Hamiltonian structure of single-helicity, incompressible magnetohydrodynamics and application to magnetorotational instability
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916500318715904 |
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| author | Furukawa, M. Hirota, M. |
| author_facet | Furukawa, M. Hirota, M. |
| contents | A four-field reduced model of single helicity, incompressible MHD is derived in cylindrical geometry. An appropriate set of noncanonical variables is found, and the Hamiltonian, the Lie-Poisson bracket and the Casimir invariants are clarified. Detailed proofs of properties of the Lie-Poisson bracket, (i) antisymmetry, (ii) Leibniz rule, and (iii) Jacobi identity, are given. Two applications are presented: the first is that the local dispersion relation of axisymmetric magnetohydrodynamics (MRI) is properly reproduced, and the second is that linear stability analyses including negative-energy MRI were successfully performed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05745 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hamiltonian structure of single-helicity, incompressible magnetohydrodynamics and application to magnetorotational instability Furukawa, M. Hirota, M. Plasma Physics A four-field reduced model of single helicity, incompressible MHD is derived in cylindrical geometry. An appropriate set of noncanonical variables is found, and the Hamiltonian, the Lie-Poisson bracket and the Casimir invariants are clarified. Detailed proofs of properties of the Lie-Poisson bracket, (i) antisymmetry, (ii) Leibniz rule, and (iii) Jacobi identity, are given. Two applications are presented: the first is that the local dispersion relation of axisymmetric magnetohydrodynamics (MRI) is properly reproduced, and the second is that linear stability analyses including negative-energy MRI were successfully performed. |
| title | Hamiltonian structure of single-helicity, incompressible magnetohydrodynamics and application to magnetorotational instability |
| topic | Plasma Physics |
| url | https://arxiv.org/abs/2410.05745 |