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

Journal Article · Wed Aug 03 00:00:00 EDT 2016 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4960128· OSTI ID:1332513

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)

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.

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

Sponsoring Organization:: USDOE

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

OSTI ID:: 1332513

Alternate ID(s):: OSTI ID: 1281331

Journal Information:: Physics of Plasmas, Vol. 23, Issue 8; ISSN 1070-664X

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

Country of Publication:: United States

Language:: English

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Cited by: 8 works

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References (82)

Relaxed plasma-vacuum systems Spies, G. O.; Lortz, D.; Kaiser, R. Physics of Plasmas, Vol. 8, Issue 8 https://doi.org/10.1063/1.1383286	journal	August 2001
Eigenvalue problems for Beltrami fields arising in a three-dimensional toroidal magnetohydrodynamic equilibrium problem Hudson, S. R.; Hole, M. J.; Dewar, R. L. Physics of Plasmas, Vol. 14, Issue 5 https://doi.org/10.1063/1.2722721	journal	May 2007
Hall magnetohydrodynamics in space and laboratory plasmas Huba, J. D. Physics of Plasmas, Vol. 2, Issue 6 https://doi.org/10.1063/1.871212	journal	June 1995
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
Relaxed Plasma Equilibria and Entropy-Related Plasma Self-Organization Principles Dewar, Robert; Hole, Matthew; McGann, Mathew Entropy, Vol. 10, Issue 4 https://doi.org/10.3390/e10040621	journal	November 2008
Generalized two-fluid equilibria: Understanding RT-1 experiments and beyond Yoshida, Z.; Mahajan, S. M.; Mizushima, T. Physics of Plasmas, Vol. 17, Issue 11 https://doi.org/10.1063/1.3505821	journal	November 2010
Relaxation and magnetic reconnection in plasmas Taylor, J. B. Reviews of Modern Physics, Vol. 58, Issue 3 https://doi.org/10.1103/RevModPhys.58.741	journal	July 1986
Generation of Flows in the Solar Atmosphere Due to Magnetofluid Coupling Mahajan, Swadesh M.; Nikol’skaya, Komunela I.; Shatashvili, Nana L. The Astrophysical Journal, Vol. 576, Issue 2 https://doi.org/10.1086/343727	journal	September 2002
First-order finite-Larmor-radius fluid modeling of tearing and relaxation in a plasma pinch King, J. R.; Sovinec, C. R.; Mirnov, V. V. Physics of Plasmas, Vol. 19, Issue 5 https://doi.org/10.1063/1.3695346	journal	May 2012
Two-fluid and magnetohydrodynamic modelling of magnetic reconnection in the MAST spherical tokamak and the solar corona Browning, P. K.; Cardnell, S.; Evans, M. Plasma Physics and Controlled Fusion, Vol. 58, Issue 1 https://doi.org/10.1088/0741-3335/58/1/014041	journal	November 2015
Magnetic islands and singular currents at rational surfaces in three-dimensional magnetohydrodynamic equilibria Loizu, J.; Hudson, S.; Bhattacharjee, A. Physics of Plasmas, Vol. 22, Issue 2 https://doi.org/10.1063/1.4906888	journal	February 2015
Two-fluid and finite Larmor radius effects on helicity evolution in a plasma pinch Sauppe, J. P.; Sovinec, C. R. Physics of Plasmas, Vol. 23, Issue 3 https://doi.org/10.1063/1.4942761	journal	March 2016
Formation and primary heating of the solar corona: Theory and simulation Mahajan, S. M.; Miklaszewski, R.; Nikol’skaya, K. I. Physics of Plasmas, Vol. 8, Issue 4 https://doi.org/10.1063/1.1350670	journal	January 2001
Nonlinear Alfvén waves in extended magnetohydrodynamics Abdelhamid, Hamdi M.; Yoshida, Zensho Physics of Plasmas, Vol. 23, Issue 2 https://doi.org/10.1063/1.4941596	journal	February 2016
Multi-region relaxed magnetohydrodynamics with anisotropy and flow Dennis, G. R.; Hudson, S. R.; Dewar, R. L. Physics of Plasmas, Vol. 21, Issue 7 https://doi.org/10.1063/1.4890847	journal	July 2014
Generalized relaxation theory and vortices in plasmas Oliveira, Samuel R.; Tajima, Toshiki Physical Review E, Vol. 52, Issue 4 https://doi.org/10.1103/PhysRevE.52.4287	journal	October 1995
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
