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This paper deals with the modelling of superconducting and resistive wireswith a helicoidal symmetry, subjected to an external field and a transportcurrent. Helicoidal structures are three-dimensional, and therefore yieldcomputationally intensive simulations in a Cartesian coordinate system. We showin this paper that by working instead with a helicoidal system of coordinates,the problem to solve can be made two-dimensional, drastically reducing thecomputational cost. We first introduce the state-of-the-art approach and applyit on the h-phi-formulation with helicoidally symmetric boundary conditions(e.g., axial external magnetic field, with or without transport current), withan emphasis on the function space discretization. Then, we extend the approachto general boundary conditions (e.g., transverse external magnetic field) andpresent numerical results with linear materials. In particular, we discuss thefrequency-dependent losses in composite wires made of superconducting filamentsembedded in a resistive matrix. Finally, we provide outlook to the applicationof the generalized model with nonlinear materials.

Helicoidal Transformation Method for Finite Element Models of Twisted Superconductors