Helicoidal Transformation Method for Finite Element Models of Twisted Superconductors

This article deals with the modeling of superconducting and resistive wires with a helicoidal symmetry, subjected to an external field and a transport current. Helicoidal structures are 3-D, and therefore yield computationally intensive simulations in a Cartesian coordinate system. We show in this article that by working instead with a helicoidal system of coordinates, the problem to solve can be made 2-D, drastically reducing the computational cost. We first introduce the state-of-the-art approach and apply it on the
$h$
-
$\phi$
-formulation with helicoidally symmetric boundary conditions (e.g., axial external magnetic field, with or without transport current), with an emphasis on the function space discretization. Then, we extend the approach to general boundary conditions (e.g., transverse external magnetic field), and we present numerical results with linear materials. In particular, we discuss the frequency-dependent losses in composite wires made of superconducting filaments embedded in a resistive matrix. Finally, we provide outlook to the application of the generalized model with nonlinear materials.