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arXiv · 1412.6228

Hamiltonian Formalism of Extended Magnetohydrodynamics

Hamdi M. Abdelhamid·Yohei Kawazura·Zensho Yoshida
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Abstract

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.

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Hamdi M. Abdelhamid, Yohei Kawazura, Zensho Yoshida. 2014-12-19. Hamiltonian Formalism of Extended Magnetohydrodynamics. https://doi.org/10.1088/1751-8113%2F48%2F23%2F235502

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