### 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 language | English (US) |
---|---|

Article number | 335502 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 46 |

Issue number | 33 |

DOIs | |

State | Published - Aug 23 2013 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*46*(33), [335502]. https://doi.org/10.1088/1751-8113/46/33/335502

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

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 46, no. 33, 335502. https://doi.org/10.1088/1751-8113/46/33/335502

}

TY - JOUR

T1 - Canonical Hamiltonian mechanics of Hall magnetohydrodynamics and its limit to ideal magnetohydrodynamics

AU - Yoshida, Z.

AU - Hameiri, E.

PY - 2013/8/23

Y1 - 2013/8/23

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84881346121&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84881346121&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/46/33/335502

DO - 10.1088/1751-8113/46/33/335502

M3 - Article

VL - 46

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 33

M1 - 335502

ER -