Multi-region relaxed Hall magnetohydrodynamics with flow

Lingam, Manasvi; Abdelhamid, Hamdi M.; Hudson, Stuart R.

doi:10.1063/1.4960128

Title: Multi-region relaxed Hall magnetohydrodynamics with flow

Abstract

The recent formulations of multi-region relaxed magnetohydrodynamics (MRxMHD) have generalized the famous Woltjer-Taylor states by incorporating a collection of “ideal barriers” that prevent global relaxation and flow. In this paper, we generalize MRxMHD with flow to include Hall effects, and thereby obtain the partially relaxed counterparts of the famous double Beltrami states as a special subset. The physical and mathematical consequences arising from the introduction of the Hall term are also presented. We demonstrate that our results (in the ideal MHD limit) constitute an important subset of ideal MHD equilibria, and we compare our approach against other variational principles proposed for deriving the partially relaxed states.

Authors:

Lingam, Manasvi ^[1];

^[2]; Hudson, Stuart R. ^[3]

Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences
Univ. of Tokyo (Japan). Graduate School of Frontier Sciences; Mansoura Univ. (Egypt). Physics Dept.
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

Publication Date:: Wed Aug 03 00:00:00 EDT 2016

Research Org.:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1332513

Alternate Identifier(s):: OSTI ID: 1281331

Grant/Contract Number:: AGS-1338944; AC02-09CH11466; AC02-09CH-11466

Resource Type:: Accepted Manuscript

Journal Name:: Physics of Plasmas

Additional Journal Information:: Journal Volume: 23; Journal Issue: 8; 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

Citation Formats


                    Lingam, Manasvi, Abdelhamid, Hamdi M., and Hudson, Stuart R. Multi-region relaxed Hall magnetohydrodynamics with flow.  United States: N. p., 2016. 
Web.  doi:10.1063/1.4960128.

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                    Lingam, Manasvi, Abdelhamid, Hamdi M., & Hudson, Stuart R. Multi-region relaxed Hall magnetohydrodynamics with flow.  United States.  https://doi.org/10.1063/1.4960128

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                    Lingam, Manasvi, Abdelhamid, Hamdi M., and Hudson, Stuart R. Wed .  
"Multi-region relaxed Hall magnetohydrodynamics with flow".  United States.  https://doi.org/10.1063/1.4960128.  https://www.osti.gov/servlets/purl/1332513.

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@article{osti_1332513,

  title        = {Multi-region relaxed Hall magnetohydrodynamics with flow},

  author       = {Lingam, Manasvi and Abdelhamid, Hamdi M. and Hudson, Stuart R.},

  abstractNote = {The recent formulations of multi-region relaxed magnetohydrodynamics (MRxMHD) have generalized the famous Woltjer-Taylor states by incorporating a collection of “ideal barriers” that prevent global relaxation and flow. In this paper, we generalize MRxMHD with flow to include Hall effects, and thereby obtain the partially relaxed counterparts of the famous double Beltrami states as a special subset. The physical and mathematical consequences arising from the introduction of the Hall term are also presented. We demonstrate that our results (in the ideal MHD limit) constitute an important subset of ideal MHD equilibria, and we compare our approach against other variational principles proposed for deriving the partially relaxed states.},

  doi          = {10.1063/1.4960128},

  journal      = {Physics of Plasmas},

  number       = 8,

  volume       = 23,

  place        = {United States},

  year         = {Wed Aug 03 00:00:00 EDT 2016},

  month        = {Wed Aug 03 00:00:00 EDT 2016}

}

Copy to clipboard

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Works referenced in this record:

Relaxed plasma-vacuum systems
journal, August 2001

Spies, G. O.; Lortz, D.; Kaiser, R.
Physics of Plasmas, Vol. 8, Issue 8
DOI: 10.1063/1.1383286

Eigenvalue problems for Beltrami fields arising in a three-dimensional toroidal magnetohydrodynamic equilibrium problem
journal, May 2007

Hudson, S. R.; Hole, M. J.; Dewar, R. L.
Physics of Plasmas, Vol. 14, Issue 5
DOI: 10.1063/1.2722721

Hall magnetohydrodynamics in space and laboratory plasmas
journal, June 1995

Huba, J. D.
Physics of Plasmas, Vol. 2, Issue 6
DOI: 10.1063/1.871212

Variational principles for stationary one- and two-fluid equilibria of axisymmetric laboratory and astrophysical plasmas
journal, December 2004

