2016/11/04 by Michael O’Neil, Antoine Cerfon, O'Neil, Michael +1
Biochemistry, Genetics and Molecular Biology · Engineering · Materials Science · #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Geomagnetism and Paleomagnetism Studies #Magnetic Bearings and Levitation Dynamics #Magnetic Properties and Applications #Numerical Analysis (math.NA) #Plasma Physics (physics.plasm-ph)
paper · pdf · doi:10.48550/arxiv.1611.01420
openalex publication_date 2016/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop an algorithm for the numerical calculation of Taylor states in\ntoroidal and toroidal shell geometries using an analytical framework developed\nfor the solution to the time-harmonic Maxwell equations. Taylor states are a\nspecial case of what are known as Beltrami fields, or linear force-free fields.\nThe scheme of this work relies on the generalized Debye source representation\nof Maxwell fields and an integral representation of Beltrami fields which\nimmediately yields a well-conditioned second-kind integral equation. This\nintegral equation has a unique solution whenever the Beltrami parameter\n\λ is not a member of a discrete, countable set of resonances which\nphysically correspond to spontaneous symmetry breaking. Several numerical\nexamples relevant to magnetohydrodynamic equilibria calculations are provided.\nLastly, our approach easily generalizes to arbitrary geometries, both bounded\nand unbounded, and of varying genus.\n