### Abstract

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 second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ 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.

Original language | English (US) |
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Pages (from-to) | 263-282 |

Number of pages | 20 |

Journal | Journal of Computational Physics |

Volume | 359 |

DOIs | |

State | Published - Apr 15 2018 |

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### Keywords

- Beltrami field
- Force-free fields
- Generalized Debye sources
- Magnetohydrodynamics
- Plasma physics
- Taylor states

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)
- Computer Science Applications

### Cite this

**An integral equation-based numerical solver for Taylor states in toroidal geometries.** / O'Neil, Michael; Cerfon, Antoine J.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - An integral equation-based numerical solver for Taylor states in toroidal geometries

AU - O'Neil, Michael

AU - Cerfon, Antoine J.

PY - 2018/4/15

Y1 - 2018/4/15

N2 - 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 second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ 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.

AB - 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 second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ 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.

KW - Beltrami field

KW - Force-free fields

KW - Generalized Debye sources

KW - Magnetohydrodynamics

KW - Plasma physics

KW - Taylor states

UR - http://www.scopus.com/inward/record.url?scp=85041680008&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041680008&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2018.01.004

DO - 10.1016/j.jcp.2018.01.004

M3 - Article

AN - SCOPUS:85041680008

VL - 359

SP - 263

EP - 282

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -