2014/11/30 by Keisuke Araki
Physics and Astronomy · #Classical mechanics #Conservation law #Equations of motion #Group (periodic table) #Helicity #Ionosphere and magnetosphere dynamics #Magnetic confinement fusion research #Magnetic field #Magnetohydrodynamics #Mathematical physics #Physics #Quantum mechanics #Semidirect product #Solar and Space Plasma Dynamics #nlin.CD #physics.plasm-ph
paper · pdf · doi:10.1088/1751-8113/48/17/175501
published as J. Phys. A: Math. Theor. 48 (2015) 175501 · In this version, some errors, typos, and some dropped references in the previous version are corrected
openalex publication_date 2015/04/02 · arxiv created 2015/04/03 · arxiv updated 2015/06/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The dynamics of a dissipationless incompressible Hall magnetohydrodynamic (HMHD) medium is formulated using Lagrangian mechanics on a semidirect product of two volume preserving diffeomorphism groups. In the case of or E 3 , the generalized Elsässer variables (GEV) introduced by (Galtier 2006 J. Plasma Phys. 72 721–69) yield remarkably simple expressions of basic formulas and equations such as the structure constants of Lie algebra, the equation of motion, and the conservation laws. Four constants of motion, where three of the four are independent, are naturally derived from the GEV representation of the equation of motion for the HMHD system: total plasma energy, magnetic helicity, hybrid helicity, and the modified cross helicity.