Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria

Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J.

doi:10.1063/1.4986013

Title: Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria

Journal Article · Fri Aug 11 00:00:00 EDT 2017 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4986013· OSTI ID:1535314

Kaltsas, D. A. ^[1]; Throumoulopoulos, G. N. ^[1];

^[2]

Univ. of Ioannina, Ioannina (Greece). Dept. of Physics
Univ. of Texas, Austin, TX (United States). Dept. of Physics and Inst. for Fusion Studies

The Hamiltonian structure of ideal translationally symmetric extended MHD (XMHD) is obtained by employing a method of Hamiltonian reduction on the three-dimensional noncanonical Poisson bracket of XMHD. The existence of the continuous spatial translation symmetry allows the introduction of Clebsch-like 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 energy-Casimir variational principles for generalized XMHD equilibrium equations with arbitrary macroscopic flows. The obtained set of generalized equations is cast into Grad-Shafranov-Bernoulli (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 ion-flow from electro-magnetic surfaces.

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Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG05-80ET-53088

OSTI ID:: 1535314

Alternate ID(s):: OSTI ID: 1374779

Journal Information:: Physics of Plasmas, Vol. 24, Issue 9; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 9 works

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References (38)

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Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J. Journal of Plasma Physics, Vol. 84, Issue 3 https://doi.org/10.1017/s0022377818000338	journal	May 2018
Direction of cascades in a magnetofluid model with electron skin depth and ion sound Larmor radius scales Miloshevich, George; Morrison, Philip J.; Tassi, Emanuele Physics of Plasmas, Vol. 25, Issue 7 https://doi.org/10.1063/1.5023089	journal	July 2018
Ellipticity conditions for the extended MHD Grad-Shafranov-Bernoulli equilibrium equations Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J. Physics of Plasmas, Vol. 26, Issue 2 https://doi.org/10.1063/1.5080997	journal	February 2019
Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J. Physics of Plasmas, Vol. 27, Issue 1 https://doi.org/10.1063/1.5125573	journal	January 2020
Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J. arXiv https://doi.org/10.48550/arxiv.1908.08821	text	January 2019
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