Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles
Abstract
Hamiltonian extended magnetohydrodynamics (XMHD) is restricted to respect helical symmetry by reducing the Poisson bracket for the three-dimensional dynamics to a helically symmetric one, as an extension of the previous study for translationally symmetric XMHD (Kaltsaset al.,Phys. Plasmas, vol. 24, 2017, 092504). Four families of Casimir invariants are obtained directly from the symmetric Poisson bracket and they are used to construct Energy–Casimir variational principles for deriving generalized XMHD equilibrium equations with arbitrary macroscopic flows. The system is then cast into the form of Grad–Shafranov–Bernoulli equilibrium equations. The axisymmetric and the translationally symmetric formulations can be retrieved as geometric reductions of the helically symmetric one. As special cases, the derivation of the corresponding equilibrium equations for incompressible plasmas is discussed and the helically symmetric equilibrium equations for the Hall MHD system are obtained upon neglecting electron inertia. An example of an incompressible double-Beltrami equilibrium is presented in connection with a magnetic configuration having non-planar helical magnetic axis.
- Authors:
- Publication Date:
- Research Org.:
- Univ. of Texas, Austin, TX (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1538937
- DOE Contract Number:
- FG05-80ET53088
- Resource Type:
- Journal Article
- Journal Name:
- Journal of Plasma Physics
- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 3; Journal ID: ISSN 0022-3778
- Publisher:
- Cambridge University Press
- Country of Publication:
- United States
- Language:
- English
- Subject:
- Physics
Citation Formats
Kaltsas, D. A., Throumoulopoulos, G. N., and Morrison, P. J. Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles. United States: N. p., 2018.
Web. doi:10.1017/s0022377818000338.
Kaltsas, D. A., Throumoulopoulos, G. N., & Morrison, P. J. Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles. United States. https://doi.org/10.1017/s0022377818000338
Kaltsas, D. A., Throumoulopoulos, G. N., and Morrison, P. J. Thu .
"Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles". United States. https://doi.org/10.1017/s0022377818000338.
@article{osti_1538937,
title = {Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles},
author = {Kaltsas, D. A. and Throumoulopoulos, G. N. and Morrison, P. J.},
abstractNote = {Hamiltonian extended magnetohydrodynamics (XMHD) is restricted to respect helical symmetry by reducing the Poisson bracket for the three-dimensional dynamics to a helically symmetric one, as an extension of the previous study for translationally symmetric XMHD (Kaltsaset al.,Phys. Plasmas, vol. 24, 2017, 092504). Four families of Casimir invariants are obtained directly from the symmetric Poisson bracket and they are used to construct Energy–Casimir variational principles for deriving generalized XMHD equilibrium equations with arbitrary macroscopic flows. The system is then cast into the form of Grad–Shafranov–Bernoulli equilibrium equations. The axisymmetric and the translationally symmetric formulations can be retrieved as geometric reductions of the helically symmetric one. As special cases, the derivation of the corresponding equilibrium equations for incompressible plasmas is discussed and the helically symmetric equilibrium equations for the Hall MHD system are obtained upon neglecting electron inertia. An example of an incompressible double-Beltrami equilibrium is presented in connection with a magnetic configuration having non-planar helical magnetic axis.},
doi = {10.1017/s0022377818000338},
url = {https://www.osti.gov/biblio/1538937},
journal = {Journal of Plasma Physics},
issn = {0022-3778},
number = 3,
volume = 84,
place = {United States},
year = {2018},
month = {5}
}
Works referenced in this record:
On Force-Free Magnetic Fields.
journal, July 1957
- Chandrasekhar, S.; Kendall, P. C.
- The Astrophysical Journal, Vol. 126
Structure and computation of two-dimensional incompressible extended MHD
journal, January 2017
- Grasso, D.; Tassi, E.; Abdelhamid, H. M.
- Physics of Plasmas, Vol. 24, Issue 1
Ideal magnetohydrodynamic equilibria with helical symmetry and incompressible flows
journal, October 1999
- Throumoulopoulos, G. N.; Tasso, H.
- Journal of Plasma Physics, Vol. 62, Issue 4
Double Curl Beltrami Flow: Diamagnetic Structures
journal, November 1998
- Mahajan, S. M.; Yoshida, Z.
- Physical Review Letters, Vol. 81, Issue 22
Persistent density perturbations at rational- q surfaces following pellet injection in the Joint European Torus
journal, November 1987
- Weller, A.; Cheetham, A. D.; Edwards, A. W.
- Physical Review Letters, Vol. 59, Issue 20
Hamiltonian four-field model for nonlinear tokamak dynamics
journal, January 1987
- Hazeltine, R. D.; Hsu, C. T.; Morrison, P. J.
