An integral equation-based numerical solver for Taylor states in toroidal geometries
Abstract
Here 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.
- Authors:
-
- New York University (NYU), NY (United States)
- Publication Date:
- Research Org.:
- New York Univ. (NYU), NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES); US Air Force Office of Scientific Research (AFOSR); US Department of the Navy, Office of Naval Research (ONR)
- OSTI Identifier:
- 1538427
- Alternate Identifier(s):
- OSTI ID: 1548839
- Grant/Contract Number:
- FG02-86ER53223; SC0012398; FA9550-10-1-0180; N00014-17-1-2059; N00014-17-1-2451
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Volume: 359; Journal Issue: C; Journal ID: ISSN 0021-9991
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; Beltrami field; generalized debye sources; plasma physics; force-free fields; Taylor states; magnetohydrodynamics
Citation Formats
O'Neil, Michael, and Cerfon, Antoine J. An integral equation-based numerical solver for Taylor states in toroidal geometries. United States: N. p., 2018.
Web. doi:10.1016/j.jcp.2018.01.004.
O'Neil, Michael, & Cerfon, Antoine J. An integral equation-based numerical solver for Taylor states in toroidal geometries. United States. https://doi.org/10.1016/j.jcp.2018.01.004
O'Neil, Michael, and Cerfon, Antoine J. Tue .
"An integral equation-based numerical solver for Taylor states in toroidal geometries". United States. https://doi.org/10.1016/j.jcp.2018.01.004. https://www.osti.gov/servlets/purl/1538427.
@article{osti_1538427,
title = {An integral equation-based numerical solver for Taylor states in toroidal geometries},
author = {O'Neil, Michael and Cerfon, Antoine J.},
abstractNote = {Here 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.},
doi = {10.1016/j.jcp.2018.01.004},
journal = {Journal of Computational Physics},
number = C,
volume = 359,
place = {United States},
year = {Tue Jan 09 00:00:00 EST 2018},
month = {Tue Jan 09 00:00:00 EST 2018}
}
Web of Science
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