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

Abstract

The application of high-temperature superconductors to accelerator magnets for future particle colliders is under study. Numerical methods are crucial for an accurate evaluation of the complex dynamical behavior of the magnets, especially concerning the magnetic field quality and thermal behavior. We present a coupled $\text{A}$-$\text{H}$ field formulation for the analysis of magneto-thermal transients in accelerator magnets. The magnetic field strength $\text{H}$ accounts for the eddy current problem in the source regions containing the superconducting domains, while the magnetic vector potential $\text{A}$ represents the magnetoquasistatic problem in the normal and non-conducting domains. Furthermore, we include a slab approximation for the source regions, making the formulation suitable for large scale models composed of thousands of tapes. In this work, the relevant equations are derived and discussed, with emphasis on the coupling conditions. The weak formulation is derived, and numerical results are provided in order to both, verify the formulation and scale it to the size of an accelerator magnet.

10 pages, 11 figures

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• Numerical Analysis of the Screening Current-Induced Magnetic Field in the HTS Insert Dipole Magnet Feather-M2.1-2
• Proof of Concept of High-Temperature Superconducting Screens for Magnetic Field-Error Cancellation in Accelerator Magnets
• On the Stability of Mixed Finite-Element Formulations for High-Temperature Superconductors
• Fully-staggered-array bulk Re-Ba-Cu-O short-period undulator: large-scale 3D electromagnetic modelling and design optimization using A-V and H-formulation methods
• Magneto-Thermal Thin Shell Approximation for 3D Finite Element Analysis of No-Insulation Coils
• What Formulation Should One Choose for Modeling a 3D HTS Motor Pole with Ferromagnetic Materials?
• An Open-Source 3D FE Quench Simulation Tool for No-Insulation HTS Pancake Coils
• Foil Conductor Model for Efficient Simulation of HTS Coils in Large Scale Applications
• Transient Finite Element Simulation of Accelerator Magnets Using Thermal Thin Shell Approximation