Goedbloed, J. P.
Physics of Plasmas, Vol. 11, Issue 12
DOI: 10.1063/1.1808453

Relaxed Plasma Equilibria and Entropy-Related Plasma Self-Organization Principles
journal, November 2008

Dewar, Robert; Hole, Matthew; McGann, Mathew
Entropy, Vol. 10, Issue 4
DOI: 10.3390/e10040621

Generalized two-fluid equilibria: Understanding RT-1 experiments and beyond
journal, November 2010

Yoshida, Z.; Mahajan, S. M.; Mizushima, T.
Physics of Plasmas, Vol. 17, Issue 11
DOI: 10.1063/1.3505821

Relaxation and magnetic reconnection in plasmas
journal, July 1986

Taylor, J. B.
Reviews of Modern Physics, Vol. 58, Issue 3
DOI: 10.1103/RevModPhys.58.741

Generation of Flows in the Solar Atmosphere Due to Magnetofluid Coupling
journal, September 2002

Mahajan, Swadesh M.; Nikol’skaya, Komunela I.; Shatashvili, Nana L.
The Astrophysical Journal, Vol. 576, Issue 2
DOI: 10.1086/343727

First-order finite-Larmor-radius fluid modeling of tearing and relaxation in a plasma pinch
journal, May 2012

King, J. R.; Sovinec, C. R.; Mirnov, V. V.
Physics of Plasmas, Vol. 19, Issue 5
DOI: 10.1063/1.3695346

Two-fluid and magnetohydrodynamic modelling of magnetic reconnection in the MAST spherical tokamak and the solar corona
journal, November 2015

Browning, P. K.; Cardnell, S.; Evans, M.
Plasma Physics and Controlled Fusion, Vol. 58, Issue 1
DOI: 10.1088/0741-3335/58/1/014041

Magnetic islands and singular currents at rational surfaces in three-dimensional magnetohydrodynamic equilibria
journal, February 2015

Loizu, J.; Hudson, S.; Bhattacharjee, A.
Physics of Plasmas, Vol. 22, Issue 2
DOI: 10.1063/1.4906888

Two-fluid and finite Larmor radius effects on helicity evolution in a plasma pinch
journal, March 2016

Sauppe, J. P.; Sovinec, C. R.
Physics of Plasmas, Vol. 23, Issue 3
DOI: 10.1063/1.4942761

Formation and primary heating of the solar corona: Theory and simulation
journal, January 2001

Mahajan, S. M.; Miklaszewski, R.; Nikol’skaya, K. I.
Physics of Plasmas, Vol. 8, Issue 4
DOI: 10.1063/1.1350670

Nonlinear Alfvén waves in extended magnetohydrodynamics
journal, February 2016

Abdelhamid, Hamdi M.; Yoshida, Zensho
Physics of Plasmas, Vol. 23, Issue 2
DOI: 10.1063/1.4941596

Multi-region relaxed magnetohydrodynamics with anisotropy and flow
journal, July 2014

Dennis, G. R.; Hudson, S. R.; Dewar, R. L.
Physics of Plasmas, Vol. 21, Issue 7
DOI: 10.1063/1.4890847

Generalized relaxation theory and vortices in plasmas
journal, October 1995

Oliveira, Samuel R.; Tajima, Toshiki
Physical Review E, Vol. 52, Issue 4
DOI: 10.1103/PhysRevE.52.4287

Azimuthally symmetric magnetohydrodynamic and two-fluid equilibria with arbitrary flows
journal, May 2001

McClements, K. G.; Thyagaraja, A.
Monthly Notices of the Royal Astronomical Society, Vol. 323, Issue 3
DOI: 10.1046/j.1365-8711.2001.04290.x

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

Turbulent relaxation of compressible plasmas with flow
journal, January 1983

Finn, John M.
Physics of Fluids, Vol. 26, Issue 12
DOI: 10.1063/1.864115

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 heuristic model for MRI turbulent stresses in Hall MHD
journal, April 2016

Lingam, Manasvi; Bhattacharjee, Amitava
Monthly Notices of the Royal Astronomical Society, Vol. 460, Issue 1
DOI: 10.1093/mnras/stw997

Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria
journal, January 1983

Hirshman, S. P.
Physics of Fluids, Vol. 26, Issue 12
DOI: 10.1063/1.864116

The infinite interface limit of multiple-region relaxed magnetohydrodynamics
journal, March 2013

