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Title: Action principles for relativistic extended magnetohydrodynamics: A unified theory of magnetofluid models

Abstract

Two types of Eulerian action principles for relativistic extended magnetohydrodynamics (MHD) are formulated. With the first, the action is extremized under the constraints of density, entropy, and Lagrangian label conservation, which leads to a Clebsch representation for a generalized momentum and a generalized vector potential. The second action arises upon transformation to physical field variables, giving rise to a covariant bracket action principle, i.e., a variational principle in which constrained variations are generated by a degenerate Poisson bracket. Upon taking appropriate limits, the action principles lead to relativistic Hall MHD and well-known relativistic ideal MHD. For the first time, the Hamiltonian formulation of relativistic Hall MHD with electron thermal inertia (akin to Comisso et al., Phys. Rev. Lett. 113, 045001 (2014) for the electron–positron plasma) is introduced. This thermal inertia effect allows for violation of the frozen-in magnetic flux condition in marked contrast to nonrelativistic Hall MHD that does satisfy the frozen-in condition. We also find the violation of the frozen-in condition is accompanied by freezing-in of an alternative flux determined by a generalized vector potential. Finally, we derive a more general 3 + 1 Poisson bracket for nonrelativistic extended MHD, one that does not assume smallness of the electronmore » ion mass ratio.« less

Authors:
 [1]; ORCiD logo [2]; ORCiD logo [2]
  1. Univ. of Tokyo, Kashiwa, Chiba (Japan). Graduate School of Frontier Sciences; Univ. of Oxford, Oxford (United Kingdom). Rudolf Peierles Centre for Theoretical Phyiscs
  2. Univ. of Texas, Austin, TX (United States). Dept. of Physics and Inst. for Fusion Studies
Publication Date:
Research Org.:
Univ. of Texas, Austin, TX (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1535295
Alternate Identifier(s):
OSTI ID: 1349332
Grant/Contract Number:  
FG02-04ER54742; FG02-04ER-54742
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 24; Journal Issue: 2; 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

Citation Formats

Kawazura, Yohei, Miloshevich, George, and Morrison, Philip J. Action principles for relativistic extended magnetohydrodynamics: A unified theory of magnetofluid models. United States: N. p., 2017. Web. doi:10.1063/1.4975013.
Kawazura, Yohei, Miloshevich, George, & Morrison, Philip J. Action principles for relativistic extended magnetohydrodynamics: A unified theory of magnetofluid models. United States. https://doi.org/10.1063/1.4975013
Kawazura, Yohei, Miloshevich, George, and Morrison, Philip J. Mon . "Action principles for relativistic extended magnetohydrodynamics: A unified theory of magnetofluid models". United States. https://doi.org/10.1063/1.4975013. https://www.osti.gov/servlets/purl/1535295.
@article{osti_1535295,
title = {Action principles for relativistic extended magnetohydrodynamics: A unified theory of magnetofluid models},
author = {Kawazura, Yohei and Miloshevich, George and Morrison, Philip J.},
abstractNote = {Two types of Eulerian action principles for relativistic extended magnetohydrodynamics (MHD) are formulated. With the first, the action is extremized under the constraints of density, entropy, and Lagrangian label conservation, which leads to a Clebsch representation for a generalized momentum and a generalized vector potential. The second action arises upon transformation to physical field variables, giving rise to a covariant bracket action principle, i.e., a variational principle in which constrained variations are generated by a degenerate Poisson bracket. Upon taking appropriate limits, the action principles lead to relativistic Hall MHD and well-known relativistic ideal MHD. For the first time, the Hamiltonian formulation of relativistic Hall MHD with electron thermal inertia (akin to Comisso et al., Phys. Rev. Lett. 113, 045001 (2014) for the electron–positron plasma) is introduced. This thermal inertia effect allows for violation of the frozen-in magnetic flux condition in marked contrast to nonrelativistic Hall MHD that does satisfy the frozen-in condition. We also find the violation of the frozen-in condition is accompanied by freezing-in of an alternative flux determined by a generalized vector potential. Finally, we derive a more general 3 + 1 Poisson bracket for nonrelativistic extended MHD, one that does not assume smallness of the electron ion mass ratio.},
doi = {10.1063/1.4975013},
journal = {Physics of Plasmas},
number = 2,
volume = 24,
place = {United States},
year = {Mon Feb 06 00:00:00 EST 2017},
month = {Mon Feb 06 00:00:00 EST 2017}
}

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Works referencing / citing this record:

Structure and structure-preserving algorithms for plasma physics
journal, April 2017


Direction of cascades in a magnetofluid model with electron skin depth and ion sound Larmor radius scales
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Relativistic Tearing Mode in Pair Plasmas and Application to Magnetic Giant Flares
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