Nonlinear stability of fluid and plasma equilibria Holm, Darryl D.; Marsden, Jerrold E.; Ratiu, Tudor Physics Reports, Vol. 123, Issue 1-2 https://doi.org/10.1016/0370-1573(85)90028-6	journal	July 1985
Turbulent relaxation of compressible plasmas with flow Finn, John M. Physics of Fluids, Vol. 26, Issue 12 https://doi.org/10.1063/1.864115	journal	January 1983
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
A heuristic model for MRI turbulent stresses in Hall MHD Lingam, Manasvi; Bhattacharjee, Amitava Monthly Notices of the Royal Astronomical Society, Vol. 460, Issue 1 https://doi.org/10.1093/mnras/stw997	journal	April 2016
Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria Hirshman, S. P. Physics of Fluids, Vol. 26, Issue 12 https://doi.org/10.1063/1.864116	journal	January 1983
The infinite interface limit of multiple-region relaxed magnetohydrodynamics Dennis, G. R.; Hudson, S. R.; Dewar, R. L. Physics of Plasmas, Vol. 20, Issue 3 https://doi.org/10.1063/1.4795739	journal	March 2013
Multi-fluid systems—Multi-Beltrami relaxed states and their implications Mahajan, Swadesh M.; Lingam, Manasvi Physics of Plasmas, Vol. 22, Issue 9 https://doi.org/10.1063/1.4931069	journal	September 2015
Relaxation of a Two-Specie Magnetofluid Steinhauer, L. C.; Ishida, A. Physical Review Letters, Vol. 79, Issue 18 https://doi.org/10.1103/PhysRevLett.79.3423	journal	November 1997
Hamiltonian and action principle formulations of plasma physics Morrison, P. J. Physics of Plasmas, Vol. 12, Issue 5 https://doi.org/10.1063/1.1882353	journal	May 2005
Hall Current Effects in Mean-Field Dynamo Theory Lingam, Manasvi; Bhattacharjee, Amitava The Astrophysical Journal, Vol. 829, Issue 1 https://doi.org/10.3847/0004-637X/829/1/51	journal	September 2016
Pressure-driven amplification and penetration of resonant magnetic perturbations Loizu, J.; Hudson, S. R.; Helander, P. Physics of Plasmas, Vol. 23, Issue 5 https://doi.org/10.1063/1.4944818	journal	May 2016
Modelling astrophysical outflows via the unified dynamo–reverse dynamo mechanism Lingam, Manasvi; Mahajan, Swadesh M. Monthly Notices of the Royal Astronomical Society: Letters, Vol. 449, Issue 1 https://doi.org/10.1093/mnrasl/slv017	journal	February 2015
Hydromagnetic Equilibrium ii. Stability in the Variational Formulation Woltjer, L. Proceedings of the National Academy of Sciences, Vol. 45, Issue 6 https://doi.org/10.1073/pnas.45.6.769	journal	June 1959
Hall Effects on Magnetic Relaxation Turner, Leaf IEEE Transactions on Plasma Science, Vol. 14, Issue 6 https://doi.org/10.1109/TPS.1986.4316633	journal	January 1986
A collisionless self-organizing model for the high-confinement (H-mode) boundary layer Mahajan, S. M.; Yoshida, Z. Physics of Plasmas, Vol. 7, Issue 2 https://doi.org/10.1063/1.873850	journal	February 2000
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
Scale hierarchy created in plasma flow Yoshida, Z.; Mahajan, S. M.; Ohsaki, S. Physics of Plasmas, Vol. 11, Issue 7 https://doi.org/10.1063/1.1762877	journal	July 2004
Formation and Stability of Impurity “Snakes” in Tokamak Plasmas Delgado-Aparicio, L.; Sugiyama, L.; Granetz, R. Physical Review Letters, Vol. 110, Issue 6 https://doi.org/10.1103/PhysRevLett.110.065006	journal	February 2013
Relaxation of Toroidal Plasma and Generation of Reverse Magnetic Fields Taylor, J. B. Physical Review Letters, Vol. 33, Issue 19 https://doi.org/10.1103/PhysRevLett.33.1139	journal	November 1974
Non-axisymmetric, multi-region relaxed magnetohydrodynamic equilibrium solutions Hudson, S. R.; Dewar, R. L.; Hole, M. J. Plasma Physics and Controlled Fusion, Vol. 54, Issue 1 https://doi.org/10.1088/0741-3335/54/1/014005	journal	December 2011
Application of Double Beltrami states to solar eruptions: Double Beltrami states and solar eruptions Kagan, D.; Mahajan, S. M. Monthly Notices of the Royal Astronomical Society https://doi.org/10.1111/j.1365-2966.2010.16741.x	journal	May 2010
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