Dennis, G. R.; Hudson, S. R.; Dewar, R. L.
Physics of Plasmas, Vol. 20, Issue 3
DOI: 10.1063/1.4795739

Multi-fluid systems—Multi-Beltrami relaxed states and their implications
journal, September 2015

Mahajan, Swadesh M.; Lingam, Manasvi
Physics of Plasmas, Vol. 22, Issue 9
DOI: 10.1063/1.4931069

Relaxation of a Two-Specie Magnetofluid
journal, November 1997

Steinhauer, L. C.; Ishida, A.
Physical Review Letters, Vol. 79, Issue 18
DOI: 10.1103/PhysRevLett.79.3423

Hamiltonian and action principle formulations of plasma physics
journal, May 2005

Morrison, P. J.
Physics of Plasmas, Vol. 12, Issue 5
DOI: 10.1063/1.1882353

Hall Current Effects in Mean-Field Dynamo Theory
journal, September 2016

Lingam, Manasvi; Bhattacharjee, Amitava
The Astrophysical Journal, Vol. 829, Issue 1
DOI: 10.3847/0004-637X/829/1/51

Pressure-driven amplification and penetration of resonant magnetic perturbations
journal, May 2016

Loizu, J.; Hudson, S. R.; Helander, P.
Physics of Plasmas, Vol. 23, Issue 5
DOI: 10.1063/1.4944818

Modelling astrophysical outflows via the unified dynamo–reverse dynamo mechanism
journal, February 2015

Lingam, Manasvi; Mahajan, Swadesh M.
Monthly Notices of the Royal Astronomical Society: Letters, Vol. 449, Issue 1
DOI: 10.1093/mnrasl/slv017

Hydromagnetic Equilibrium ii. Stability in the Variational Formulation
journal, June 1959

Woltjer, L.
Proceedings of the National Academy of Sciences, Vol. 45, Issue 6
DOI: 10.1073/pnas.45.6.769

Hall Effects on Magnetic Relaxation
journal, January 1986

Turner, Leaf
IEEE Transactions on Plasma Science, Vol. 14, Issue 6
DOI: 10.1109/TPS.1986.4316633

A collisionless self-organizing model for the high-confinement (H-mode) boundary layer
journal, February 2000

Mahajan, S. M.; Yoshida, Z.
Physics of Plasmas, Vol. 7, Issue 2
DOI: 10.1063/1.873850

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

Scale hierarchy created in plasma flow
journal, July 2004

Yoshida, Z.; Mahajan, S. M.; Ohsaki, S.
Physics of Plasmas, Vol. 11, Issue 7
DOI: 10.1063/1.1762877

Formation and Stability of Impurity “Snakes” in Tokamak Plasmas
journal, February 2013

Delgado-Aparicio, L.; Sugiyama, L.; Granetz, R.
Physical Review Letters, Vol. 110, Issue 6
DOI: 10.1103/PhysRevLett.110.065006

Relaxation of Toroidal Plasma and Generation of Reverse Magnetic Fields
journal, November 1974

Taylor, J. B.
Physical Review Letters, Vol. 33, Issue 19
DOI: 10.1103/PhysRevLett.33.1139

Non-axisymmetric, multi-region relaxed magnetohydrodynamic equilibrium solutions
journal, December 2011

Hudson, S. R.; Dewar, R. L.; Hole, M. J.
Plasma Physics and Controlled Fusion, Vol. 54, Issue 1
DOI: 10.1088/0741-3335/54/1/014005

Application of Double Beltrami states to solar eruptions: Double Beltrami states and solar eruptions
journal, May 2010

Kagan, D.; Mahajan, S. M.
Monthly Notices of the Royal Astronomical Society
DOI: 10.1111/j.1365-2966.2010.16741.x

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

Double Curl Beltrami Flow: Diamagnetic Structures
journal, November 1998

Mahajan, S. M.; Yoshida, Z.
Physical Review Letters, Vol. 81, Issue 22
DOI: 10.1103/PhysRevLett.81.4863

Stability of Field-Reversed, Force-Free, Plasma Equilibria with Mass Flow
journal, May 1979

Sudan, R. N.
Physical Review Letters, Vol. 42, Issue 19
DOI: 10.1103/PhysRevLett.42.1277

Relaxed plasma-vacuum systems with pressure
journal, July 2003

Spies, G. O.
Physics of Plasmas, Vol. 10, Issue 7
DOI: 10.1063/1.1584047

Magnetic fluctuations and Hall magnetohydrodynamic turbulence in the solar wind
journal, January 2004

