Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria

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

doi:10.1063/1.5125573

Title: Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria

Abstract

The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flow under constrained perturbations. The dynamically accessible, second-order variation of the Hamiltonian, which can potentially provide explicit stability criteria for generic equilibria, is also obtained. Moreover, we examine the Lagrangian stability of the general quasineutral two-fluid model written in terms of MHD-like variables, by finding the action and the Hamiltonian functionals of the linearized dynamics, working within a mixed Lagrangian-Eulerian framework. Upon neglecting electron mass, we derive a HMHD energy principle, and in addition, the perturbed induction equation arises from Hamilton's equations of motion in view of a consistency condition for the relation between the perturbed magnetic potential and the canonical variables.

Authors:

^[1];

^[2]

Univ. of Ioannina (Greece)
Univ. of Texas, Austin, TX (United States)

Publication Date:: Thu Jan 02 00:00:00 EST 2020

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

Sponsoring Org.:: USDOE

OSTI Identifier:: 1801010

Alternate Identifier(s):: OSTI ID: 1581013

Grant/Contract Number:: FG05-80ET53088; FG05-80ET-53088

Resource Type:: Accepted Manuscript

Journal Name:: Physics of Plasmas

Additional Journal Information:: Journal Volume: 27; Journal Issue: 1; Journal ID: ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Physics; Hamiltonian mechanics; Hamiltonian field theory; Calculus of variations; Magnetic fields; Hall effect; Lagrangian field theories; Stability theory; Tokamaks; Magnetohydrodynamics; Partial differential equations

Citation Formats


                    Kaltsas, D. A., Throumoulopoulos, G. N., and Morrison, P. J. Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria.  United States: N. p., 2020. 
Web.  doi:10.1063/1.5125573.

Copy to clipboard


                    Kaltsas, D. A., Throumoulopoulos, G. N., & Morrison, P. J. Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria.  United States.  https://doi.org/10.1063/1.5125573

Copy to clipboard


                    Kaltsas, D. A., Throumoulopoulos, G. N., and Morrison, P. J. Thu .  
"Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria".  United States.  https://doi.org/10.1063/1.5125573.  https://www.osti.gov/servlets/purl/1801010.

Copy to clipboard


                    
@article{osti_1801010,

  title        = {Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria},

  author       = {Kaltsas, D. A. and Throumoulopoulos, G. N. and Morrison, P. J.},

  abstractNote = {The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flow under constrained perturbations. The dynamically accessible, second-order variation of the Hamiltonian, which can potentially provide explicit stability criteria for generic equilibria, is also obtained. Moreover, we examine the Lagrangian stability of the general quasineutral two-fluid model written in terms of MHD-like variables, by finding the action and the Hamiltonian functionals of the linearized dynamics, working within a mixed Lagrangian-Eulerian framework. Upon neglecting electron mass, we derive a HMHD energy principle, and in addition, the perturbed induction equation arises from Hamilton's equations of motion in view of a consistency condition for the relation between the perturbed magnetic potential and the canonical variables.},

  doi          = {10.1063/1.5125573},

  journal      = {Physics of Plasmas},

  number       = 1,

  volume       = 27,

  place        = {United States},

  year         = {Thu Jan 02 00:00:00 EST 2020},

  month        = {Thu Jan 02 00:00:00 EST 2020}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1063/1.5125573

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 7 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Variational principle for linear stability of flowing plasmas in Hall magnetohydrodynamics
journal, February 2006

Hirota, M.; Yoshida, Z.; Hameiri, E.
Physics of Plasmas, Vol. 13, Issue 2
DOI: 10.1063/1.2169734

Ellipticity conditions for the extended MHD Grad-Shafranov-Bernoulli equilibrium equations
journal, February 2019

Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J.
Physics of Plasmas, Vol. 26, Issue 2
DOI: 10.1063/1.5080997

Über die Ausbreitung von Wellen in einem Plasma
journal, January 1959

Lüst, Reimar
Fortschritte der Physik, Vol. 7, Issue 9
DOI: 10.1002/prop.19590070902

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
DOI: 10.1017/S0022377818000338

Two variational principles for incompressible plasmas
journal, November 1999

Spiess, Peter; Elsässer, Klaus
Physics of Plasmas, Vol. 6, Issue 11
DOI: 10.1063/1.873687

Variational principles for equilibrium states with plasma flow
journal, September 1998

