TY - JOUR

T1 - Hamiltonian formalism of extended magnetohydrodynamics

AU - Abdelhamid, H. M.

AU - Kawazura, Y.

AU - Yoshida, Z.

N1 - Publisher Copyright:
© 2015 IOP Publishing Ltd.

PY - 2015/6/10

Y1 - 2015/6/10

N2 - The extended magnetohydrodynamics (MHD) system, including the Hall effect and the electron inertia effect, has a Hamiltonian structure embodied by a noncanonical Poisson algebra on an infinite-dimensional phase space. A nontrivial part of the formulation is the proof of Jacobis identity for the Poisson bracket. We unearth a basic Lie algebra that generates the Poisson bracket. A class of similar Poisson algebra may be generated by the same Lie algebra, which encompasses the Hall MHD system and inertial MHD system.

AB - The extended magnetohydrodynamics (MHD) system, including the Hall effect and the electron inertia effect, has a Hamiltonian structure embodied by a noncanonical Poisson algebra on an infinite-dimensional phase space. A nontrivial part of the formulation is the proof of Jacobis identity for the Poisson bracket. We unearth a basic Lie algebra that generates the Poisson bracket. A class of similar Poisson algebra may be generated by the same Lie algebra, which encompasses the Hall MHD system and inertial MHD system.

KW - extended magnetohydrodynamics

KW - Hamiltonian dynamics

KW - Jacobi's identity

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U2 - 10.1088/1751-8113/48/23/235502

DO - 10.1088/1751-8113/48/23/235502

M3 - Article

AN - SCOPUS:84929999286

SN - 1751-8113

VL - 48

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 23

M1 - 235502

ER -