Hamiltonian formalism of extended magnetohydrodynamics

H. M. Abdelhamid, Y. Kawazura, Z. Yoshida

Research output: Contribution to journalArticlepeer-review

40 Citations (Scopus)


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.

Original languageEnglish
Article number235502
JournalJournal of Physics A: Mathematical and Theoretical
Issue number23
Publication statusPublished - 2015 Jun 10


  • extended magnetohydrodynamics
  • Hamiltonian dynamics
  • Jacobi's identity


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