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

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

doi:10.1063/1.4986013

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:2567726

Kaltsas, D. A.; Throumoulopoulos, G. N.;

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:: FG05-80ET53088

OSTI ID:: 2567726

Alternate ID(s):: OSTI ID: 1535314
OSTI ID: 1374779

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

Publisher:: American Institute of PhysicsCopyright Statement

Country of Publication:: United States

Language:: English

References (32)

Über die Ausbreitung von Wellen in einem Plasma Lüst, Reimar Fortschritte der Physik, Vol. 7, Issue 9 https://doi.org/10.1002/prop.19590070902	journal	January 1959
Singular Casimir Elements of the Euler Equation and Equilibrium Points Yoshida, Zensho; Morrison, Philip J.; Dobarro, Fernando Journal of Mathematical Fluid Mechanics, Vol. 16, Issue 1 https://doi.org/10.1007/s00021-013-0143-4	journal	April 2013
Inertial magnetohydrodynamics Lingam, M.; Morrison, P. J.; Tassi, E. Physics Letters A, Vol. 379, Issue 6 https://doi.org/10.1016/j.physleta.2014.12.008	journal	March 2015
Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics Lingam, Manasvi; Miloshevich, George; Morrison, Philip J. Physics Letters A, Vol. 380, Issue 31-32 https://doi.org/10.1016/j.physleta.2016.05.024	journal	July 2016
Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field Moawad, S. M. Journal of Plasma Physics, Vol. 79, Issue 5 https://doi.org/10.1017/S0022377813000627	journal	June 2013
Azimuthally symmetric magnetohydrodynamic and two-fluid equilibria with arbitrary flows McClements, K. G.; Thyagaraja, A. Monthly Notices of the Royal Astronomical Society, Vol. 323, Issue 3 https://doi.org/10.1046/j.1365-8711.2001.04290.x	journal	May 2001
Variational principles for stationary one- and two-fluid equilibria of axisymmetric laboratory and astrophysical plasmas Goedbloed, J. P. Physics of Plasmas, Vol. 11, Issue 12 https://doi.org/10.1063/1.1808453	journal	December 2004
On Hall magnetohydrodynamics equilibria Throumoulopoulos, G. N.; Tasso, H. Physics of Plasmas, Vol. 13, Issue 10 https://doi.org/10.1063/1.2358111	journal	October 2006
On the variational approach to axisymmetric magnetohydrodynamic equilibria Andreussi, T.; Pegoraro, F. Physics of Plasmas, Vol. 15, Issue 9 https://doi.org/10.1063/1.2980426	journal	September 2008
Two-fluid low-collisionality equilibrium model and application to spherical torus plasmas Ishida, Akio; Steinhauer, Loren C.; Peng, Y. -K. Martin Physics of Plasmas, Vol. 17, Issue 12 https://doi.org/10.1063/1.3526600	journal	December 2010
Hamiltonian magnetohydrodynamics: Helically symmetric formulation, Casimir invariants, and equilibrium variational principles Andreussi, T.; Morrison, P. J.; Pegoraro, F. Physics of Plasmas, Vol. 19, Issue 5 https://doi.org/10.1063/1.4714761	journal	May 2012
Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory Andreussi, T.; Morrison, P. J.; Pegoraro, F. Physics of Plasmas, Vol. 20, Issue 9 https://doi.org/10.1063/1.4819779	journal	September 2013
Ertel's vorticity theorem and new flux surfaces in multi-fluid plasmas Hameiri, Eliezer Physics of Plasmas, Vol. 20, Issue 9 https://doi.org/10.1063/1.4820769	journal	September 2013
On energy conservation in extended magnetohydrodynamics Kimura, Keiji; Morrison, P. J. Physics of Plasmas, Vol. 21, Issue 8 https://doi.org/10.1063/1.4890955	journal	August 2014
Action principles for extended magnetohydrodynamic models Keramidas Charidakos, I.; Lingam, M.; Morrison, P. J. Physics of Plasmas, Vol. 21, Issue 9 https://doi.org/10.1063/1.4896336	journal	September 2014
