 34, no. 3, pp. 1–6, May 2024.doi:10.1109/TASC.2023.3340648

    work page doi:10.1109/tasc.2023.3340648 2024

  29. [29]

    Modeling of contact resistivity and simplification of 3D homogenization strategy for the H formulation,

    S. Wang, H. Yong, and Y. Zhou, “Modeling of contact resistivity and simplification of 3D homogenization strategy for the H formulation,”Supercond. Sci. Technol., vol. 37, no. 7, p. 075019, Jun. 2024.doi:10.1088/1361-6668/ad541f

    work page doi:10.1088/1361-6668/ad541f 2024

  30. [30]

    Study of the demagnetization behavior of no-insulation persistent-current mode HTS coils under external AC fields by 3D FEM simulation,

    Z. Zhong, W. Wu, G. Ma, and Z. Jin, “Study of the demagnetization behavior of no-insulation persistent-current mode HTS coils under external AC fields by 3D FEM simulation,”Supercond. Sci. Technol., vol. 37, no. 4, p. 045011, Mar. 2024.doi: 10.1088/1361-6668/ad2300

    work page doi:10.1088/1361-6668/ad2300 2024

  31. [31]

    Fast and accurate 3D FEM model for electromagnetic simulations of no-insulation HTS coils based on polygon-anisotropic-resistivity,

    Z. Zhong, W. Wu, and Z. Jin, “Fast and accurate 3D FEM model for electromagnetic simulations of no-insulation HTS coils based on polygon-anisotropic-resistivity,”Supercond. Sci. Technol., vol. 37, no. 9, 09LT01, Aug. 2024.doi:10.1088/1361-6668/ad68d6

    work page doi:10.1088/1361-6668/ad68d6 2024

  32. [32]

    Magnetisation loss behaviour in insulated and non-insulated HTS REBCO double-pancake and racetrack coils at 77 K,

    B. G. Koshy et al., “Magnetisation loss behaviour in insulated and non-insulated HTS REBCO double-pancake and racetrack coils at 77 K,”Supercond. Sci. Technol., vol. 38, no. 4, p. 045004, Mar. 2025.doi:10.1088/1361-6668/adbce2

    work page doi:10.1088/1361-6668/adbce2 2025

  33. [33]

    Electromagnetic modeling of no-insulation REBCO coils based on T–A formulation: From 2D to 3D,

    Y. Chen et al., “Electromagnetic modeling of no-insulation REBCO coils based on T–A formulation: From 2D to 3D,”Supercond. Sci. Technol., vol. 39, no. 2, p. 025005, Feb. 2026. doi:10.1088/1361-6668/ae3a1e

    work page doi:10.1088/1361-6668/ae3a1e 2026

  34. [34]

    Enhanced Model for Non-Insulated HTS Coils,

    S. Sorti, L. Balconi, G. Crespi, L. Rossi, C. Santini, and M. Statera, “Enhanced Model for Non-Insulated HTS Coils,”IEEE Trans. Appl. Supercond., vol. 35, no. 5, pp. 1–5, Aug. 2025. doi:10.1109/TASC.2025.3546873

    work page doi:10.1109/tasc.2025.3546873 2025

  35. [35]

    Thermo-Electromagnetic Design, Operation, and Protection Simulations of a 40 T HTS NI Final Cooling Solenoid for a Muon Collider,

    T. Mulder et al., “Thermo-Electromagnetic Design, Operation, and Protection Simulations of a 40 T HTS NI Final Cooling Solenoid for a Muon Collider,”IEEE Trans. Appl. Supercond., vol. 35, no. 5, pp. 1–5, Aug. 2025.doi:10.1109/TASC.2025.3530379

    work page doi:10.1109/tasc.2025.3530379 2025

  36. [36]

    Calculation of alternating current losses in stacks and coils made of second generation high temperature superconducting tapes for large scale applications,

