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Abstract
We present a numerical method for the solution of threedimensional linear magnetostatic problems by embedding their geometry into a symmetric domain and Fourier expansion in the symmetry coordinate, leading to a set of decoupled twodimensional problems. Special cases include axial and translational symmetry. To keep the treatment universal, a framework for the Fourier decomposition of the vector potential formulation is developed in the covariant formalism with general curvilinear coordinates. Under the restriction of homogeneous material parameters along the symmetry direction, but not on fields and current densities, this leads to a decoupled set of twodimensional equations in both, zeroth (nonoscillatory) and nonzero (oscillatory) harmonics. For the latter it is possible to eliminate one component of the vector potential resulting in a fully transverse vector potential orthogonal to the transverse magnetic field. In addition to the Poissonlike equation for the longitudinal component of the nonoscillatory problem, a general curlcurl Helmholtz equation describes the transverse problem covering both, nonoscillatory and oscillatory case. The resulting variational forms are treated by the usual nodal finite element method for the longitudinal problem and by a twodimensional edge element method for the transverse problem. The numerical solution can be computed independently for each harmonic using fewer degrees of freedom than a threedimensional simulation at comparable accuracy. These properties make the developed approach useful for the analysis of perturbation harmonics in magnetic plasma confinement devices in cylindrical coordinates or magnetic flux coordinates. The method is validated on analytical and numerical test cases and applied to a racetrackshaped coil setup.
Original language  English 

Article number  108401 
Journal  Computer Physics Communications 
Volume  277 
DOIs  
Publication status  Published  Aug 2022 
Keywords
 Curvilinear coordinates
 Edge elements
 Finite element method
 Fourier series
 Magnetostatics
ASJC Scopus subject areas
 Hardware and Architecture
 General Physics and Astronomy
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EUROfusion  Transport and Heating in Fusion Plasmas
Kernbichler, W., Albert, C., Eder, M., Kasilov, S., Markl, M., Buchholz, R., Graßler, G. S., Kamendje, R. L., Babin, R. & Lainer, P.
1/01/21 → 31/12/27
Project: Research project