An integral equation-based numerical solver for Taylor states in toroidal geometries

JOURNAL OF COMPUTATIONAL PHYSICS

卷:359

Article

O'Neil, Michael^1,2  Cerfon, Antoine J.¹ 

[1] NYU, Courant Inst, 251 Mercer St, New York, NY 10003 USA

[2] NYU, Tandon Sch Engn, New York, NY 10003 USA

关键词: Beltrami field;    Generalized Debye sources;    Plasma physics;    Force-free fields;    Taylor states;    Magnetohydrodynamics;   

DOI  :  10.1016/j.jcp.2018.01.004

来源: Elsevier

【 摘 要 】

We present an algorithm for the numerical calculation of Taylor states in toroidal and toroidal-shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. Taylor states are a special case of what are known as Beltrami fields, or linear force-free fields. The scheme of this work relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned secondkind integral equation. This integral equation has a unique solution whenever the Beltrami parameter lambda is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free