    V. M. R. Zermeno, A. B. Abrahamsen, N. Mijatovic, B. B. Jensen, and M. P. Sørensen, “Calculation of alternating current losses in stacks and coils made of second generation high temperature superconducting tapes for large scale applications,”Journal of Applied Physics, vol. 114, no. 17, p. 173901, Nov. 2013.doi:10.1063/1.4827375 28 May 2026 EXTRA homogeni...

    work page doi:10.1063/1.4827375 2013

  37. [37]

    3D modeling and simulation of 2G HTS stacks and coils,

    V. M. R. Zermeño and F. Grilli, “3D modeling and simulation of 2G HTS stacks and coils,” Supercond. Sci. Technol., vol. 27, no. 4, p. 044025, Mar. 2014.doi: 10.1088/0953-2048/27/4/044025

    work page doi:10.1088/0953-2048/27/4/044025 2014

  38. [38]

    Numerical models for ac loss calculation in large-scale applications of HTS coated conductors,

    L. Quéval, V. M. R. Zermeño, and F. Grilli, “Numerical models for ac loss calculation in large-scale applications of HTS coated conductors,”Supercond. Sci. Technol., vol. 29, no. 2, p. 024007, Feb. 2016.doi:10.1088/0953-2048/29/2/024007

    work page doi:10.1088/0953-2048/29/2/024007 2016

  39. [39]

    Advanced electromagnetic modeling of large-scale high-temperature superconductor systems based on H and T-A formulations,

    E. Berrospe-Juarez, F. Trillaud, V. M. R. Zermeño, and F. Grilli, “Advanced electromagnetic modeling of large-scale high-temperature superconductor systems based on H and T-A formulations,”Supercond. Sci. Technol., vol. 34, no. 4, p. 044002, Feb. 2021.doi: 10.1088/1361-6668/abde87

    work page doi:10.1088/1361-6668/abde87 2021

  40. [40]

    3D homogenization of the T-A formulation for the analysis of coils with complex geometries,

    C. R. Vargas-Llanos, F. Huber, N. Riva, M. Zhang, and F. Grilli, “3D homogenization of the T-A formulation for the analysis of coils with complex geometries,”Supercond. Sci. Technol., vol. 35, no. 12, p. 124001, Oct. 2022.doi:10.1088/1361-6668/ac9932

    work page doi:10.1088/1361-6668/ac9932 2022

  41. [41]

    Use of the J-A Approach to Model Homogenized 2G Tape Stacks and HTS Bulks,

    B. M. O. Santos, G. dos Santos, F. G. d. R. Martins, F. Sass, G. G. Sotelo, and R. de Andrade, “Use of the J-A Approach to Model Homogenized 2G Tape Stacks and HTS Bulks,” IEEE Trans. Appl. Supercond., vol. 34, no. 3, pp. 1–5, May 2024.doi: 10.1109/TASC.2024.3356495

    work page doi:10.1109/tasc.2024.3356495 2024

  42. [42]

    Foil Conductor Model for Efficient Simulation of HTS Coils in Large Scale Applications,

    E. Paakkunainen, L. Denis, C. Geuzaine, P. Rasilo, and S. Schöps, “Foil Conductor Model for Efficient Simulation of HTS Coils in Large Scale Applications,”IEEE Trans. Appl. Supercond., vol. 35, no. 5, pp. 1–5, Aug. 2025.doi:10.1109/TASC.2024.3517573

    work page doi:10.1109/tasc.2024.3517573 2025

  43. [43]

    Magnetic Field Conforming Formulations for Foil Windings,

    L. Denis, E. Paakkunainen, P. Rasilo, S. Schöps, B. Vanderheyden, and C. Geuzaine, “Magnetic Field Conforming Formulations for Foil Windings,”IEEE Trans. Magn., vol. 61, no. 8, pp. 1–7, Aug. 2025.doi:10.1109/TMAG.2025.3584111

    work page doi:10.1109/tmag.2025.3584111 2025

  44. [44]

