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

Kawazura, Yohei; Miloshevich, George; Morrison, Philip J.

doi:10.1063/1.4975013

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

Journal Article · Mon Feb 06 00:00:00 EST 2017 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4975013· OSTI ID:1535295

Kawazura, Yohei ^[1];

^[2];

^[2]

Univ. of Tokyo, Kashiwa, Chiba (Japan). Graduate School of Frontier Sciences; Univ. of Oxford, Oxford (United Kingdom). Rudolf Peierles Centre for Theoretical Phyiscs
Univ. of Texas, Austin, TX (United States). Dept. of Physics and Inst. for Fusion Studies

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.

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

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-04ER54742; FG02-04ER-54742

OSTI ID:: 1535295

Alternate ID(s):: OSTI ID: 1349332

Journal Information:: Physics of Plasmas, Vol. 24, Issue 2; ISSN 1070-664X

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

Country of Publication:: United States

Language:: English

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Cited by: 18 works

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Relativistic Tearing Mode in Pair Plasmas and Application to Magnetic Giant Flares Yang, S. D. The Astrophysical Journal, Vol. 880, Issue 1 https://doi.org/10.3847/1538-4357/ab29f6	journal	July 2019

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