Krishan, V.
Journal of Geophysical Research, Vol. 109, Issue A11
DOI: 10.1029/2004JA010496

Some improvements in the theory of plasma relaxation
journal, April 2014

Hameiri, Eliezer
Physics of Plasmas, Vol. 21, Issue 4
DOI: 10.1063/1.4871391

Equilibrium of a Magnetically Confined Plasma in a Toroid
journal, January 1958

Kruskal, M. D.; Kulsrud, R. M.
Physics of Fluids, Vol. 1, Issue 4
DOI: 10.1063/1.1705884

Measurements of the momentum and current transport from tearing instability in the Madison Symmetric Torus reversed-field pinch
journal, May 2009

Kuritsyn, A.; Fiksel, G.; Almagri, A. F.
Physics of Plasmas, Vol. 16, Issue 5
DOI: 10.1063/1.3090325

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

On Hydromagnetic Equilibrium
journal, September 1958

Woltjer, L.
Proceedings of the National Academy of Sciences, Vol. 44, Issue 9
DOI: 10.1073/pnas.44.9.833

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

Stepped pressure profile equilibria in cylindrical plasmas via partial Taylor relaxation
journal, December 2006

Hole, M. J.; Hudson, S. R.; Dewar, R. L.
Journal of Plasma Physics, Vol. 72, Issue 06
DOI: 10.1017/S0022377806005861

Energy Transformation Mechanism in the Solar Atmosphere Associated with Magnetofluid Coupling: Explosive and Eruptive Events
journal, May 2002

Ohsaki, Shuichi; Shatashvili, Nana L.; Yoshida, Zensho
The Astrophysical Journal, Vol. 570, Issue 1
DOI: 10.1086/339499

Relaxation of a quasisymmetric rotating plasma: A model of Jupiter’s magnetosphere
journal, September 2005

Shiraishi, Jun-ya; Ohsaki, Shuichi; Yoshida, Zensho
Physics of Plasmas, Vol. 12, Issue 9
DOI: 10.1063/1.2041655

Entropy production and plasma relaxation
journal, January 1987

Hameiri, Eliezer; Bhattacharjee, A.
Physical Review A, Vol. 35, Issue 2
DOI: 10.1103/PhysRevA.35.768

The action principle for generalized fluid motion including gyroviscosity
journal, November 2014

Lingam, M.; Morrison, P. J.
Physics Letters A, Vol. 378, Issue 47
DOI: 10.1016/j.physleta.2014.10.013

Validation of single-fluid and two-fluid magnetohydrodynamic models of the helicity injected torus spheromak experiment with the NIMROD code
journal, August 2013

Akcay, Cihan; Kim, Charlson C.; Victor, Brian S.
Physics of Plasmas, Vol. 20, Issue 8
DOI: 10.1063/1.4817951

Three-dimensional free boundary calculations using a spectral Green's function method
journal, December 1986

Hirshman, S. P.; van RIJ, W. I.; Merkel, P.
Computer Physics Communications, Vol. 43, Issue 1
DOI: 10.1016/0010-4655(86)90058-5

Self-organization during spherical torus formation by flux rope merging in the Mega Ampere Spherical Tokamak
journal, April 2014

Browning, P. K.; Stanier, A.; Ashworth, G.
Plasma Physics and Controlled Fusion, Vol. 56, Issue 6
DOI: 10.1088/0741-3335/56/6/064009

Overview of results from the MST reversed field pinch experiment
journal, September 2013

Sarff, J. S.; Almagri, A. F.; Anderson, J. K.
Nuclear Fusion, Vol. 53, Issue 10
DOI: 10.1088/0029-5515/53/10/104017

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
DOI: 10.1098/rsta.1960.0010

Minimum energy states of the cylindrical plasma pinch in single-fluid and Hall magnetohydrodynamics
journal, January 2012

Khalzov, I. V.; Ebrahimi, F.; Schnack, D. D.
Physics of Plasmas, Vol. 19, Issue 1
DOI: 10.1063/1.3676600

Magnetofluid Coupling: Eruptive Events in the Solar Corona
journal, September 2001

Ohsaki, Shuichi; Shatashvili, Nana L.; Yoshida, Zensho
The Astrophysical Journal, Vol. 559, Issue 1
DOI: 10.1086/323651