Hameiri, Eliezer
Physics of Plasmas, Vol. 5, Issue 9
DOI: 10.1063/1.872995

Hamiltonian magnetohydrodynamics: symmetric formulation, Casimir invariants, and equilibrium variational principles
text, January 2012

Andreussi, Tommaso; Morrison, Philip J.; Pegoraro, Francesco
arXiv
DOI: 10.48550/arxiv.1202.0468

The effects of sheared toroidal rotation on stability limits in tokamak plasmas
journal, October 2011

Chapman, I. T.; Walkden, N. R.; Graves, J. P.
Plasma Physics and Controlled Fusion, Vol. 53, Issue 12
DOI: 10.1088/0741-3335/53/12/125002

Inertial magnetohydrodynamics
journal, March 2015

Lingam, M.; Morrison, P. J.; Tassi, E.
Physics Letters A, Vol. 379, Issue 6
DOI: 10.1016/j.physleta.2014.12.008

Stabilization of the internal kink mode in a tokamak by toroidal plasma rotation
journal, March 2000

Wahlberg, C.; Bondeson, A.
Physics of Plasmas, Vol. 7, Issue 3
DOI: 10.1063/1.873889

Lyapunov stability of perfect fluid and multifluid plasma equilibria
journal, June 1997

Elsässer, Klaus; Spieß, Peter
Physics Letters A, Vol. 230, Issue 1-2
DOI: 10.1016/S0375-9601(97)00220-X

Ballooning mode stability in the Hall-magnetohydrodynamics model
journal, March 2005

Torasso, R.; Hameiri, Eliezer
Physics of Plasmas, Vol. 12, Issue 3
DOI: 10.1063/1.1851993

Ertel's vorticity theorem and new flux surfaces in multi-fluid plasmas
journal, September 2013

Hameiri, Eliezer
Physics of Plasmas, Vol. 20, Issue 9
DOI: 10.1063/1.4820769

Canonical Hamiltonian mechanics of Hall magnetohydrodynamics and its limit to ideal magnetohydrodynamics
journal, July 2013

Yoshida, Z.; Hameiri, E.
Journal of Physics A: Mathematical and Theoretical, Vol. 46, Issue 33
DOI: 10.1088/1751-8113/46/33/335502

A powerful local shear instability in weakly magnetized disks. I - Linear analysis. II - Nonlinear evolution
journal, July 1991

Balbus, Steven A.; Hawley, John F.
The Astrophysical Journal, Vol. 376
DOI: 10.1086/170270

On Hamiltonian and Action Principle Formulations of Plasma Dynamics
conference, January 2009

Morrison, P. J.; Eliasson, Bengt; Shukla, Padma K.
NEW DEVELOPMENTS IN NONLINEAR PLASMA PHYSICS: Proceedings of the 2009 ICTP Summer College on Plasma Physics and International Symposium on Cutting Edge Plasma Physics, AIP Conference Proceedings
DOI: 10.1063/1.3266810

A sufficient condition for the ideal instability of shear flow with parallel magnetic field
journal, April 1991

Chen, X. L.; Morrison, P. J.
Physics of Fluids B: Plasma Physics, Vol. 3, Issue 4
DOI: 10.1063/1.859841

The free energy of Maxwell–Vlasov equilibria
journal, June 1990

Morrison, P. J.; Pfirsch, D.
Physics of Fluids B: Plasma Physics, Vol. 2, Issue 6
DOI: 10.1063/1.859246

Hydromagnetic stability of a diffuse linear pinch
journal, June 1960

Newcomb, William A.
Annals of Physics, Vol. 10, Issue 2
DOI: 10.1016/0003-4916(60)90023-3

Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics
journal, July 2016

Lingam, Manasvi; Miloshevich, George; Morrison, Philip J.
Physics Letters A, Vol. 380, Issue 31-32
DOI: 10.1016/j.physleta.2016.05.024

Shear flow destabilization of a slowly rotating tokamak
journal, January 1998

Chu, M. S.
Physics of Plasmas, Vol. 5, Issue 1
DOI: 10.1063/1.872687

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
DOI: 10.1063/1.4714761

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
DOI: 10.1063/1.4986013

On energy conservation in extended magnetohydrodynamics
text, January 2014

Kimura, Keiji; Morrison, P. J.
arXiv
DOI: 10.48550/arxiv.1406.2745

Variational Stability Problem for MHD Model with Hall Effect
journal, January 1999

