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 -