Variational principle with singular perturbation of hall magnetohydrodynamics
journal, June 2005

Ohsaki, Shuichi; Yoshida, Zensho
Physics of Plasmas, Vol. 12, Issue 6
DOI: 10.1063/1.1936585

Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics
journal, November 2015

Dewar, R. L.; Yoshida, Z.; Bhattacharjee, A.
Journal of Plasma Physics, Vol. 81, Issue 6
DOI: 10.1017/S0022377815001336

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

Nonlinear three-dimensional simulation for self-organization and flow generation in two-fluid plasmas
journal, December 2004

Numata, Ryusuke; Yoshida, Zensho; Hayashi, Takaya
Computer Physics Communications, Vol. 164, Issue 1-3
DOI: 10.1016/j.cpc.2004.06.041

Computation of multi-region relaxed magnetohydrodynamic equilibria
journal, November 2012

Hudson, S. R.; Dewar, R. L.; Dennis, G.
Physics of Plasmas, Vol. 19, Issue 11
DOI: 10.1063/1.4765691

Variational Principles and Self-Organization in Two-Fluid Plasmas
journal, February 2002

Yoshida, Z.; Mahajan, S. M.
Physical Review Letters, Vol. 88, Issue 9
DOI: 10.1103/PhysRevLett.88.095001

Pressure-driven amplification and penetration of resonant magnetic perturbations
journal, May 2016

Loizu, J.; Hudson, S. R.; Helander, P.
Physics of Plasmas, Vol. 23, Issue 5
DOI: 10.1063/1.4944818

Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets
journal, September 2015

Loizu, J.; Hudson, S. R.; Bhattacharjee, A.
Physics of Plasmas, Vol. 22, Issue 9
DOI: 10.1063/1.4931094

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

A Theorem on Force-Free Magnetic Fields
journal, June 1958

Woltjer, L.
Proceedings of the National Academy of Sciences, Vol. 44, Issue 6
DOI: 10.1073/pnas.44.6.489

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

Nonlinear Alfvén/Beltrami waves—An integrable structure built around the Casimir
journal, May 2012

Yoshida, Z.
Communications in Nonlinear Science and Numerical Simulation, Vol. 17, Issue 5
DOI: 10.1016/j.cnsns.2011.04.010

Equilibria and stability in partially relaxed plasma–vacuum systems
journal, July 2007

Hole, M. J.; Hudson, S. R.; Dewar, R. L.
Nuclear Fusion, Vol. 47, Issue 8
DOI: 10.1088/0029-5515/47/8/004

Relaxed MHD states of a multiple region plasma
journal, May 2009

Hole, M. J.; Mills, R.; Hudson, S. R.
Nuclear Fusion, Vol. 49, Issue 6
DOI: 10.1088/0029-5515/49/6/065019

Magnetohydrodynamic stability of plasmas with ideal and relaxed regions
journal, October 2009

Mills, R. L.; Hole, M. J.; Dewar, R. L.
Journal of Plasma Physics, Vol. 75, Issue 5
DOI: 10.1017/S0022377809008095

Evaluation of Turner relaxed state as a model of long-lived ion-trapping structures in plasma focus and Z-pinches
journal, March 2011

Auluck, S. K. H.
Physics of Plasmas, Vol. 18, Issue 3
DOI: 10.1063/1.3554701

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
DOI: 10.1063/1.1354149

Multi-region relaxed magnetohydrodynamics with flow
journal, April 2014

Dennis, G. R.; Hudson, S. R.; Dewar, R. L.
Physics of Plasmas, Vol. 21, Issue 4
DOI: 10.1063/1.4870008

Relaxation of a two-species magnetofluid and application to finite-β flowing plasmas
journal, July 1998

Steinhauer, L. C.; Ishida, A.
Physics of Plasmas, Vol. 5, Issue 7
DOI: 10.1063/1.872948

Ideal MHD
book, July 2014

Freidberg, Jeffrey P.
DOI: 10.1017/CBO9780511795046

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Multi-region relaxed magnetohydrodynamics with anisotropy and flow

Journal Article Dennis, G. R., E-mail: graham.dennis@anu.edu.au ; Dewar, R. L. ; Hole, M. J. ; ... - Physics of Plasmas