Dgisonis, V. I.
Fusion Technology, Vol. 35, Issue 1T
DOI: 10.13182/FST99-A11963845

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
DOI: 10.1088/0741-3335/50/8/085014

Hamiltonian Magnetohydrodynamics: Lagrangian, Eulerian, and Dynamically Accessible Stability - Theory
text, January 2013

Andreussi, T.; Morrison, P. J.; Pegoraro, F.
arXiv
DOI: 10.48550/arxiv.1308.0737

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
DOI: 10.1103/PhysRevLett.45.790

Remarkable connections between extended magnetohydrodynamics models
journal, July 2015

Lingam, M.; Morrison, P. J.; Miloshevich, G.
Physics of Plasmas, Vol. 22, Issue 7
DOI: 10.1063/1.4926821

Kelvin–Helmholtz Instability in the Solar Atmosphere, Solar Wind and Geomagnetosphere
journal, April 2016

Mishin, V. V.; Tomozov, V. M.
Solar Physics, Vol. 291, Issue 11
DOI: 10.1007/s11207-016-0891-4

Hall magnetohydrodynamics: Conservation laws and Lyapunov stability
journal, January 1987

Holm, Darryl D.
Physics of Fluids, Vol. 30, Issue 5
DOI: 10.1063/1.866246

An energy principle for hydromagnetic stability problems
journal, February 1958

Bernstein, I. B.; Frieman, E. A.; Kruskal, Martin David
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 244, Issue 1236, p. 17-40
DOI: 10.1098/rspa.1958.0023

Hamiltonian structure and stability analysis of a reduced four-field model for plasmas in the presence of a strong guide field
journal, December 2012

Tassi, E.; Ratiu, T. S.; Lazzaro, E.
Journal of Physics: Conference Series, Vol. 401
DOI: 10.1088/1742-6596/401/1/012023

Influence of the Hall effect and electron inertia in collisionless magnetic reconnection
text, January 2015

Andrés, Nahuel; Dmitruk, Pablo; Gómez, Daniel
arXiv
DOI: 10.48550/arxiv.1509.01169

Stability of long field-reversed configurations
journal, February 2002

Barnes, D. C.
Physics of Plasmas, Vol. 9, Issue 2
DOI: 10.1063/1.1435425

A sufficient condition for the linear stability of magnetohydrodynamic equilibria with field aligned incompressible flows
journal, December 2007

Throumoulopoulos, G. N.; Tasso, H.
Physics of Plasmas, Vol. 14, Issue 12
DOI: 10.1063/1.2817957

Hamiltonian description of the ideal fluid
journal, April 1998

Morrison, P. J.
Reviews of Modern Physics, Vol. 70, Issue 2
DOI: 10.1103/RevModPhys.70.467

Hamiltonian formalism of extended magnetohydrodynamics
journal, May 2015

Abdelhamid, H. M.; Kawazura, Y.; Yoshida, Z.
Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue 23
DOI: 10.1088/1751-8113/48/23/235502

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
DOI: 10.1063/1.866640

Geospace Environmental Modeling (GEM) Magnetic Reconnection Challenge
journal, March 2001

Birn, J.; Drake, J. F.; Shay, M. A.
Journal of Geophysical Research: Space Physics, Vol. 106, Issue A3
DOI: 10.1029/1999JA900449

Linear stability of static equilibrium states in the Hall-magnetohydrodynamics model
journal, November 2004

Hameiri, Eliezer; Torasso, R.
Physics of Plasmas, Vol. 11, Issue 11
DOI: 10.1063/1.1784453

Dynamically accessible perturbations and magnetohydrodynamic stability
journal, July 2003

Hameiri, Eliezer
Physics of Plasmas, Vol. 10, Issue 7
DOI: 10.1063/1.1577122

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
DOI: 10.1063/1.4819779

A quarter-century of H-mode studies
journal, November 2007

Wagner, F.
Plasma Physics and Controlled Fusion, Vol. 49, Issue 12B
DOI: 10.1088/0741-3335/49/12B/S01

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
DOI: 10.1063/1.4891321

A theory for the pressure pedestal in high (H) mode tokamak discharges
journal, March 2005

Guzdar, P. N.; Mahajan, S. M.; Yoshida, Z.
Physics of Plasmas, Vol. 12, Issue 3
DOI: 10.1063/1.1852468

Derivation of the Hall and extended magnetohydrodynamics brackets
journal, June 2016

