A class of three-dimensional gyroviscous magnetohydrodynamic models

Lingam, Manasvi; Morrison, Philip J.; Wurm, Alexander

doi:10.1017/s0022377820001038

A class of three-dimensional gyroviscous magnetohydrodynamic models

Journal Article · Tue Sep 22 04:00:00 EDT 2020 · Journal of Plasma Physics

DOI:https://doi.org/10.1017/s0022377820001038· OSTI ID:1850238

^[1]; ; Wurm, Alexander

OSTI

A Hamiltonian and action principle formalism for deriving three-dimensional gyroviscous magnetohydrodynamic models is presented. The uniqueness of the approach in constructing the gyroviscous tensor from first principles and its ability to explain the origin of the gyromap and the gyroviscous terms are highlighted. The procedure allows for the specification of free functions, which can be used to generate a wide range of gyroviscous models. Through the process of reduction, the noncanonical Hamiltonian bracket is obtained and briefly analysed.

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

Sponsoring Organization:: USDOE

DOE Contract Number:: FG05-80ET53088

OSTI ID:: 1850238

Journal Information:: Journal of Plasma Physics, Journal Name: Journal of Plasma Physics Journal Issue: 5 Vol. 86; ISSN 0022-3778

Publisher:: Cambridge University Press

Country of Publication:: United States

Language:: English

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Hamiltonian formulation of reduced magnetohydrodynamics Morrison, P. J.; Hazeltine, R. D. Physics of Fluids, Vol. 27, Issue 4 https://doi.org/10.1063/1.864718	journal	January 1984
Variational Principle in Magnetohydrodynamics Merches, Ioan Physics of Fluids, Vol. 12, Issue 10 https://doi.org/10.1063/1.1692333	journal	January 1969
A compressible Hamiltonian electromagnetic gyrofluid model Waelbroeck, F. L.; Tassi, E. Communications in Nonlinear Science and Numerical Simulation, Vol. 17, Issue 5 https://doi.org/10.1016/j.cnsns.2011.04.015	journal	May 2012
The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum Theories Holm, Darryl D.; Marsden, Jerrold E.; Ratiu, Tudor S. Advances in Mathematics, Vol. 137, Issue 1 https://doi.org/10.1006/aima.1998.1721	journal	July 1998
A hierarchy of noncanonical Hamiltonian systems: circulation laws in an extended phase space Yoshida, Z.; J. Morrison, P. Fluid Dynamics Research, Vol. 46, Issue 3 https://doi.org/10.1088/0169-5983/46/3/031412	journal	May 2014
Dynamo theories Rincon, François Journal of Plasma Physics, Vol. 85, Issue 4 https://doi.org/10.1017/S0022377819000539	journal	August 2019
Hierarchical structure of noncanonical Hamiltonian systems Yoshida, Z.; Morrison, P. J. Physica Scripta, Vol. 91, Issue 2 https://doi.org/10.1088/0031-8949/91/2/024001	journal	January 2016
Finite-Larmor-radius magnetohydrodynamic equations for microturbulence Hasegawa, Akira Physics of Fluids, Vol. 26, Issue 10 https://doi.org/10.1063/1.864065	journal	January 1983
A Hamiltonian five-field gyrofluid model Keramidas Charidakos, I.; Waelbroeck, F. L.; Morrison, P. J. Physics of Plasmas, Vol. 22, Issue 11 https://doi.org/10.1063/1.4936102	journal	November 2015
Hamiltonian four-field model for nonlinear tokamak dynamics Hazeltine, R. D.; Hsu, C. T.; Morrison, P. J. Physics of Fluids, Vol. 30, Issue 10 https://doi.org/10.1063/1.866527	journal	January 1987
On energy conservation in extended magnetohydrodynamics Kimura, Keiji; Morrison, P. J. Physics of Plasmas, Vol. 21, Issue 8 https://doi.org/10.1063/1.4890955	journal	August 2014
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
