Translationally symmetric extended MHD via Hamiltonian reduction: EnergyCasimir equilibria
Abstract
The Hamiltonian structure of ideal translationally symmetric extended MHD (XMHD) is obtained by employing a method of Hamiltonian reduction on the threedimensional noncanonical Poisson bracket of XMHD. The existence of the continuous spatial translation symmetry allows the introduction of Clebschlike forms for the magnetic and velocity fields. Upon employing the chain rule for functional derivatives, the 3D Poisson bracket is reduced to its symmetric counterpart. The sets of symmetric Hall, Inertial, and extended MHD Casimir invariants are identified, and used to obtain energyCasimir variational principles for generalized XMHD equilibrium equations with arbitrary macroscopic flows. The obtained set of generalized equations is cast into GradShafranovBernoulli (GSB) type, and special cases are investigated: static plasmas, equilibria with longitudinal flows only, and Hall MHD equilibria, where the electron inertia is neglected. The barotropic Hall MHD equilibrium equations are derived as a limiting case of the XMHD GSB system, and a numerically computed equilibrium configuration is presented that shows the separation of ionflow from electromagnetic surfaces.
 Authors:

 Univ. of Ioannina, Ioannina (Greece). Dept. of Physics
 Univ. of Texas, Austin, TX (United States). Dept. of Physics and Inst. for Fusion Studies
 Publication Date:
 Research Org.:
 Univ. of Texas, Austin, TX (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1535314
 Alternate Identifier(s):
 OSTI ID: 1374779
 Grant/Contract Number:
 FG0580ET53088
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 24; Journal Issue: 9; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; physics
Citation Formats
Kaltsas, D. A., Throumoulopoulos, G. N., and Morrison, P. J. Translationally symmetric extended MHD via Hamiltonian reduction: EnergyCasimir equilibria. United States: N. p., 2017.
Web. doi:10.1063/1.4986013.
Kaltsas, D. A., Throumoulopoulos, G. N., & Morrison, P. J. Translationally symmetric extended MHD via Hamiltonian reduction: EnergyCasimir equilibria. United States. doi:10.1063/1.4986013.
Kaltsas, D. A., Throumoulopoulos, G. N., and Morrison, P. J. Fri .
"Translationally symmetric extended MHD via Hamiltonian reduction: EnergyCasimir equilibria". United States. doi:10.1063/1.4986013. https://www.osti.gov/servlets/purl/1535314.
@article{osti_1535314,
title = {Translationally symmetric extended MHD via Hamiltonian reduction: EnergyCasimir equilibria},
author = {Kaltsas, D. A. and Throumoulopoulos, G. N. and Morrison, P. J.},
abstractNote = {The Hamiltonian structure of ideal translationally symmetric extended MHD (XMHD) is obtained by employing a method of Hamiltonian reduction on the threedimensional noncanonical Poisson bracket of XMHD. The existence of the continuous spatial translation symmetry allows the introduction of Clebschlike forms for the magnetic and velocity fields. Upon employing the chain rule for functional derivatives, the 3D Poisson bracket is reduced to its symmetric counterpart. The sets of symmetric Hall, Inertial, and extended MHD Casimir invariants are identified, and used to obtain energyCasimir variational principles for generalized XMHD equilibrium equations with arbitrary macroscopic flows. The obtained set of generalized equations is cast into GradShafranovBernoulli (GSB) type, and special cases are investigated: static plasmas, equilibria with longitudinal flows only, and Hall MHD equilibria, where the electron inertia is neglected. The barotropic Hall MHD equilibrium equations are derived as a limiting case of the XMHD GSB system, and a numerically computed equilibrium configuration is presented that shows the separation of ionflow from electromagnetic surfaces.},
doi = {10.1063/1.4986013},
journal = {Physics of Plasmas},
number = 9,
volume = 24,
place = {United States},
year = {2017},
month = {8}
}
Web of Science
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Works referencing / citing this record:
Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles
journal, May 2018
 Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J.
 Journal of Plasma Physics, Vol. 84, Issue 3
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Ellipticity conditions for the extended MHD GradShafranovBernoulli equilibrium equations
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 Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J.
 Physics of Plasmas, Vol. 26, Issue 2
EnergyCasimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria
journal, January 2020
 Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J.
 Physics of Plasmas, Vol. 27, Issue 1