Electromagnetic Simulation of No-Insulation Coils Using H – <inline-formula><tex-math notation="LaTeX">$\phi$</tex-math></inline-formula> Thin Shell Approximation

When simulating no-insulation high-temperature superconducting pancake coils with the finite element (FE) method, the high aspect ratio of the thin turn-to-turn contact layer (T2TCL) leads to unfavorable meshes in these thin layers as manifested by a high number of degrees of freedom (DoF) or mesh elements of poor quality which decrease the accuracy of the simulation results. To mitigate this issue, we propose to collapse the T2TCL volume into a surface using a thin shell approximation (TSA) for three-dimensional FE analysis. A <inline-formula><tex-math notation="LaTeX">$\vec{H}-\phi$</tex-math></inline-formula> formulation is used and solves for the magnetic field strength <inline-formula><tex-math notation="LaTeX">$\vec{H}$</tex-math></inline-formula> in conducting domains and the magnetic scalar potential <inline-formula><tex-math notation="LaTeX">$\phi$</tex-math></inline-formula> in insulating domains. This formulation avoids spurious currents and reduces the number of DoF in insulating domains. Automatically created thick cuts are used to deal with multiply connected domains. Particular attention is paid to the interpretation of these cuts and the corresponding basis functions in the context of pancake coil geometries. The efficiency of the formulation facilitates the resolution of each turn. In this way, local phenomena such as quench can be captured in a straightforward way. The TSA formulation is verified by comparison against a reference model with volumetrically meshed T2TCL and is shown to be accurate and efficient, significantly reducing the solution time while reducing the effort for creating high-quality meshes. The TSA is implemented in an open-source FE framework and the source code is shared alongside this paper.