- Physics of Fluids, Vol. 30, Issue 10
Studies on Magneto-Hydrodynamic Waves and other Anisotropic Wave Motions
journal, March 1960
- Lighthill, M. J.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 252, Issue 1014
Lyapunov stability analysis of magnetohydrodynamic plasma equilibria with axisymmetric toroidal flow
journal, January 1988
- Almaguer, Juan Antonio; Hameiri, Eliezer; Herrera, Julio
- Physics of Fluids, Vol. 31, Issue 7
Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field
journal, June 2013
- Moawad, S. M.
- Journal of Plasma Physics, Vol. 79, Issue 5
Action principles for relativistic extended magnetohydrodynamics: A unified theory of magnetofluid models
journal, February 2017
- Kawazura, Yohei; Miloshevich, George; Morrison, Philip J.
- Physics of Plasmas, Vol. 24, Issue 2
Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria
journal, September 2017
- Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J.
- Physics of Plasmas, Vol. 24, Issue 9
Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory
journal, September 2013
- Andreussi, T.; Morrison, P. J.; Pegoraro, F.
- Physics of Plasmas, Vol. 20, Issue 9
Hamiltonian magnetohydrodynamics: Helically symmetric formulation, Casimir invariants, and equilibrium variational principles
journal, May 2012
- Andreussi, T.; Morrison, P. J.; Pegoraro, F.
- Physics of Plasmas, Vol. 19, Issue 5
On the variational approach to axisymmetric magnetohydrodynamic equilibria
journal, September 2008
- Andreussi, T.; Pegoraro, F.
- Physics of Plasmas, Vol. 15, Issue 9
Hamiltonian description of the ideal fluid
journal, April 1998
- Morrison, P. J.
- Reviews of Modern Physics, Vol. 70, Issue 2
On the Stability of Plasma in Static Equilibrium
journal, January 1958
- Kruskal, M. D.; Oberman, C. R.
- Physics of Fluids, Vol. 1, Issue 4
MHD equilibrium variational principles with symmetry
journal, March 2010
- Andreussi, T.; Morrison, P. J.; Pegoraro, F.
- Plasma Physics and Controlled Fusion, Vol. 52, Issue 5
Helical equilibria and magnetic structures in the reversed field pinch and analogies to the tokamak and stellarator
journal, November 2009
- Puiatti, M. E.; Alfier, A.; Auriemma, F.
- Plasma Physics and Controlled Fusion, Vol. 51, Issue 12
Astrophysical jets and outflows
journal, January 2005
- de Gouveia Dal Pino, Elisabete M.
- Advances in Space Research, Vol. 35, Issue 5
Inertial magnetohydrodynamics
journal, March 2015
- Lingam, M.; Morrison, P. J.; Tassi, E.
- Physics Letters A, Vol. 379, Issue 6
Theory and observations of magnetic islands
journal, September 2009
- Waelbroeck, F. L.
- Nuclear Fusion, Vol. 49, Issue 10
Force-free helical equilibria
journal, November 1973
- Barberio-Corsetti, P.
- Plasma Physics, Vol. 15, Issue 11
Variational Principles and Self-Organization in Two-Fluid Plasmas
journal, February 2002
- Yoshida, Z.; Mahajan, S. M.
- Physical Review Letters, Vol. 88, Issue 9
Hall magnetohydrodynamics: Conservation laws and Lyapunov stability
journal, January 1987
- Holm, Darryl D.
- Physics of Fluids, Vol. 30, Issue 5
Helically symmetric equilibria with pressure anisotropy and incompressible plasma flow
journal, December 2017
- Evangelias, A.; Kuiroukidis, A.; Throumoulopoulos, G. N.
- Plasma Physics and Controlled Fusion, Vol. 60, Issue 2
Noncanonical Hamiltonian Density Formulation of Hydrodynamics and Ideal Magnetohydrodynamics
journal, September 1980
- Morrison, Philip J.; Greene, John M.
- Physical Review Letters, Vol. 45, Issue 10
JET snake magnetohydrodynamic equilibria
journal, June 2011
- Cooper, W. A.; Graves, J. P.; Sauter, O.
- Nuclear Fusion, Vol. 51, Issue 7
Nonlinear stability of fluid and plasma equilibria
journal, July 1985
- Holm, Darryl D.; Marsden, Jerrold E.; Ratiu, Tudor
- Physics Reports, Vol. 123, Issue 1-2
On Hall magnetohydrodynamics equilibria
journal, October 2006
- Throumoulopoulos, G. N.; Tasso, H.
- Physics of Plasmas, Vol. 13, Issue 10
Stellarator and tokamak plasmas: a comparison
journal, November 2012
- Helander, P.; Beidler, C. D.; Bird, T. M.
- Plasma Physics and Controlled Fusion, Vol. 54, Issue 12
Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics
journal, August 2014
- Morrison, P. J.; Lingam, M.; Acevedo, R.
