Closed orbits of MHD equilibria with orientation-reversing symmetry
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909416646770688 |
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| author | Perrella, David |
| author_facet | Perrella, David |
| contents | As a generalisation of the periodic orbit structure often seen in reflection or mirror symmetric MHD equilibria, we consider equilibria with other orientation-reversing symmetries. An example of such a symmetry, which is a not a reflection, is the parity transformation $(x,y,z) \mapsto (-x,-y,-z)$ in $\mathbb{R}^3$. It is shown under any orientation-reversing isometry, that if the pressure function is assumed to have toroidally nested level sets, then all orbits on the tori are necessarily periodic. The techniques involved are almost entirely topological in nature and give rise to a handy index describing how a diffeomorphism of $\mathbb{R}^3$ alters the poloidal and toroidal curves of an invariant embedded 2-torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04504 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Closed orbits of MHD equilibria with orientation-reversing symmetry Perrella, David Dynamical Systems Mathematical Physics Differential Geometry 35Q31, 76W05, 53Z05, 53C80 (Primary) 37C10 (Secondary) As a generalisation of the periodic orbit structure often seen in reflection or mirror symmetric MHD equilibria, we consider equilibria with other orientation-reversing symmetries. An example of such a symmetry, which is a not a reflection, is the parity transformation $(x,y,z) \mapsto (-x,-y,-z)$ in $\mathbb{R}^3$. It is shown under any orientation-reversing isometry, that if the pressure function is assumed to have toroidally nested level sets, then all orbits on the tori are necessarily periodic. The techniques involved are almost entirely topological in nature and give rise to a handy index describing how a diffeomorphism of $\mathbb{R}^3$ alters the poloidal and toroidal curves of an invariant embedded 2-torus. |
| title | Closed orbits of MHD equilibria with orientation-reversing symmetry |
| topic | Dynamical Systems Mathematical Physics Differential Geometry 35Q31, 76W05, 53Z05, 53C80 (Primary) 37C10 (Secondary) |
| url | https://arxiv.org/abs/2411.04504 |