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

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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\mathbf {A}}}\!-\!{{\mathbf {H}}}$</tex-math></inline-formula>field formulation for the analysis of magneto-thermal transients in accelerator magnets. The magnetic field strength <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\mathbf {H}}}$</tex-math></inline-formula>accounts for the eddy current problem in the source regions containing the superconducting domains, while the magnetic vector potential <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\mathbf {A}}}$</tex-math></inline-formula>represents the magnetoquasistatic problem in the normal and nonconducting domains. Furthermore, we include a thin-shell approximation for the source regions, making the formulation suitable for large-scale models composed of thousands of tapes. In this article, 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.