An Action Principle for Relativistic MHD

Abstract

A covariant action principle for ideal relativistic magnetohydrodynamics (MHD) in terms of natural Eulerian field variables is given. This is done by generalizing the covariant Poisson bracket theory of Marsden et al., which uses a noncanonical bracket to effect constrained variations of an action functional. Various implications and extensions of this action principle are also discussed. Two significant by-products of this formalism are the introduction of a new divergence-free 4-vector variable for the magnetic field, and a new Lie-dragged form for the theory.

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Cited by in corpus (12)

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• Lagrangian and Dirac constraints for the ideal incompressible fluid and magnetohydrodynamics
• On the structure and statistical theory of turbulence of extended magnetohydrodynamics
• Hamiltonian Magnetohydrodynamics: Lagrangian, Eulerian, and Dynamically Accessible Stability -- Examples with Translation Symmetry
• Anomalous magnetohydrodynamics in the extreme relativistic domain
• Magnetic Connections in Curved Spacetime
• Covariant Magnetic Connection Hypersurfaces
• A class of three-dimensional gyroviscous magnetohydrodynamic models
• A geometric look at MHD and the Braginsky dynamo
• Revealing Noncanonical Hamiltonian Structures in Relativistic Fluid Dynamics