D'Avignon, Eric C.; Morrison, Philip J.; Lingam, Manasvi
Physics of Plasmas, Vol. 23, Issue 6
DOI: 10.1063/1.4952641

Hamiltonian Formalism of Extended Magnetohydrodynamics
text, January 2014

Abdelhamid, Hamdi M.; Kawazura, Yohei; Yoshida, Zensho
arXiv
DOI: 10.48550/arxiv.1412.6228

Stabilization of ballooning modes with sheared toroidal rotation
journal, October 1995

Miller, R. L.; Waelbroeck, F. L.; Hassam, A. B.
Physics of Plasmas, Vol. 2, Issue 10
DOI: 10.1063/1.871067

Variational formulation for a multifluid flowing plasma with application to the internal tilt mode of a field-reversed configuration
journal, January 1988

Ishida, A.; Momota, H.; Steinhauer, L. C.
Physics of Fluids, Vol. 31, Issue 10
DOI: 10.1063/1.866959

Ideal and resistive magnetohydrodynamic instabilities in cylindrical geometry with a sheared flow along the axis
journal, March 2017

Brunetti, D.; Lazzaro, E.; Nowak, S.
Plasma Physics and Controlled Fusion, Vol. 59, Issue 5
DOI: 10.1088/1361-6587/aa6423

Free-energy expressions for Vlasov equilibria
journal, October 1989

Morrison, P. J.; Pfirsch, D.
Physical Review A, Vol. 40, Issue 7
DOI: 10.1103/PhysRevA.40.3898

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
DOI: 10.1063/1.4964900

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
DOI: 10.1017/S0022377813000627

On Hydromagnetic Stability of Stationary Equilibria
journal, October 1960

Frieman, E.; Rotenberg, Manuel
Reviews of Modern Physics, Vol. 32, Issue 4
DOI: 10.1103/RevModPhys.32.898

Erratum: “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory” [Phys. Plasmas 20, 092104 (2013)]
journal, March 2015

Andreussi, T.; Morrison, P. J.; Pegoraro, F.
Physics of Plasmas, Vol. 22, Issue 3
DOI: 10.1063/1.4916504

Influence of the Hall effect and electron inertia in collisionless magnetic reconnection
journal, February 2016

Andrés, Nahuel; Dmitruk, Pablo; Gómez, Daniel
Physics of Plasmas, Vol. 23, Issue 2
DOI: 10.1063/1.4942418

Action principles for extended magnetohydrodynamic models
journal, September 2014

Keramidas Charidakos, I.; Lingam, M.; Morrison, P. J.
Physics of Plasmas, Vol. 21, Issue 9
DOI: 10.1063/1.4896336

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
DOI: 10.1016/0370-1573(85)90028-6

Suppression of turbulence and transport by sheared flow
journal, January 2000

Terry, P. W.
Reviews of Modern Physics, Vol. 72, Issue 1
DOI: 10.1103/RevModPhys.72.109

On energy conservation in extended magnetohydrodynamics
journal, August 2014

Kimura, Keiji; Morrison, P. J.
Physics of Plasmas, Vol. 21, Issue 8
DOI: 10.1063/1.4890955

Pyridine nucleotides in glucose metabolism and diabetes: a review
journal, January 2000

Wahlberg, Gustaf; Adamson, Ulf; Svensson, Jan
Diabetes/Metabolism Research and Reviews, Vol. 16, Issue 1
DOI: 10.1002/(sici)1520-7560(200001/02)16:1<33::aid-dmrr79>3.0.co;2-s

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
DOI: 10.1016/0370-1573(85)90028-6

Similar Records in DOE PAGES and OSTI.GOV collections:

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

Journal Article Kaltsas, D. A. ; Throumoulopoulos, G. N. ; Morrison, P. J. - Physics of Plasmas

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 equationsmore »« less
Cited by 9
https://doi.org/10.1063/1.4986013

Full Text Available
Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory

Journal Article Andreussi, T. ; Morrison, P. J. ; Pegoraro, F. - Physics of Plasmas

Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in particular, by using three kinds of energy principles. First, the Lagrangian variable energy principle is described and sufficient stability conditions are presented. Next, plasma flows are described in terms of Eulerian variables and the noncanonical Hamiltonian formulation of MHD is exploited. For symmetric equilibria, the energy-Casimir principle is expanded to second order and sufficient conditions for stability to symmetric perturbation are obtained. Then, dynamically accessible variations, i.e., variations that explicitly preserve invariants of the system, are introduced and the respectivemore »« less
https://doi.org/10.1063/1.4819779
Linear stability analysis via simulated annealing and accelerated relaxation

