Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Examples with translation symmetry
Abstract
Because different constraints are imposed, stability conditions for dissipationless fluids and magnetofluids may take different forms when derived within the Lagrangian, Eulerian (energy-Casimir), or dynamically accessible frameworks. This is in particular the case when flows are present. These differences are explored explicitly here by working out in detail two magnetohydrodynamic examples: convection against gravity in a stratified fluid and translationally invariant perturbations of a rotating magnetized plasma pinch. In this second example, we show in explicit form how to perform the time-dependent relabeling introduced in Andreussi et al. [Phys. Plasmas 20, 092104 (2013)] that makes it possible to reformulate Eulerian equilibria with flows as Lagrangian equilibria in the relabeled variables. The procedures detailed in the present article provide a paradigm that can be applied to more general plasma configurations and in addition extended to more general plasma descriptions where dissipation is absent.
- Authors:
-
- SITAEL S.p.A., Pisa (Italy)
- Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies and Dept. of Physics
- Dipt. di Fisica E. Fermi, Pisa (Italy)
- Publication Date:
- Research Org.:
- Univ. of Texas, Austin, TX (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1535285
- Alternate Identifier(s):
- OSTI ID: 1329491
- Grant/Contract Number:
- FG02-04ER54742; FG02-04ER-54742
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 23; Journal Issue: 10; Journal ID: ISSN 1070-664X
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; physics
Citation Formats
Andreussi, T., Morrison, P. J., and Pegoraro, F. Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Examples with translation symmetry. United States: N. p., 2016.
Web. doi:10.1063/1.4964900.
Andreussi, T., Morrison, P. J., & Pegoraro, F. Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Examples with translation symmetry. United States. https://doi.org/10.1063/1.4964900
Andreussi, T., Morrison, P. J., and Pegoraro, F. Thu .
"Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Examples with translation symmetry". United States. https://doi.org/10.1063/1.4964900. https://www.osti.gov/servlets/purl/1535285.
@article{osti_1535285,
title = {Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Examples with translation symmetry},
author = {Andreussi, T. and Morrison, P. J. and Pegoraro, F.},
abstractNote = {Because different constraints are imposed, stability conditions for dissipationless fluids and magnetofluids may take different forms when derived within the Lagrangian, Eulerian (energy-Casimir), or dynamically accessible frameworks. This is in particular the case when flows are present. These differences are explored explicitly here by working out in detail two magnetohydrodynamic examples: convection against gravity in a stratified fluid and translationally invariant perturbations of a rotating magnetized plasma pinch. In this second example, we show in explicit form how to perform the time-dependent relabeling introduced in Andreussi et al. [Phys. Plasmas 20, 092104 (2013)] that makes it possible to reformulate Eulerian equilibria with flows as Lagrangian equilibria in the relabeled variables. The procedures detailed in the present article provide a paradigm that can be applied to more general plasma configurations and in addition extended to more general plasma descriptions where dissipation is absent.},
doi = {10.1063/1.4964900},
journal = {Physics of Plasmas},
number = 10,
volume = 23,
place = {United States},
year = {Thu Oct 20 00:00:00 EDT 2016},
month = {Thu Oct 20 00:00:00 EDT 2016}
}
Web of Science
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