    Paakkunainen, L

    E. Paakkunainen, L. Denis, B. Vanderheyden, C. Geuzaine, P. Rasilo, and S. Schöps, Homogenization of HTS coils with the h, h-phi, and t-omega foil conductor model, Mar. 2026. doi:10.48550/arXiv.2604.00154arXiv:2604.00154 [cs]

    work page doi:10.48550/arxiv.2604.00154arxiv:2604.00154 2026

  45. [45]

    3D general simultaneous multi-scale homogeneous T-A model for electromagnetic simulations of large-scale REBCO coils with complex geometries,

    L. Wang and J. Zheng, “3D general simultaneous multi-scale homogeneous T-A model for electromagnetic simulations of large-scale REBCO coils with complex geometries,”Supercond. Sci. Technol., vol. 38, no. 8, p. 085005, Aug. 2025.doi:10.1088/1361-6668/adef88

    work page doi:10.1088/1361-6668/adef88 2025

  46. [46]

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

    L. Denis, B. Vanderheyden, and C. Geuzaine, “Simultaneous Multi-Scale Homogeneous H-Phi Thin-Shell Model for Efficient Simulations of Stacked HTS Coils,”IEEE Trans. Appl. Supercond., vol. 36, no. 5, pp. 1–7, Aug. 2026.doi:10.1109/TASC.2026.3652981

    work page doi:10.1109/tasc.2026.3652981 2026

  47. [47]

    Surface Contact Approximation for Magneto-Thermal Finite Element Analysis of No-Insulation HTS Coils

    E. Schnaubelt, L. Denis, M. Wozniak, J. Dular, and A. Verweij,Surface Contact Approximation for Magneto-Thermal Finite Element Analysis of No-Insulation HTS Coils, 2026.doi:10.48550/arXiv.2605.28574arXiv:2605.28574

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2605.28574arxiv:2605.28574 2026

  48. [48]

    Models and Methods for Transient Magneto-Thermal Finite Element Simulation of Superconducting Magnets,

    E. Schnaubelt, “Models and Methods for Transient Magneto-Thermal Finite Element Simulation of Superconducting Magnets,” Ph.D. dissertation, TU Darmstadt, May 2025.doi: 10.26083/tuprints-00031402

    work page doi:10.26083/tuprints-00031402 2025

  49. [49]

    Homology and cohomology computation in finite element modeling,

    M. Pellikka, S. Suuriniemi, L. Kettunen, and C. Geuzaine, “Homology and Cohomology Computation in Finite Element Modeling,”SIAM J. Sci. Comput., Oct. 2013.doi: 10.1137/130906556

    work page doi:10.1137/130906556 2013

  50. [50]

    Critical Persistent Currents in Hard Superconductors,

    Y. B. Kim, C. F. Hempstead, and A. R. Strnad, “Critical Persistent Currents in Hard Superconductors,”Phys. Rev. Lett., vol. 9, no. 7, pp. 306–309, Oct. 1962.doi: 10.1103/PhysRevLett.9.306

    work page doi:10.1103/physrevlett.9.306 1962

  51. [51]

    Theory of Flux Creep in Hard Superconductors,

    P. W. Anderson, “Theory of Flux Creep in Hard Superconductors,”Phys. Rev. Lett., vol. 9, no. 7, pp. 309–311, Oct. 1962.doi:10.1103/PhysRevLett.9.309

    work page doi:10.1103/physrevlett.9.309 1962

  52. [52]

    A Coupled A–H Formulation for Magneto-Thermal Transients in High-Temperature Superconducting Magnets,

    L. Bortot et al., “A Coupled A–H Formulation for Magneto-Thermal Transients in High-Temperature Superconducting Magnets,”IEEE Trans. Appl. Supercond., vol. 30, no. 5, pp. 1–11, Aug. 2020.doi:10.1109/TASC.2020.2969476

    work page doi:10.1109/tasc.2020.2969476 2020

  53. [53]

    An Open-Source Finite Element Quench Simulation Tool for Superconducting Magnets,

