Multisymplectic magnetohydrodynamics
Abstract
A multisymplectic formulation of ideal magnetohydrodynamics (MHD) is developed based on the Clebsch variable variational principle in which the Lagrangian consists of the kinetic minus the potential energy of the MHD fluid modified by constraints using Lagrange multipliers that ensure mass conservation, entropy advection with the flow, the Lin constraint, and Faraday's equation (i.e. the magnetic flux is Lie dragged with the flow). The analysis is also carried out using the magnetic vector potential Ã where α=Ã. d x is Lie dragged with the flow, and B=∇×Ã. The multisymplectic conservation laws give rise to the Eulerian momentum and energy conservation laws. The symplecticity or structural conservation laws for the multisymplectic system corresponds to the conservation of phase space. It corresponds to taking derivatives of the momentum and energy conservation laws and combining them to produce n(n1)/2 extra conservation laws, where n is the number of independent variables. Noether's theorem for the multisymplectic MHD system is derived, including the case of nonCartesian space coordinates, where the metric plays a role in the equations.
 Publication:

Journal of Plasma Physics
 Pub Date:
 October 2014
 DOI:
 10.1017/S0022377814000257
 arXiv:
 arXiv:1312.4890
 Bibcode:
 2014JPlPh..80..707W
 Keywords:

 Mathematical Physics
 EPrint:
 34 pages, 0 figures