We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes pressure anisotropy and general plasma flows. This anisotropic extension to our previous isotropic model is motivated by Sun and Finn's model of relaxed anisotropic magnetohydrodynamic equilibria. We prove that as the number of plasma regions becomes infinite, our anisotropic extension of MRxMHD reduces to anisotropic ideal MHD with flow. The continuously nested flux surface limit of our MRxMHD model is the first variational principle for anisotropic plasma equilibria with general flow fields.
https://doi.org/10.1063/1.4890847

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Title: Multi-region relaxed Hall magnetohydrodynamics with flow

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Citation Formats

Relaxed plasma-vacuum systems journal, August 2001

Eigenvalue problems for Beltrami fields arising in a three-dimensional toroidal magnetohydrodynamic equilibrium problem journal, May 2007

Hall magnetohydrodynamics in space and laboratory plasmas journal, June 1995

Variational principles for stationary one- and two-fluid equilibria of axisymmetric laboratory and astrophysical plasmas journal, December 2004

Relaxed Plasma Equilibria and Entropy-Related Plasma Self-Organization Principles journal, November 2008

Generalized two-fluid equilibria: Understanding RT-1 experiments and beyond journal, November 2010

Relaxation and magnetic reconnection in plasmas journal, July 1986

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First-order finite-Larmor-radius fluid modeling of tearing and relaxation in a plasma pinch journal, May 2012

Two-fluid and magnetohydrodynamic modelling of magnetic reconnection in the MAST spherical tokamak and the solar corona journal, November 2015

Magnetic islands and singular currents at rational surfaces in three-dimensional magnetohydrodynamic equilibria journal, February 2015

Two-fluid and finite Larmor radius effects on helicity evolution in a plasma pinch journal, March 2016

Formation and primary heating of the solar corona: Theory and simulation journal, January 2001

Nonlinear Alfvén waves in extended magnetohydrodynamics journal, February 2016

Multi-region relaxed magnetohydrodynamics with anisotropy and flow journal, July 2014

Generalized relaxation theory and vortices in plasmas journal, October 1995

Azimuthally symmetric magnetohydrodynamic and two-fluid equilibria with arbitrary flows journal, May 2001

Nonlinear stability of fluid and plasma equilibria journal, July 1985

Turbulent relaxation of compressible plasmas with flow journal, January 1983

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

A heuristic model for MRI turbulent stresses in Hall MHD journal, April 2016

Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria journal, January 1983

The infinite interface limit of multiple-region relaxed magnetohydrodynamics journal, March 2013

Multi-fluid systems—Multi-Beltrami relaxed states and their implications journal, September 2015

Relaxation of a Two-Specie Magnetofluid journal, November 1997

Hamiltonian and action principle formulations of plasma physics journal, May 2005

Hall Current Effects in Mean-Field Dynamo Theory journal, September 2016

Pressure-driven amplification and penetration of resonant magnetic perturbations journal, May 2016

Modelling astrophysical outflows via the unified dynamo–reverse dynamo mechanism journal, February 2015

Hydromagnetic Equilibrium ii. Stability in the Variational Formulation journal, June 1959

Hall Effects on Magnetic Relaxation journal, January 1986

A collisionless self-organizing model for the high-confinement (H-mode) boundary layer journal, February 2000

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

Scale hierarchy created in plasma flow journal, July 2004

Formation and Stability of Impurity “Snakes” in Tokamak Plasmas journal, February 2013

Relaxation of Toroidal Plasma and Generation of Reverse Magnetic Fields journal, November 1974

Non-axisymmetric, multi-region relaxed magnetohydrodynamic equilibrium solutions journal, December 2011

Application of Double Beltrami states to solar eruptions: Double Beltrami states and solar eruptions journal, May 2010

Remarkable connections between extended magnetohydrodynamics models journal, July 2015

Double Curl Beltrami Flow: Diamagnetic Structures journal, November 1998

Stability of Field-Reversed, Force-Free, Plasma Equilibria with Mass Flow journal, May 1979

Relaxed plasma-vacuum systems with pressure journal, July 2003

Magnetic fluctuations and Hall magnetohydrodynamic turbulence in the solar wind journal, January 2004

Some improvements in the theory of plasma relaxation journal, April 2014

Equilibrium of a Magnetically Confined Plasma in a Toroid journal, January 1958

Measurements of the momentum and current transport from tearing instability in the Madison Symmetric Torus reversed-field pinch journal, May 2009

Hamiltonian description of the ideal fluid journal, April 1998

On Hydromagnetic Equilibrium journal, September 1958

Hamiltonian formalism of extended magnetohydrodynamics journal, May 2015

Stepped pressure profile equilibria in cylindrical plasmas via partial Taylor relaxation journal, December 2006