Erratum: “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory” [Phys. Plasmas 20, 092104 (2013)] Andreussi, T.; Morrison, P. J.; Pegoraro, F. Physics of Plasmas, Vol. 22, Issue 3 https://doi.org/10.1063/1.4916504	journal	March 2015
Remarkable connections between extended magnetohydrodynamics models Lingam, M.; Morrison, P. J.; Miloshevich, G. Physics of Plasmas, Vol. 22, Issue 7 https://doi.org/10.1063/1.4926821	journal	July 2015
Two-fluid equilibrium with flow: FLOW2 Guazzotto, L.; Betti, R. Physics of Plasmas, Vol. 22, Issue 9 https://doi.org/10.1063/1.4929854	journal	September 2015
Derivation of the Hall and extended magnetohydrodynamics brackets D'Avignon, Eric C.; Morrison, Philip J.; Lingam, Manasvi Physics of Plasmas, Vol. 23, Issue 6 https://doi.org/10.1063/1.4952641	journal	June 2016
Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Examples with translation symmetry Andreussi, T.; Morrison, P. J.; Pegoraro, F. Physics of Plasmas, Vol. 23, Issue 10 https://doi.org/10.1063/1.4964900	journal	October 2016
Structure and computation of two-dimensional incompressible extended MHD Grasso, D.; Tassi, E.; Abdelhamid, H. M. Physics of Plasmas, Vol. 24, Issue 1 https://doi.org/10.1063/1.4974039	journal	January 2017
Structure and structure-preserving algorithms for plasma physics Morrison, P. J. Physics of Plasmas, Vol. 24, Issue 5 https://doi.org/10.1063/1.4982054	journal	April 2017
Hamiltonian four-field model for nonlinear tokamak dynamics Hazeltine, R. D.; Hsu, C. T.; Morrison, P. J. Physics of Fluids, Vol. 30, Issue 10 https://doi.org/10.1063/1.866527	journal	January 1987
Formalism for multi-fluid equilibria with flow Steinhauer, Loren C. Physics of Plasmas, Vol. 6, Issue 7 https://doi.org/10.1063/1.873230	journal	July 1999
Hamiltonian formulation and analysis of a collisionless fluid reconnection model Tassi, E.; Morrison, P. J.; Waelbroeck, F. L. Plasma Physics and Controlled Fusion, Vol. 50, Issue 8 https://doi.org/10.1088/0741-3335/50/8/085014	journal	June 2008
MHD equilibrium variational principles with symmetry Andreussi, T.; Morrison, P. J.; Pegoraro, F. Plasma Physics and Controlled Fusion, Vol. 52, Issue 5 https://doi.org/10.1088/0741-3335/52/5/055001	journal	March 2010
Canonical Hamiltonian mechanics of Hall magnetohydrodynamics and its limit to ideal magnetohydrodynamics Yoshida, Z.; Hameiri, E. Journal of Physics A: Mathematical and Theoretical, Vol. 46, Issue 33 https://doi.org/10.1088/1751-8113/46/33/335502	journal	July 2013
Hamiltonian formalism of extended magnetohydrodynamics Abdelhamid, H. M.; Kawazura, Y.; Yoshida, Z. Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue 23 https://doi.org/10.1088/1751-8113/48/23/235502	journal	May 2015
Studies on Magneto-Hydrodynamic Waves and other Anisotropic Wave Motions Lighthill, M. J. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 252, Issue 1014 https://doi.org/10.1098/rsta.1960.0010	journal	March 1960
Modification of magnetohydrodynamic waves by the relativistic Hall effect Kawazura, Yohei Physical Review E, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevE.96.013207	journal	July 2017
Noncanonical Hamiltonian Density Formulation of Hydrodynamics and Ideal Magnetohydrodynamics Morrison, Philip J.; Greene, John M. Physical Review Letters, Vol. 45, Issue 10 https://doi.org/10.1103/PhysRevLett.45.790	journal	September 1980
Hamiltonian description of the ideal fluid Morrison, P. J. Reviews of Modern Physics, Vol. 70, Issue 2 https://doi.org/10.1103/RevModPhys.70.467	journal	April 1998

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