- Physics of Plasmas, Vol. 21, Issue 8
Tokamak Magnetohydrodynamic Equilibrium States with Axisymmetric Boundary and a 3D Helical Core
journal, July 2010
- Cooper, W. A.; Graves, J. P.; Pochelon, A.
- Physical Review Letters, Vol. 105, Issue 3
Bifurcation to 3D Helical Magnetic Equilibrium in an Axisymmetric Toroidal Device
journal, December 2011
- Bergerson, W. F.; Auriemma, F.; Chapman, B. E.
- Physical Review Letters, Vol. 107, Issue 25
On energy conservation in extended magnetohydrodynamics
journal, August 2014
- Kimura, Keiji; Morrison, P. J.
- Physics of Plasmas, Vol. 21, Issue 8
Stability of compressible reduced magnetohydrodynamic equilibria—Analogy with magnetorotational instability
journal, April 2013
- Morrison, P. J.; Tassi, E.; Tronko, N.
- Physics of Plasmas, Vol. 20, Issue 4
Hamiltonian formulation and analysis of a collisionless fluid reconnection model
journal, June 2008
- Tassi, E.; Morrison, P. J.; Waelbroeck, F. L.
- Plasma Physics and Controlled Fusion, Vol. 50, Issue 8
Beltrami fields in plasmas: High-confinement mode boundary layers and high beta equilibria
journal, May 2001
- Yoshida, Z.; Mahajan, S. M.; Ohsaki, S.
- Physics of Plasmas, Vol. 8, Issue 5
A 3D approach to equilibrium, stability and transport studies in RFX-mod improved regimes
journal, November 2010
- Terranova, D.; Bonfiglio, D.; Boozer, A. H.
- Plasma Physics and Controlled Fusion, Vol. 52, Issue 12
Snake-like phenomena in Tore Supra following pellet injection
journal, April 1997
- Pecquet, A. -L; Cristofani, P.; Mattioli, M.
- Nuclear Fusion, Vol. 37, Issue 4
The Confinement of Plasma by the Heliotron Magnetic Field
journal, July 1961
- Uo, Kōji
- Journal of the Physical Society of Japan, Vol. 16, Issue 7
Singular Casimir Elements of the Euler Equation and Equilibrium Points
journal, April 2013
- Yoshida, Zensho; Morrison, Philip J.; Dobarro, Fernando
- Journal of Mathematical Fluid Mechanics, Vol. 16, Issue 1
Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Examples with translation symmetry
journal, October 2016
- Andreussi, T.; Morrison, P. J.; Pegoraro, F.
- Physics of Plasmas, Vol. 23, Issue 10
Self-organized helical equilibria as a new paradigm for ohmically heated fusion plasmas
journal, June 2009
- Lorenzini, R.; Martines, E.; Piovesan, P.
- Nature Physics, Vol. 5, Issue 8
Magnetohydrodynamic equilibrium. III - Helically symmetric fields. IV - Nonequilibrium of nonsymmetric hydrodynamic topologies
journal, August 1982
- Tsinganos, K. C.
- The Astrophysical Journal, Vol. 259
Remarkable connections between extended magnetohydrodynamics models
journal, July 2015
- Lingam, M.; Morrison, P. J.; Miloshevich, G.
- Physics of Plasmas, Vol. 22, Issue 7
Über die Ausbreitung von Wellen in einem Plasma
journal, January 1959
- Lüst, Reimar
- Fortschritte der Physik, Vol. 7, Issue 9
Two-fluid equilibrium with flow: FLOW2
journal, September 2015
- Guazzotto, L.; Betti, R.
- Physics of Plasmas, Vol. 22, Issue 9
Linear stability of certain translationally symmetric MHD equilibria with incompressible flow
journal, January 2017
- Moawad, S. M.; Ramadan, A. A.; Ibrahim, D. A.
- Results in Physics, Vol. 7
Some Stable Hydromagnetic Equilibria
journal, January 1958
- Johnson, J. L.; Oberman, C. R.; Kulsrud, R. M.
- Physics of Fluids, Vol. 1, Issue 4
Ertel's vorticity theorem and new flux surfaces in multi-fluid plasmas
journal, September 2013
- Hameiri, Eliezer
- Physics of Plasmas, Vol. 20, Issue 9
High β relaxed states with internal conductor plasma configuration
journal, May 2001
- Iqbal, M.; Mirza, A. M.; Murtaza, G.
- Physics of Plasmas, Vol. 8, Issue 5
Magnetic Fields in Astrophysical Jets: From Launch to Termination
journal, June 2012
- Pudritz, Ralph E.; Hardcastle, Martin J.; Gabuzda, Denise C.
- Space Science Reviews, Vol. 169, Issue 1-4