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:

 Department of Physics, University of Ioannina, GR 451 10 Ioannina, Greece
 Department of Physics and Institute for Fusion Studies, University of Texas, Austin, Texas 78712, USA
 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; FG0580ET53088
 Resource Type:
 Journal Article: 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:
 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},
issn = {1070664X},
number = 9,
volume = 24,
place = {United States},
year = {2017},
month = {9}
}
Web of Science