Hamiltonian Formalism of Extended Magnetohydrodynamics

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 Jacobi's identity for th...

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Bibliographic Details
Published inarXiv.org
Main Authors Abdelhamid, Hamdi M, Kawazura, Yohei, Yoshida, Zensho
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.01.2015
Subjects
Algebra
Computational fluid dynamics
Hall effect
Lie groups
Magnetohydrodynamics
Physics - Plasma Physics
Quantum theory
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Summary: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 Jacobi's 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.
ISSN:2331-8422
DOI:10.48550/arxiv.1412.6228