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Approximate symmetries of guiding-centre motion
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Burby, J. W., Kallinikos, N. and MacKay, Robert S. (2021) Approximate symmetries of guiding-centre motion. Journal of Physics A: Mathematical and Theoretical, 54 (12). 125202. doi:10.1088/1751-8121/abe58a ISSN 1751-8113.
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Official URL: https://doi.org/10.1088/1751-8121/abe58a
Abstract
In a strong, inhomogeneous magnetic field, charged particle dynamics may be studied in the guiding-centre approximation, which is known to be Hamiltonian. When the magnetic field is quasisymmetric, the first-order guiding-centre Hamiltonian structure admits a continuous symmetry, and therefore a conserved quantity in addition to the energy. Since the first-order guiding-centre system is only an approximation, it is also interesting to consider approximate symmetries of the guiding-centre Hamiltonian structure. We find that any approximate spatial symmetry coincides with quasisymmetry at first order. For approximate phase-space symmetries, we derive weaker conditions than quasisymmetry. The latter include "weak quasisymmetry" as a subcase, recently proposed by Rodriguez et al. Our results, however, show that weak quasisymmetry is necessarily non-spatial at first order. Finally, if the magnetic field is constrained to satisfy magnetohydrostatic force balance then an approximate symmetry must agree with quasisymmetry to first order.
| 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): | Quasisymmetric groups, Hamiltonian systems , Approximation theory | |||||||||
| Journal or Publication Title: | Journal of Physics A: Mathematical and Theoretical | |||||||||
| Publisher: | IOP Publishing Ltd | |||||||||
| ISSN: | 1751-8113 | |||||||||
| Official Date: | 2 March 2021 | |||||||||
| Dates: |
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| Volume: | 54 | |||||||||
| Number: | 12 | |||||||||
| Article Number: | 125202 | |||||||||
| DOI: | 10.1088/1751-8121/abe58a | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1751-8121/abe58a | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Copyright Holders: | © 2021 IOP Publishing Ltd | |||||||||
| Date of first compliant deposit: | 11 February 2021 | |||||||||
| Date of first compliant Open Access: | 2 March 2022 | |||||||||
| RIOXX Funder/Project Grant: |
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