Double Curl Beltrami Flow: Diamagnetic Structures Mahajan, S. M.; Yoshida, Z. Physical Review Letters, Vol. 81, Issue 22 https://doi.org/10.1103/PhysRevLett.81.4863	journal	November 1998
Stability of Field-Reversed, Force-Free, Plasma Equilibria with Mass Flow Sudan, R. N. Physical Review Letters, Vol. 42, Issue 19 https://doi.org/10.1103/PhysRevLett.42.1277	journal	May 1979
Relaxed plasma-vacuum systems with pressure Spies, G. O. Physics of Plasmas, Vol. 10, Issue 7 https://doi.org/10.1063/1.1584047	journal	July 2003
Magnetic fluctuations and Hall magnetohydrodynamic turbulence in the solar wind Krishan, V. Journal of Geophysical Research, Vol. 109, Issue A11 https://doi.org/10.1029/2004JA010496	journal	January 2004
Some improvements in the theory of plasma relaxation Hameiri, Eliezer Physics of Plasmas, Vol. 21, Issue 4 https://doi.org/10.1063/1.4871391	journal	April 2014
Equilibrium of a Magnetically Confined Plasma in a Toroid Kruskal, M. D.; Kulsrud, R. M. Physics of Fluids, Vol. 1, Issue 4 https://doi.org/10.1063/1.1705884	journal	January 1958
Measurements of the momentum and current transport from tearing instability in the Madison Symmetric Torus reversed-field pinch Kuritsyn, A.; Fiksel, G.; Almagri, A. F. Physics of Plasmas, Vol. 16, Issue 5 https://doi.org/10.1063/1.3090325	journal	May 2009
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
On Hydromagnetic Equilibrium Woltjer, L. Proceedings of the National Academy of Sciences, Vol. 44, Issue 9 https://doi.org/10.1073/pnas.44.9.833	journal	September 1958
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
Stepped pressure profile equilibria in cylindrical plasmas via partial Taylor relaxation Hole, M. J.; Hudson, S. R.; Dewar, R. L. Journal of Plasma Physics, Vol. 72, Issue 06 https://doi.org/10.1017/S0022377806005861	journal	December 2006
Energy Transformation Mechanism in the Solar Atmosphere Associated with Magnetofluid Coupling: Explosive and Eruptive Events Ohsaki, Shuichi; Shatashvili, Nana L.; Yoshida, Zensho The Astrophysical Journal, Vol. 570, Issue 1 https://doi.org/10.1086/339499	journal	May 2002
Relaxation of a quasisymmetric rotating plasma: A model of Jupiter’s magnetosphere Shiraishi, Jun-ya; Ohsaki, Shuichi; Yoshida, Zensho Physics of Plasmas, Vol. 12, Issue 9 https://doi.org/10.1063/1.2041655	journal	September 2005
Entropy production and plasma relaxation Hameiri, Eliezer; Bhattacharjee, A. Physical Review A, Vol. 35, Issue 2 https://doi.org/10.1103/PhysRevA.35.768	journal	January 1987
The action principle for generalized fluid motion including gyroviscosity Lingam, M.; Morrison, P. J. Physics Letters A, Vol. 378, Issue 47 https://doi.org/10.1016/j.physleta.2014.10.013	journal	November 2014
Validation of single-fluid and two-fluid magnetohydrodynamic models of the helicity injected torus spheromak experiment with the NIMROD code Akcay, Cihan; Kim, Charlson C.; Victor, Brian S. Physics of Plasmas, Vol. 20, Issue 8 https://doi.org/10.1063/1.4817951	journal	August 2013
Three-dimensional free boundary calculations using a spectral Green's function method Hirshman, S. P.; van RIJ, W. I.; Merkel, P. Computer Physics Communications, Vol. 43, Issue 1 https://doi.org/10.1016/0010-4655(86)90058-5	journal	December 1986
Self-organization during spherical torus formation by flux rope merging in the Mega Ampere Spherical Tokamak Browning, P. K.; Stanier, A.; Ashworth, G. Plasma Physics and Controlled Fusion, Vol. 56, Issue 6 https://doi.org/10.1088/0741-3335/56/6/064009	journal	April 2014
Overview of results from the MST reversed field pinch experiment Sarff, J. S.; Almagri, A. F.; Anderson, J. K. Nuclear Fusion, Vol. 53, Issue 10 https://doi.org/10.1088/0029-5515/53/10/104017	journal	September 2013
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
Minimum energy states of the cylindrical plasma pinch in single-fluid and Hall magnetohydrodynamics Khalzov, I. V.; Ebrahimi, F.; Schnack, D. D. Physics of Plasmas, Vol. 19, Issue 1 https://doi.org/10.1063/1.3676600	journal	January 2012
