Canonical Hamiltonian mechanics of Hall magnetohydrodynamics and its limit to ideal magnetohydrodynamics

Z. Yoshida, E. Hameiri

Research output: Contribution to journalArticle

Abstract

While a microscopic system is usually governed by canonical Hamiltonian mechanics, that of a macroscopic system is often noncanonical, reflecting a degenerate Poisson structure underlying the coarse-grained phase space. Probing into symplectic leaves (local structures in a foliated phase space), we may be able to elucidate the order of transition from micro to macro. The Lagrangian guides our analysis. We formulate canonized Hamiltonian systems of Hall magnetohydrodynamics (HMHD) which have a hierarchized set of canonical variables; the simplest system is the subclass in which the ion vorticity and magnetic field have integral surfaces. Renormalizing the singularity scaled by the reciprocal Hall parameter (as the ion vorticity surfaces and the magnetic surfaces are set to merge), we delineate the singular limit to ideal magnetohydrodynamics (MHD). The formulated canonical equations will be useful in the study of ordered structures and dynamics (with integrable vortex lines) in HMHD and their singular limit to MHD, such as magnetic confinement systems, shocks or vortical dynamics.

Original languageEnglish (US)
Article number335502
JournalJournal of Physics A: Mathematical and Theoretical
Volume46
Issue number33
DOIs
StatePublished - Aug 23 2013

Fingerprint

Hamiltonian Mechanics
Hamiltonians
Magnetohydrodynamics
magnetohydrodynamics
Mechanics
Singular Limit
Vorticity
vorticity
Phase Space
Surface integral
Poisson Structure
Ions
Local Structure
leaves
Hamiltonian Systems
Macros
Vortex
Shock
Leaves
ions

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Modeling and Simulation
  • Statistics and Probability

Cite this

Canonical Hamiltonian mechanics of Hall magnetohydrodynamics and its limit to ideal magnetohydrodynamics. / Yoshida, Z.; Hameiri, E.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 46, No. 33, 335502, 23.08.2013.

Research output: Contribution to journalArticle

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