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Relaxation of a quasisymmetric rotating plasma: A model of Jupiter’s magnetosphere journal, September 2005

Entropy production and plasma relaxation journal, January 1987

The action principle for generalized fluid motion including gyroviscosity journal, November 2014

Validation of single-fluid and two-fluid magnetohydrodynamic models of the helicity injected torus spheromak experiment with the NIMROD code journal, August 2013

Three-dimensional free boundary calculations using a spectral Green's function method journal, December 1986

Self-organization during spherical torus formation by flux rope merging in the Mega Ampere Spherical Tokamak journal, April 2014

Overview of results from the MST reversed field pinch experiment journal, September 2013

Studies on Magneto-Hydrodynamic Waves and other Anisotropic Wave Motions journal, March 1960

Minimum energy states of the cylindrical plasma pinch in single-fluid and Hall magnetohydrodynamics journal, January 2012

Magnetofluid Coupling: Eruptive Events in the Solar Corona journal, September 2001

Variational principle with singular perturbation of hall magnetohydrodynamics journal, June 2005

Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics journal, November 2015

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

Nonlinear three-dimensional simulation for self-organization and flow generation in two-fluid plasmas journal, December 2004

Computation of multi-region relaxed magnetohydrodynamic equilibria journal, November 2012

Variational Principles and Self-Organization in Two-Fluid Plasmas journal, February 2002

Pressure-driven amplification and penetration of resonant magnetic perturbations journal, May 2016

Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets journal, September 2015

On Hydromagnetic Stability of Stationary Equilibria journal, October 1960

A Theorem on Force-Free Magnetic Fields journal, June 1958

Action principles for extended magnetohydrodynamic models journal, September 2014

Nonlinear stability of fluid and plasma equilibria journal, July 1985

Nonlinear Alfvén/Beltrami waves—An integrable structure built around the Casimir journal, May 2012

Equilibria and stability in partially relaxed plasma–vacuum systems journal, July 2007

Relaxed plasma-vacuum systems
journal, August 2001

Eigenvalue problems for Beltrami fields arising in a three-dimensional toroidal magnetohydrodynamic equilibrium problem
journal, May 2007

Hall magnetohydrodynamics in space and laboratory plasmas
journal, June 1995

Variational principles for stationary one- and two-fluid equilibria of axisymmetric laboratory and astrophysical plasmas
journal, December 2004

Relaxed Plasma Equilibria and Entropy-Related Plasma Self-Organization Principles
journal, November 2008

Generalized two-fluid equilibria: Understanding RT-1 experiments and beyond
journal, November 2010

Relaxation and magnetic reconnection in plasmas
journal, July 1986

Generation of Flows in the Solar Atmosphere Due to Magnetofluid Coupling
journal, September 2002

First-order finite-Larmor-radius fluid modeling of tearing and relaxation in a plasma pinch
journal, May 2012

Two-fluid and magnetohydrodynamic modelling of magnetic reconnection in the MAST spherical tokamak and the solar corona
journal, November 2015

Magnetic islands and singular currents at rational surfaces in three-dimensional magnetohydrodynamic equilibria
journal, February 2015

Two-fluid and finite Larmor radius effects on helicity evolution in a plasma pinch
journal, March 2016

Formation and primary heating of the solar corona: Theory and simulation
journal, January 2001

Nonlinear Alfvén waves in extended magnetohydrodynamics
journal, February 2016

Multi-region relaxed magnetohydrodynamics with anisotropy and flow
journal, July 2014

Generalized relaxation theory and vortices in plasmas
journal, October 1995

Azimuthally symmetric magnetohydrodynamic and two-fluid equilibria with arbitrary flows
journal, May 2001

Nonlinear stability of fluid and plasma equilibria
journal, July 1985

Turbulent relaxation of compressible plasmas with flow
journal, January 1983

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

A heuristic model for MRI turbulent stresses in Hall MHD
journal, April 2016

Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria
journal, January 1983

The infinite interface limit of multiple-region relaxed magnetohydrodynamics
journal, March 2013

Multi-fluid systems—Multi-Beltrami relaxed states and their implications
journal, September 2015

Relaxation of a Two-Specie Magnetofluid
journal, November 1997

Hamiltonian and action principle formulations of plasma physics
journal, May 2005