Magnetofluid Coupling: Eruptive Events in the Solar Corona Ohsaki, Shuichi; Shatashvili, Nana L.; Yoshida, Zensho The Astrophysical Journal, Vol. 559, Issue 1 https://doi.org/10.1086/323651	journal	September 2001
Variational principle with singular perturbation of hall magnetohydrodynamics Ohsaki, Shuichi; Yoshida, Zensho Physics of Plasmas, Vol. 12, Issue 6 https://doi.org/10.1063/1.1936585	journal	June 2005
Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics Dewar, R. L.; Yoshida, Z.; Bhattacharjee, A. Journal of Plasma Physics, Vol. 81, Issue 6 https://doi.org/10.1017/S0022377815001336	journal	November 2015
Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics Morrison, P. J.; Lingam, M.; Acevedo, R. Physics of Plasmas, Vol. 21, Issue 8 https://doi.org/10.1063/1.4891321	journal	August 2014
A theory for the pressure pedestal in high (H) mode tokamak discharges Guzdar, P. N.; Mahajan, S. M.; Yoshida, Z. Physics of Plasmas, Vol. 12, Issue 3 https://doi.org/10.1063/1.1852468	journal	March 2005
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
Nonlinear three-dimensional simulation for self-organization and flow generation in two-fluid plasmas Numata, Ryusuke; Yoshida, Zensho; Hayashi, Takaya Computer Physics Communications, Vol. 164, Issue 1-3 https://doi.org/10.1016/j.cpc.2004.06.041	journal	December 2004
Computation of multi-region relaxed magnetohydrodynamic equilibria Hudson, S. R.; Dewar, R. L.; Dennis, G. Physics of Plasmas, Vol. 19, Issue 11 https://doi.org/10.1063/1.4765691	journal	November 2012
Variational Principles and Self-Organization in Two-Fluid Plasmas Yoshida, Z.; Mahajan, S. M. Physical Review Letters, Vol. 88, Issue 9 https://doi.org/10.1103/PhysRevLett.88.095001	journal	February 2002
Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets Loizu, J.; Hudson, S. R.; Bhattacharjee, A. Physics of Plasmas, Vol. 22, Issue 9 https://doi.org/10.1063/1.4931094	journal	September 2015
On Hydromagnetic Stability of Stationary Equilibria Frieman, E.; Rotenberg, Manuel Reviews of Modern Physics, Vol. 32, Issue 4 https://doi.org/10.1103/RevModPhys.32.898	journal	October 1960
A Theorem on Force-Free Magnetic Fields Woltjer, L. Proceedings of the National Academy of Sciences, Vol. 44, Issue 6 https://doi.org/10.1073/pnas.44.6.489	journal	June 1958
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
Nonlinear Alfvén/Beltrami waves—An integrable structure built around the Casimir Yoshida, Z. Communications in Nonlinear Science and Numerical Simulation, Vol. 17, Issue 5 https://doi.org/10.1016/j.cnsns.2011.04.010	journal	May 2012
Equilibria and stability in partially relaxed plasma–vacuum systems Hole, M. J.; Hudson, S. R.; Dewar, R. L. Nuclear Fusion, Vol. 47, Issue 8 https://doi.org/10.1088/0029-5515/47/8/004	journal	July 2007
Relaxed MHD states of a multiple region plasma Hole, M. J.; Mills, R.; Hudson, S. R. Nuclear Fusion, Vol. 49, Issue 6 https://doi.org/10.1088/0029-5515/49/6/065019	journal	May 2009
Magnetohydrodynamic stability of plasmas with ideal and relaxed regions Mills, R. L.; Hole, M. J.; Dewar, R. L. Journal of Plasma Physics, Vol. 75, Issue 5 https://doi.org/10.1017/S0022377809008095	journal	October 2009
Evaluation of Turner relaxed state as a model of long-lived ion-trapping structures in plasma focus and Z-pinches Auluck, S. K. H. Physics of Plasmas, Vol. 18, Issue 3 https://doi.org/10.1063/1.3554701	journal	March 2011
Beltrami fields in plasmas: High-confinement mode boundary layers and high beta equilibria Yoshida, Z.; Mahajan, S. M.; Ohsaki, S. Physics of Plasmas, Vol. 8, Issue 5 https://doi.org/10.1063/1.1354149	journal	May 2001
Multi-region relaxed magnetohydrodynamics with flow Dennis, G. R.; Hudson, S. R.; Dewar, R. L. Physics of Plasmas, Vol. 21, Issue 4 https://doi.org/10.1063/1.4870008	journal	April 2014
Relaxation of a two-species magnetofluid and application to finite-β flowing plasmas Steinhauer, L. C.; Ishida, A. Physics of Plasmas, Vol. 5, Issue 7 https://doi.org/10.1063/1.872948	journal	July 1998
Ideal MHD Freidberg, Jeffrey P. https://doi.org/10.1017/CBO9780511795046	book	July 2014

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