Abstract
In this paper, we present numerical schemes based on the boundary-element (BE) and finite-element (FE) methods for the calculation of magnetohydrodynamic (MHD) equilibrium configurations in helically symmetric systems. The present schemes, in which helical symmetry is taken into account, allow us to reduce the storage-space in comparison with fully three-dimensional schemes.
In this paper, first, we introduce a variational form of the helically symmetric MHD equilibrium equation in twisted coordinates to obtain an FE formulation. Secondly, we introduce a boundary integral equation for a BE formulation. The simultaneous equations to be iteratively solved are also derived in the above formulations. Finally, both FE and BE solutions are shown to be in good agreement with the exact one for the linear equilibrium equation. Moreover, it is shown that, in nonlinear equilibrium calculations, FE and BE solutions sufficiently fast converge by the Marder-Weitzner iteration while they vibrate with slowly decreasing amplitudes by the Picard iteration.
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