Metastability of stratified magnetohydrostatic equilibria and their relaxation
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929620181319680 |
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| author | Hosking, David N. Wasserman, David Cowley, Steven C. |
| author_facet | Hosking, David N. Wasserman, David Cowley, Steven C. |
| contents | Motivated by explosive releases of energy in fusion, space and astrophysical plasmas, we consider the nonlinear stability of stratified magnetohydrodynamic (MHD) equilibria against two-dimensional interchanges of straight magnetic-flux tubes. We demonstrate that, even within this restricted class of dynamics, the linear stability of an equilibrium does not guarantee its nonlinear stability: equilibria can be metastable. We show that the minimum-energy state accessible to a metastable equilibrium under non-diffusive 2D dynamics can be found by solving a combinatorial optimisation problem. These minimum-energy states are, to good approximation, the final states reached by our simulations of destabilised metastable equilibria for which turbulent mixing is suppressed by viscosity. To predict the result of fully turbulent relaxation, we construct a statistical mechanical theory based on the maximisation of Boltzmann's mixing entropy. This theory is analogous to the Lynden-Bell statistical mechanics of collisionless stellar systems and plasma, and to the Robert-Sommeria-Miller (RSM) theory of 2D vortex turbulence. Our theory reproduces well the results of our numerical simulations for sufficiently large perturbations to the metastable equilibrium. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01336 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Metastability of stratified magnetohydrostatic equilibria and their relaxation Hosking, David N. Wasserman, David Cowley, Steven C. High Energy Astrophysical Phenomena Fluid Dynamics Plasma Physics Motivated by explosive releases of energy in fusion, space and astrophysical plasmas, we consider the nonlinear stability of stratified magnetohydrodynamic (MHD) equilibria against two-dimensional interchanges of straight magnetic-flux tubes. We demonstrate that, even within this restricted class of dynamics, the linear stability of an equilibrium does not guarantee its nonlinear stability: equilibria can be metastable. We show that the minimum-energy state accessible to a metastable equilibrium under non-diffusive 2D dynamics can be found by solving a combinatorial optimisation problem. These minimum-energy states are, to good approximation, the final states reached by our simulations of destabilised metastable equilibria for which turbulent mixing is suppressed by viscosity. To predict the result of fully turbulent relaxation, we construct a statistical mechanical theory based on the maximisation of Boltzmann's mixing entropy. This theory is analogous to the Lynden-Bell statistical mechanics of collisionless stellar systems and plasma, and to the Robert-Sommeria-Miller (RSM) theory of 2D vortex turbulence. Our theory reproduces well the results of our numerical simulations for sufficiently large perturbations to the metastable equilibrium. |
| title | Metastability of stratified magnetohydrostatic equilibria and their relaxation |
| topic | High Energy Astrophysical Phenomena Fluid Dynamics Plasma Physics |
| url | https://arxiv.org/abs/2401.01336 |