Journal Article Furukawa, M. ; Morrison, P. J. - Physics of Plasmas

Simulated annealing (SA) is a kind of relaxation method for finding equilibria of Hamiltonian systems. A set of evolution equations is solved with SA, which is derived from the original Hamiltonian system so that the energy of the system changes monotonically while preserving Casimir invariants inherent to noncanonical Hamiltonian systems. The energy extremum reached by SA is an equilibrium. Since SA searches for an energy extremum, it can also be used for stability analysis when initiated from a state where a perturbation is added to an equilibrium. The procedure of the stability analysis is explained, and some examples are shown.more »« less
https://doi.org/10.1063/5.0101095
Hamiltonian description of the ideal fluid

Journal Article Morrison, P J - Reviews of Modern Physics

The Hamiltonian viewpoint of fluid mechanical systems with few and infinite number of degrees of freedom is described. Rudimentary concepts of finite-degree-of-freedom Hamiltonian dynamics are reviewed, in the context of the passive advection of a scalar or tracer field by a fluid. The notions of integrability, invariant-tori, chaos, overlap criteria, and invariant-tori breakup are described in this context. Preparatory to the introduction of field theories, systems with an infinite number of degrees of freedom, elements of functional calculus and action principles of mechanics are reviewed. The action principle for the ideal compressible fluid is described in terms of Lagrangian ormore »« less
https://doi.org/10.1103/RevModPhys.70.467
Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Examples with translation symmetry

Journal Article Andreussi, T. ; Morrison, P. J. ; Pegoraro, F. - Physics of Plasmas

Because different constraints are imposed, stability conditions for dissipationless fluids and magnetofluids may take different forms when derived within the Lagrangian, Eulerian (energy-Casimir), or dynamically accessible frameworks. This is in particular the case when flows are present. These differences are explored explicitly here by working out in detail two magnetohydrodynamic examples: convection against gravity in a stratified fluid and translationally invariant perturbations of a rotating magnetized plasma pinch. In this second example, we show in explicit form how to perform the time-dependent relabeling introduced in Andreussi et al. [Phys. Plasmas 20, 092104 (2013)] that makes it possible to reformulate Eulerianmore »« less
Cited by 13
https://doi.org/10.1063/1.4964900

Full Text Available

Similar Records

Title: Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria

Abstract

Citation Formats

Variational principle for linear stability of flowing plasmas in Hall magnetohydrodynamics journal, February 2006

Ellipticity conditions for the extended MHD Grad-Shafranov-Bernoulli equilibrium equations journal, February 2019

Über die Ausbreitung von Wellen in einem Plasma journal, January 1959

Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles journal, May 2018

Two variational principles for incompressible plasmas journal, November 1999

Variational principles for equilibrium states with plasma flow journal, September 1998

Hamiltonian magnetohydrodynamics: symmetric formulation, Casimir invariants, and equilibrium variational principles text, January 2012

The effects of sheared toroidal rotation on stability limits in tokamak plasmas journal, October 2011

Inertial magnetohydrodynamics journal, March 2015

Stabilization of the internal kink mode in a tokamak by toroidal plasma rotation journal, March 2000

Lyapunov stability of perfect fluid and multifluid plasma equilibria journal, June 1997

Ballooning mode stability in the Hall-magnetohydrodynamics model journal, March 2005

Ertel's vorticity theorem and new flux surfaces in multi-fluid plasmas journal, September 2013

Canonical Hamiltonian mechanics of Hall magnetohydrodynamics and its limit to ideal magnetohydrodynamics journal, July 2013

A powerful local shear instability in weakly magnetized disks. I - Linear analysis. II - Nonlinear evolution journal, July 1991

On Hamiltonian and Action Principle Formulations of Plasma Dynamics conference, January 2009

A sufficient condition for the ideal instability of shear flow with parallel magnetic field journal, April 1991

The free energy of Maxwell–Vlasov equilibria journal, June 1990

Hydromagnetic stability of a diffuse linear pinch journal, June 1960

Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics journal, July 2016

Shear flow destabilization of a slowly rotating tokamak journal, January 1998

Hamiltonian magnetohydrodynamics: Helically symmetric formulation, Casimir invariants, and equilibrium variational principles journal, May 2012

Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria journal, September 2017

On energy conservation in extended magnetohydrodynamics text, January 2014

Variational Stability Problem for MHD Model with Hall Effect journal, January 1999

Hamiltonian formulation and analysis of a collisionless fluid reconnection model journal, June 2008

Hamiltonian Magnetohydrodynamics: Lagrangian, Eulerian, and Dynamically Accessible Stability - Theory text, January 2013

Noncanonical Hamiltonian Density Formulation of Hydrodynamics and Ideal Magnetohydrodynamics journal, September 1980

Remarkable connections between extended magnetohydrodynamics models journal, July 2015

Kelvin–Helmholtz Instability in the Solar Atmosphere, Solar Wind and Geomagnetosphere journal, April 2016

Hall magnetohydrodynamics: Conservation laws and Lyapunov stability journal, January 1987

An energy principle for hydromagnetic stability problems journal, February 1958

Hamiltonian structure and stability analysis of a reduced four-field model for plasmas in the presence of a strong guide field journal, December 2012

Influence of the Hall effect and electron inertia in collisionless magnetic reconnection text, January 2015

Stability of long field-reversed configurations journal, February 2002

A sufficient condition for the linear stability of magnetohydrodynamic equilibria with field aligned incompressible flows journal, December 2007

Hamiltonian description of the ideal fluid journal, April 1998

Hamiltonian formalism of extended magnetohydrodynamics journal, May 2015

Lyapunov stability analysis of magnetohydrodynamic plasma equilibria with axisymmetric toroidal flow journal, January 1988

Geospace Environmental Modeling (GEM) Magnetic Reconnection Challenge journal, March 2001

Linear stability of static equilibrium states in the Hall-magnetohydrodynamics model journal, November 2004

Dynamically accessible perturbations and magnetohydrodynamic stability journal, July 2003

Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory journal, September 2013

A quarter-century of H-mode studies journal, November 2007

Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics journal, August 2014

A theory for the pressure pedestal in high (H) mode tokamak discharges journal, March 2005

Derivation of the Hall and extended magnetohydrodynamics brackets journal, June 2016

Hamiltonian Formalism of Extended Magnetohydrodynamics text, January 2014

Stabilization of ballooning modes with sheared toroidal rotation journal, October 1995

Variational formulation for a multifluid flowing plasma with application to the internal tilt mode of a field-reversed configuration journal, January 1988

Ideal and resistive magnetohydrodynamic instabilities in cylindrical geometry with a sheared flow along the axis journal, March 2017

Free-energy expressions for Vlasov equilibria journal, October 1989

Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Examples with translation symmetry journal, October 2016

Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field journal, June 2013

On Hydromagnetic Stability of Stationary Equilibria journal, October 1960

Erratum: “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory” [Phys. Plasmas 20, 092104 (2013)] journal, March 2015

Influence of the Hall effect and electron inertia in collisionless magnetic reconnection journal, February 2016

Action principles for extended magnetohydrodynamic models journal, September 2014

Nonlinear stability of fluid and plasma equilibria journal, July 1985

Suppression of turbulence and transport by sheared flow journal, January 2000

On energy conservation in extended magnetohydrodynamics journal, August 2014

Pyridine nucleotides in glucose metabolism and diabetes: a review journal, January 2000

Nonlinear stability of fluid and plasma equilibria journal, July 1985

Variational principle for linear stability of flowing plasmas in Hall magnetohydrodynamics
journal, February 2006

Ellipticity conditions for the extended MHD Grad-Shafranov-Bernoulli equilibrium equations
journal, February 2019

Über die Ausbreitung von Wellen in einem Plasma
journal, January 1959

Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles
journal, May 2018

Two variational principles for incompressible plasmas
journal, November 1999

Variational principles for equilibrium states with plasma flow
journal, September 1998

Hamiltonian magnetohydrodynamics: symmetric formulation, Casimir invariants, and equilibrium variational principles
text, January 2012

The effects of sheared toroidal rotation on stability limits in tokamak plasmas
journal, October 2011

Inertial magnetohydrodynamics
journal, March 2015

Stabilization of the internal kink mode in a tokamak by toroidal plasma rotation
journal, March 2000

Lyapunov stability of perfect fluid and multifluid plasma equilibria
journal, June 1997

Ballooning mode stability in the Hall-magnetohydrodynamics model
journal, March 2005

