TY - JOUR

T1 - Action principles for relativistic extended magnetohydrodynamics

T2 - A unified theory of magnetofluid models

AU - Kawazura, Yohei

AU - Miloshevich, George

AU - Morrison, Philip J.

N1 - Funding Information:
The work of Y.K. was supported by JSPS KAKENHI Grant No. 26800279. G.M. and P.J.M. were supported by the U.S. Department of Energy under Contract No. DE-FG02-04ER-54742. P.J.M. would also like to acknowledge the support from the Alexander von Humboldt Foundation and the hospitality of the Numerical Plasma Physics Division of the IPP, Max Planck, Garching.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - 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.

AB - 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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U2 - 10.1063/1.4975013

DO - 10.1063/1.4975013

M3 - Article

AN - SCOPUS:85011706543

VL - 24

JO - Physics of Plasmas

JF - Physics of Plasmas

SN - 1070-664X

IS - 2

M1 - 022103

ER -