2023/11/23 by Julien Dular, Dular, Julien, François Henrotte +9
Engineering · Mathematics · #Accelerator Physics (physics.acc-ph) #Boundary (topology) #Boundary value problem #Cartesian coordinate system #Computer science #Condensed matter physics #Coordinate system #Discretization #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Field (mathematics) #Finite element method #Geometry #Magnetic field #Materials science #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Nonlinear system #Numerical methods for differential equations #Physics #Quantum mechanics #Resistive touchscreen #Superconducting Materials and Applications #Superconductivity #Symmetry (geometry)
paper · pdf · doi:10.48550/arxiv.2311.13919
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper deals with the modelling of superconducting and resistive wires with a helicoidal symmetry, subjected to an external field and a transport current. Helicoidal structures are three-dimensional, and therefore yield computationally intensive simulations in a Cartesian coordinate system. We show in this paper that by working instead with a helicoidal system of coordinates, the problem to solve can be made two-dimensional, 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 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.