Symmetry of the pressure tensor in macromolecular fluids Olmsted, R. D.; Snider, R. F. The Journal of Chemical Physics, Vol. 65, Issue 9 https://doi.org/10.1063/1.433594	journal	November 1976
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
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
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
Fluid model of collisionless plasma with finite Larmor radius effects Smolyakov, A. I.; Pogutse, I. O.; Hirose, A. Physics of Plasmas, Vol. 2, Issue 12 https://doi.org/10.1063/1.871001	journal	December 1995
A generalized reduced fluid model with finite ion-gyroradius effects Hsu, C. T.; Hazeltine, R. D.; Morrison, P. J. Physics of Fluids, Vol. 29, Issue 5 https://doi.org/10.1063/1.865665	journal	January 1986
Hybrid Vlasov-MHD models: Hamiltonian vs. non-Hamiltonian Tronci, Cesare; Tassi, Emanuele; Camporeale, Enrico Plasma Physics and Controlled Fusion, Vol. 56, Issue 9 https://doi.org/10.1088/0741-3335/56/9/095008	journal	July 2014
Hamiltonian gyrofluid reductions of gyrokinetic equations Tassi, E. Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 46 https://doi.org/10.1088/1751-8121/ab4a31	journal	October 2019
A low-frequency variational model for energetic particle effects in the pressure-coupling scheme Close, Alexander R. D.; Burby, Joshua W.; Tronci, Cesare Journal of Plasma Physics, Vol. 84, Issue 4 https://doi.org/10.1017/S0022377818000697	journal	July 2018
Local and nonlocal advected invariants and helicities in magnetohydrodynamics and gas dynamics: II. Noether's theorems and Casimirs Webb, G. M.; Dasgupta, B.; McKenzie, J. F. Journal of Physics A: Mathematical and Theoretical, Vol. 47, Issue 9 https://doi.org/10.1088/1751-8113/47/9/095502	journal	February 2014
A gyro-Landau-fluid transport model Waltz, R. E.; Staebler, G. M.; Dorland, W. Physics of Plasmas, Vol. 4, Issue 7 https://doi.org/10.1063/1.872228	journal	July 1997
Variational approach to low-frequency kinetic-MHD in the current coupling scheme Burby, Joshua W.; Tronci, Cesare Plasma Physics and Controlled Fusion, Vol. 59, Issue 4 https://doi.org/10.1088/1361-6587/aa5c5b	journal	March 2017
Symmetry of the stress tensor McLennan, J. A. Physica, Vol. 32, Issue 4 https://doi.org/10.1016/0031-8914(66)90002-4	journal	April 1966
Fluid formalism for collisionless magnetized plasmas Ramos, J. J. Physics of Plasmas, Vol. 12, Issue 5 https://doi.org/10.1063/1.1884128	journal	May 2005
Variational principles for gravity and fluids Kopczyński, Wojciech Annals of Physics, Vol. 203, Issue 2 https://doi.org/10.1016/0003-4916(90)90173-L	journal	November 1990
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
Stability of Beltrami flows Yoshida, Z.; Ohsaki, S.; Ito, A. Journal of Mathematical Physics, Vol. 44, Issue 5 https://doi.org/10.1063/1.1567798	journal	May 2003
Nonlinear finite-Larmor-radius effects in reduced fluid models Brizard, A. J.; Denton, R. E.; Rogers, B. Physics of Plasmas, Vol. 15, Issue 8 https://doi.org/10.1063/1.2965827	journal	August 2008
Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions Batt, J�rgen; Morrison, Philip J.; Rein, Gerhard Archive for Rational Mechanics and Analysis, Vol. 130, Issue 2 https://doi.org/10.1007/BF00375154	journal	January 1995
A Hamiltonian electromagnetic gyrofluid model Waelbroeck, F. L.; Hazeltine, R. D.; Morrison, P. J. Physics of Plasmas, Vol. 16, Issue 3 https://doi.org/10.1063/1.3087972	journal	March 2009

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