Ertel's vorticity theorem and new flux surfaces in multi-fluid plasmas
journal, September 2013

Canonical Hamiltonian mechanics of Hall magnetohydrodynamics and its limit to ideal magnetohydrodynamics
journal, July 2013

A powerful local shear instability in weakly magnetized disks. I - Linear analysis. II - Nonlinear evolution
journal, July 1991

On Hamiltonian and Action Principle Formulations of Plasma Dynamics
conference, January 2009

A sufficient condition for the ideal instability of shear flow with parallel magnetic field
journal, April 1991

The free energy of Maxwell–Vlasov equilibria
journal, June 1990

Hydromagnetic stability of a diffuse linear pinch
journal, June 1960

Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics
journal, July 2016

Shear flow destabilization of a slowly rotating tokamak
journal, January 1998

Hamiltonian magnetohydrodynamics: Helically symmetric formulation, Casimir invariants, and equilibrium variational principles
journal, May 2012

Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria
journal, September 2017

On energy conservation in extended magnetohydrodynamics
text, January 2014

Variational Stability Problem for MHD Model with Hall Effect
journal, January 1999

Hamiltonian formulation and analysis of a collisionless fluid reconnection model
journal, June 2008

Hamiltonian Magnetohydrodynamics: Lagrangian, Eulerian, and Dynamically Accessible Stability - Theory
text, January 2013

Noncanonical Hamiltonian Density Formulation of Hydrodynamics and Ideal Magnetohydrodynamics
journal, September 1980

Remarkable connections between extended magnetohydrodynamics models
journal, July 2015

Kelvin–Helmholtz Instability in the Solar Atmosphere, Solar Wind and Geomagnetosphere
journal, April 2016

Hall magnetohydrodynamics: Conservation laws and Lyapunov stability
journal, January 1987

An energy principle for hydromagnetic stability problems
journal, February 1958

Hamiltonian structure and stability analysis of a reduced four-field model for plasmas in the presence of a strong guide field
journal, December 2012

Influence of the Hall effect and electron inertia in collisionless magnetic reconnection
text, January 2015

Stability of long field-reversed configurations
journal, February 2002

A sufficient condition for the linear stability of magnetohydrodynamic equilibria with field aligned incompressible flows
journal, December 2007

Hamiltonian description of the ideal fluid
journal, April 1998

Hamiltonian formalism of extended magnetohydrodynamics
journal, May 2015

Lyapunov stability analysis of magnetohydrodynamic plasma equilibria with axisymmetric toroidal flow
journal, January 1988

Geospace Environmental Modeling (GEM) Magnetic Reconnection Challenge
journal, March 2001

Linear stability of static equilibrium states in the Hall-magnetohydrodynamics model
journal, November 2004

Dynamically accessible perturbations and magnetohydrodynamic stability
journal, July 2003

Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory
journal, September 2013

A quarter-century of H-mode studies
journal, November 2007

Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics
journal, August 2014

A theory for the pressure pedestal in high (H) mode tokamak discharges
journal, March 2005

Derivation of the Hall and extended magnetohydrodynamics brackets
journal, June 2016

Hamiltonian Formalism of Extended Magnetohydrodynamics
text, January 2014

Stabilization of ballooning modes with sheared toroidal rotation
journal, October 1995

Variational formulation for a multifluid flowing plasma with application to the internal tilt mode of a field-reversed configuration
journal, January 1988

Ideal and resistive magnetohydrodynamic instabilities in cylindrical geometry with a sheared flow along the axis
journal, March 2017

Free-energy expressions for Vlasov equilibria
journal, October 1989

Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Examples with translation symmetry
journal, October 2016

Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field
journal, June 2013

On Hydromagnetic Stability of Stationary Equilibria
journal, October 1960

Erratum: “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory” [Phys. Plasmas 20, 092104 (2013)]
journal, March 2015

Influence of the Hall effect and electron inertia in collisionless magnetic reconnection
journal, February 2016

Action principles for extended magnetohydrodynamic models
journal, September 2014

Nonlinear stability of fluid and plasma equilibria
journal, July 1985

Suppression of turbulence and transport by sheared flow
journal, January 2000

On energy conservation in extended magnetohydrodynamics
journal, August 2014

Pyridine nucleotides in glucose metabolism and diabetes: a review
journal, January 2000

Nonlinear stability of fluid and plasma equilibria
journal, July 1985