Hamiltonian Formalism of Extended Magnetohydrodynamics

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.

arXiv comment17 pages

References in corpus (4)

• Hamiltonian formulation and analysis of a collisionless fluid reconnection model
• On energy conservation in extended magnetohydrodynamics
• Action Principles for Extended MHD Models
• Inertial magnetohydrodynamics

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