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Generalized Grad-Shafranov equation for non-axisymmetric MHD equilibria
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Burby, J. W., Kallinikos, N. and MacKay, Robert S. (2020) Generalized Grad-Shafranov equation for non-axisymmetric MHD equilibria. Physics of Plasmas, 27 (10). 102504 . doi:10.1063/5.0015420 ISSN 1070-664X.
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Official URL: https://doi.org/10.1063/5.0015420
Abstract
The structure of static MHD equilibria that admit continuous families of Euclidean symmetries is well understood. Such field configurations are governed by the classical Grad-Shafranov equation, which is a single elliptic PDE in two space dimensions. By revealing a hidden symmetry, we show that in fact all smooth solutions of the equilibrium equations with non-vanishing pressure gradients away from the magnetic axis satisfy a generalization of the Grad-Shafranov equation. In contrast to solutions of the classical Grad-Shafranov equation, solutions of the generalized equation are not automatically equilibria, but instead only satisfy force balance averaged over the one-parameter hidden symmetry. We then explain how the generalized Grad-Shafranov equation can be used to reformulate the problem of finding exact three-dimensional smooth solutions of the equilibrium equations as finding an optimal volume-preserving symmetry.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
Library of Congress Subject Headings (LCSH): | Plasma dynamics, Magnetohydrodynamics | |||||||||
Journal or Publication Title: | Physics of Plasmas | |||||||||
Publisher: | American Institute of Physics | |||||||||
ISSN: | 1070-664X | |||||||||
Official Date: | 2 September 2020 | |||||||||
Dates: |
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Volume: | 27 | |||||||||
Number: | 10 | |||||||||
Article Number: | 102504 | |||||||||
DOI: | 10.1063/5.0015420 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Reuse Statement (publisher, data, author rights): | The following article has been accepted by Physics of Plasmas. After it is published, it will be found at https://aip.scitation.org/journal/php | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Copyright Holders: | © 2020 Author(s). Published under license by AIP Publishing. | |||||||||
Date of first compliant deposit: | 16 September 2020 | |||||||||
Date of first compliant Open Access: | 17 September 2020 | |||||||||
RIOXX Funder/Project Grant: |
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