Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Modelling Conduction Cooling of Superconducting Accelerator Magnets using a Thermal Thin Shell Approximation

Emma Vancayseele, Erik Schnaubelt, Louis Denis, Christophe Geuzaine, Arjan Verweij, Mariusz Wozniak

TL;DR

This work extends the FiQuS framework to include collar and pole regions in superconducting accelerator magnets and applies a thermal thin shell approximation (TSA) to efficiently model insulation. By coupling a TSA-based thermal model to a magneto-thermal solver with non-conforming meshes, it achieves accurate temperature predictions (within $2\%$ to $4\%$ of a fully meshed reference) while delivering up to a $5\times$ reduction in computational time. The approach is validated against fully resolved reference solutions and applied to a 12 T dipole using current ramp scenarios, demonstrating robust performance beyond traditional high-heat-flux quench cases. Additionally, the TSA is used to explore conduction cooling configurations through the collar, revealing material-dependent sensitivities and guiding design choices for future magnets, with the code publicly available for reproducible research.

Abstract

Understanding the thermal behaviour of superconducting accelerator magnets is essential to ensure stable and reliable operation. This work presents an extension of the Finite Element Quench Simulator (FiQuS) Multipole module to include collar and pole regions of accelerator magnets, which influences the overall thermal response. A thermal thin shell approximation (TSA), which is shown to be effective in previous works, is employed to model thermal insulation layers efficiently, replacing an insulation surface mesh. The main novelty of this work lies in the development of a method to model the thermal connection between the magnet winding and the collar and pole regions via the TSA. To assess the accuracy and computational efficiency of the novel method, temperature and field variations are computed for a current ramp-up scenario. The thermal solution is coupled to a fully resolved magnetodynamic solution to capture the interaction between thermal and electromagnetic behaviour. The results obtained with the TSA are then compared to classical finite element (FE) solutions with explicitly meshed insulation domains. The TSA predicts the maximum temperature within 2-4% of the reference solution while substantially reducing mesh complexity and achieving up to a 5 times speed-up in computation time. While the TSA has traditionally been employed for short-duration quench simulations with high heat fluxes between magnet turns, these results demonstrate its reliability and efficiency for current ramp scenarios with low heat fluxes, significantly expanding its application range beyond what has been previously reported in the literature. To illustrate potential applications of this new functionality, conduction cooling through the collar region is studied, comparing different cooling configurations and collar materials.

Modelling Conduction Cooling of Superconducting Accelerator Magnets using a Thermal Thin Shell Approximation

TL;DR

This work extends the FiQuS framework to include collar and pole regions in superconducting accelerator magnets and applies a thermal thin shell approximation (TSA) to efficiently model insulation. By coupling a TSA-based thermal model to a magneto-thermal solver with non-conforming meshes, it achieves accurate temperature predictions (within to of a fully meshed reference) while delivering up to a reduction in computational time. The approach is validated against fully resolved reference solutions and applied to a 12 T dipole using current ramp scenarios, demonstrating robust performance beyond traditional high-heat-flux quench cases. Additionally, the TSA is used to explore conduction cooling configurations through the collar, revealing material-dependent sensitivities and guiding design choices for future magnets, with the code publicly available for reproducible research.

Abstract

Understanding the thermal behaviour of superconducting accelerator magnets is essential to ensure stable and reliable operation. This work presents an extension of the Finite Element Quench Simulator (FiQuS) Multipole module to include collar and pole regions of accelerator magnets, which influences the overall thermal response. A thermal thin shell approximation (TSA), which is shown to be effective in previous works, is employed to model thermal insulation layers efficiently, replacing an insulation surface mesh. The main novelty of this work lies in the development of a method to model the thermal connection between the magnet winding and the collar and pole regions via the TSA. To assess the accuracy and computational efficiency of the novel method, temperature and field variations are computed for a current ramp-up scenario. The thermal solution is coupled to a fully resolved magnetodynamic solution to capture the interaction between thermal and electromagnetic behaviour. The results obtained with the TSA are then compared to classical finite element (FE) solutions with explicitly meshed insulation domains. The TSA predicts the maximum temperature within 2-4% of the reference solution while substantially reducing mesh complexity and achieving up to a 5 times speed-up in computation time. While the TSA has traditionally been employed for short-duration quench simulations with high heat fluxes between magnet turns, these results demonstrate its reliability and efficiency for current ramp scenarios with low heat fluxes, significantly expanding its application range beyond what has been previously reported in the literature. To illustrate potential applications of this new functionality, conduction cooling through the collar region is studied, comparing different cooling configurations and collar materials.
Paper Structure (14 sections, 2 equations, 10 figures, 3 tables)

This paper contains 14 sections, 2 equations, 10 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Magneto-thermal formulation
  4. Thin shell approximation
  5. General idea and closest neighbour mapping
  6. Appropriate length scaling
  7. Reference solution
  8. Results and discussion
  9. Mesh quality: parameter study
  10. Fully resolved mesh models
  11. TSA mesh
  12. TSA performance
  13. Example: cooling hole position study
  14. Conclusion

Figures (10)

  • Figure 1: Illustration of the electromagnetic computational domain $\Omega_\mathrm{EM}$ and thermal computational domain $\Omega_\mathrm{TH}$ for a 12 T dipole magnet design suggested in Foussat2026. Only a quarter of the magnet is shown. The collar, pole, and ground insulation regions have been newly integrated into FiQuS. The materials are specified in Tab. \ref{['tab:materials']}.
  • Figure 2: Visualisation of the collar TSA and its internal discretisation. The lengths are not to scale for readability. The first and second TSLs replace the cable and ground insulation respectively, as depicted in Fig. \ref{['fig:tsa']}.
  • Figure 3: Visualisation of the modelled material area in the TSA for the collar. TSL$_1$ and TSL$_2$ are indicated by thicker lines. The darker region represents the model without length correction.
  • Figure 4: Illustration of a free closest neighbour map and an enforced map. For clarity, only the collar temperature is shown at a specific point in time, for a quenching simulation and a stainless steel collar. Note the difference in local temperatures.
  • Figure 5: Maximum temperature during a current ramp (gray) for fully resolved mesh with different mesh sizes (colour bar) and a TSA model (black). TSA models without scaling and no cooling are also plotted for comparison. Mesh size parameters are specified in Tab. \ref{['tab:reference_mesh_table']} and Fig. \ref{['fig:relative_error']} for the TSA.
  • ...and 5 more figures