Hall Current Effects in Mean-Field Dynamo Theory
journal, September 2016

Pressure-driven amplification and penetration of resonant magnetic perturbations
journal, May 2016

Modelling astrophysical outflows via the unified dynamo–reverse dynamo mechanism
journal, February 2015

Hydromagnetic Equilibrium ii. Stability in the Variational Formulation
journal, June 1959

Hall Effects on Magnetic Relaxation
journal, January 1986

A collisionless self-organizing model for the high-confinement (H-mode) boundary layer
journal, February 2000

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

Scale hierarchy created in plasma flow
journal, July 2004

Formation and Stability of Impurity “Snakes” in Tokamak Plasmas
journal, February 2013

Relaxation of Toroidal Plasma and Generation of Reverse Magnetic Fields
journal, November 1974

Non-axisymmetric, multi-region relaxed magnetohydrodynamic equilibrium solutions
journal, December 2011

Application of Double Beltrami states to solar eruptions: Double Beltrami states and solar eruptions
journal, May 2010

Remarkable connections between extended magnetohydrodynamics models
journal, July 2015

Double Curl Beltrami Flow: Diamagnetic Structures
journal, November 1998

Stability of Field-Reversed, Force-Free, Plasma Equilibria with Mass Flow
journal, May 1979

Relaxed plasma-vacuum systems with pressure
journal, July 2003

Magnetic fluctuations and Hall magnetohydrodynamic turbulence in the solar wind
journal, January 2004

Some improvements in the theory of plasma relaxation
journal, April 2014

Equilibrium of a Magnetically Confined Plasma in a Toroid
journal, January 1958

Measurements of the momentum and current transport from tearing instability in the Madison Symmetric Torus reversed-field pinch
journal, May 2009

Hamiltonian description of the ideal fluid
journal, April 1998

On Hydromagnetic Equilibrium
journal, September 1958

Hamiltonian formalism of extended magnetohydrodynamics
journal, May 2015

Stepped pressure profile equilibria in cylindrical plasmas via partial Taylor relaxation
journal, December 2006

Energy Transformation Mechanism in the Solar Atmosphere Associated with Magnetofluid Coupling: Explosive and Eruptive Events
journal, May 2002

Relaxation of a quasisymmetric rotating plasma: A model of Jupiter’s magnetosphere
journal, September 2005

Entropy production and plasma relaxation
journal, January 1987

The action principle for generalized fluid motion including gyroviscosity
journal, November 2014

Validation of single-fluid and two-fluid magnetohydrodynamic models of the helicity injected torus spheromak experiment with the NIMROD code
journal, August 2013

Three-dimensional free boundary calculations using a spectral Green's function method
journal, December 1986

Self-organization during spherical torus formation by flux rope merging in the Mega Ampere Spherical Tokamak
journal, April 2014

Overview of results from the MST reversed field pinch experiment
journal, September 2013

Studies on Magneto-Hydrodynamic Waves and other Anisotropic Wave Motions
journal, March 1960

Minimum energy states of the cylindrical plasma pinch in single-fluid and Hall magnetohydrodynamics
journal, January 2012

Magnetofluid Coupling: Eruptive Events in the Solar Corona
journal, September 2001

Variational principle with singular perturbation of hall magnetohydrodynamics
journal, June 2005

Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics
journal, November 2015

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

Nonlinear three-dimensional simulation for self-organization and flow generation in two-fluid plasmas
journal, December 2004

Computation of multi-region relaxed magnetohydrodynamic equilibria
journal, November 2012

Variational Principles and Self-Organization in Two-Fluid Plasmas
journal, February 2002

Pressure-driven amplification and penetration of resonant magnetic perturbations
journal, May 2016

Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets
journal, September 2015

On Hydromagnetic Stability of Stationary Equilibria
journal, October 1960

A Theorem on Force-Free Magnetic Fields
journal, June 1958

Action principles for extended magnetohydrodynamic models
journal, September 2014

Nonlinear stability of fluid and plasma equilibria
journal, July 1985

Nonlinear Alfvén/Beltrami waves—An integrable structure built around the Casimir
journal, May 2012

Equilibria and stability in partially relaxed plasma–vacuum systems
journal, July 2007

Relaxed MHD states of a multiple region plasma
journal, May 2009

Magnetohydrodynamic stability of plasmas with ideal and relaxed regions
journal, October 2009

Evaluation of Turner relaxed state as a model of long-lived ion-trapping structures in plasma focus and Z-pinches
journal, March 2011