Motion of magnetic flux lines in magnetohydrodynamics
Abstract
A gaugefree description of magnetohydrodynamic flows of an ideal incompressible fluid, which takes into account the freezingin of the magnetic field and the presence of cross invariants containing the vorticity, is obtained. This description is an extension of the canonical formalism wellknown in ordinary hydrodynamics to the dynamics of frozenin flux lines. Magnetohydrodynamics is studied as the longwavelength limit of the twofluid model of a plasma, in which the existence of two frozenin fields — curls of the generalized momenta of the electron and ion fluids — follows from the symmetry of each component with respect to relabeling of the Lagrangian labels. The cross invariants in magnetohydrodynamics are limits of special combinations of topological invariants of the twofluid model. A variational principle is formulated for the dynamics of frozenin magnetic flux lines, and the Casimir functionals of the noncanonical Poisson brackets are found.
 Publication:

Soviet Journal of Experimental and Theoretical Physics
 Pub Date:
 August 1999
 DOI:
 10.1134/1.558984
 Bibcode:
 1999JETP...89..299R
 Keywords:

 Vorticity;
 Variational Principle;
 Canonical Formalism;
 Poisson Bracket;
 Incompressible Fluid