    A. Vitrano, M. Wozniak, E. Schnaubelt, T. Mulder, E. Ravaioli, and A. Verweij, “An Open-Source Finite Element Quench Simulation Tool for Superconducting Magnets,”IEEE Trans. Appl. Supercond., vol. 33, no. 5, pp. 1–6, Aug. 2023.doi: 10.1109/TASC.2023.3259332

    work page doi:10.1109/tasc.2023.3259332 2023

  54. [54]

    An open-source 3D FE quench simulation tool for no-insulation HTS pancake coils,

    S. Atalay et al., “An open-source 3D FE quench simulation tool for no-insulation HTS pancake coils,”Supercond. Sci. Technol., vol. 37, no. 6, p. 065005, May 2024.doi: 10.1088/1361-6668/ad3f83 29 May 2026 EXTRA homogenisation method for 3D FE simulation of NI coils L. Denis et al

    work page doi:10.1088/1361-6668/ad3f83 2024

  55. [55]

    Geuzaine, J

    C. Geuzaine and J.-F. Remacle, “Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities,”Int. J. Numer. Methods Eng., vol. 79, no. 11, pp. 1309–1331, May 2009.doi:10.1002/nme.2579

    work page doi:10.1002/nme.2579 2009

  56. [56]

    Schnaubelt and L

    E. Schnaubelt and L. Denis,CERNGetDP 2026.4.4, https://gitlab.cern.ch/steam/cerngetdp/-/releases/2026.4.4, Apr. 2026

    2026

  57. [57]

    A general envi- ronment for the treatment of discrete problems and its application to the finite element method,

    P. Dular, C. Geuzaine, F. Henrotte, and W. Legros, “A general environment for the treatment of discrete problems and its application to the finite element method,”IEEE Trans. Magn., vol. 34, no. 5, pp. 3395–3398, Sep. 1998.doi:10.1109/20.717799

    work page doi:10.1109/20.717799 1998

  58. [58]

    Denis and E

    L. Denis and E. Schnaubelt,STEAM SDK Analysis for ’Explicit Turn Resolution with Anisotropic Homogenisation for Efficient 3D Magneto-Thermal Finite-Element Simulation of Large-Scale No-Insulation HTS Magnets’, https://gitlab.cern.ch/steam/analyses/anisotropic- homogenization-of-ni-hts-magnets/-/tags/initial_arxiv_submission, May 2026

    2026

  59. [59]

    MUMPS: A General Purpose Distributed Memory Sparse Solver,

    P. R. Amestoy, I. S. Duff, J.-Y. L’Excellent, and J. Koster, “MUMPS: A General Purpose Distributed Memory Sparse Solver,” inApplied Parallel Computing. New Paradigms for HPC in Industry and Academia, T. Sørevik, F. Manne, A. H. Gebremedhin, and R. Moe, Eds., Berlin, Heidelberg: Springer, 2001, pp. 121–130.doi:10.1007/3-540-70734-4_16

    work page doi:10.1007/3-540-70734-4_16 2001

  60. [60]

    SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems,

    X. S. Li and J. W. Demmel, “SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems,”ACM Trans. Math. Softw., vol. 29, no. 2, pp. 110–140, Jun. 2003.doi:10.1145/779359.779361

    work page doi:10.1145/779359.779361 2003

  61. [61]

    Newly Released Capabilities in the Distributed-Memory SuperLU Sparse Direct Solver,

    X. S. Li, P. Lin, Y. Liu, and P. Sao, “Newly Released Capabilities in the Distributed-Memory SuperLU Sparse Direct Solver,”ACM Trans. Math. Softw., vol. 49, no. 1, 10:1–10:20, Mar. 2023.doi:10.1145/3577197

    work page doi:10.1145/3577197 2023

  62. [62]

    Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries,

    S. Balay, W. D. Gropp, L. C. McInnes, and B. F. Smith, “Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries,” inModern Software Tools for Scientific Computing, E. Arge, A. M. Bruaset, and H. P. Langtangen, Eds., Boston, MA: Birkhäuser, 1997, pp. 163–202.doi:10.1007/978-1-4612-1986-6_8

    work page doi:10.1007/978-1-4612-1986-6_8 1997

  63. [63]

    Investigation on the electrical contact resistance of soldered metal insulation REBCO coil,

    J. Lee, J. Mun, J. Kim, and S. Kim, “Investigation on the Electrical Contact Resistance of Soldered Metal Insulation REBCO Coil,”IEEE Trans. Appl. Supercond., vol. 31, no. 5, pp. 1–5, Aug. 2021.doi:10.1109/TASC.2021.3063653

    work page doi:10.1109/tasc.2021.3063653 2021

  64. [64]

    No-Insulation Coil Under Time-Varying Condition: Magnetic Coupling With External Coil,

    S. Hahn et al., “No-Insulation Coil Under Time-Varying Condition: Magnetic Coupling With External Coil,”IEEE Trans. Appl. Supercond., vol. 23, no. 3, pp. 4601705–4601705, Jun. 2013.doi:10.1109/TASC.2013.2240756

    work page doi:10.1109/tasc.2013.2240756 2013

  65. [65]

    Mag- netic field and temperature scaling of the critical current of REBCO tapes,

    G. Succi, A. Ballarino, S. C. Hopkins, C. Barth, and Y. Yang, “Magnetic Field and Temperature Scaling of the Critical Current of REBCO Tapes,”IEEE Trans. Appl. Supercond., vol. 34, no. 3, pp. 1–7, May 2024.doi:10.1109/TASC.2024.3370137

    work page doi:10.1109/tasc.2024.3370137 2024

  66. [66]

    Overall thermal conductance and thermal contact resistance in no-insulation REBCO magnet,

    J. Seok, D. Kim, and S. Kim, “Overall Thermal Conductance and Thermal Contact Resistance in No-Insulation REBCO Magnet,”IEEE Trans. Appl. Supercond., vol. 28, no. 3, pp. 1–5, Apr. 2018.doi:10.1109/TASC.2017.2785825

    work page doi:10.1109/tasc.2017.2785825 2018

  67. [67]

    Effective Time Constants at 4.2 to 70 K in ReBCO Pancake Coils With Different Inter-Turn Resistances,

    T. H. Nes et al., “Effective Time Constants at 4.2 to 70 K in ReBCO Pancake Coils With Different Inter-Turn Resistances,”IEEE Trans. Appl. Supercond., vol. 32, no. 4, pp. 1–6, Jun. 2022.doi:10.1109/TASC.2022.3148968

    work page doi:10.1109/tasc.2022.3148968 2022

  68. [68]

    CUDI: A model for calculation of electrodynamic and thermal behaviour of superconducting Rutherford cables,

    A. P. Verweij, “CUDI: A model for calculation of electrodynamic and thermal behaviour of superconducting Rutherford cables,”Cryogenics, This Issue Contains Papers from CHATS-2005: Workshop on Computation of Thermohydraulic Transients in Superconductors, vol. 46, no. 7, pp. 619–626, Jul. 2006.doi:10.1016/j.cryogenics.2006.01.009

    work page doi:10.1016/j.cryogenics.2006.01.009 2005

  69. [69]

    Systematic Study of the Contact Resistance Between REBCO Tapes: Pressure Dependence in the Case of No-Insulation, Metal Co-Winding and Metal-Insulation,

    M. Bonura, C. Barth, A. Joudrier, J. F. Troitino, A. Fête, and C. Senatore, “Systematic Study of the Contact Resistance Between REBCO Tapes: Pressure Dependence in the Case of No-Insulation, Metal Co-Winding and Metal-Insulation,”IEEE Trans. Appl. Supercond., vol. 29, no. 5, pp. 1–5, Aug. 2019.doi:10.1109/TASC.2019.2893564 30

    work page doi:10.1109/tasc.2019.2893564 2019