Derivation of the Hall and extended magnetohydrodynamics brackets

Journal Article · Wed Jun 15 04:00:00 EDT 2016 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4952641· OSTI ID:22598965

Lingam, Manasvi ^[1]

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1. Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544 (United States)

There are several plasma models intermediate in complexity between ideal magnetohydrodynamics (MHD) and two-fluid theory, with Hall and Extended MHD being two important examples. In this paper, we investigate several aspects of these theories, with the ultimate goal of deriving the noncanonical Poisson brackets used in their Hamiltonian formulations. We present fully Lagrangian actions for each, as opposed to the fully Eulerian, or mixed Eulerian-Lagrangian, actions that have appeared previously. As an important step in this process, we exhibit each theory's two advected fluxes (in analogy to ideal MHD's advected magnetic flux), discovering also that with the correct choice of gauge they have corresponding Lie-dragged potentials resembling the electromagnetic vector potential, and associated conserved helicities. Finally, using the Euler-Lagrange map, we show how to derive the noncanonical Eulerian brackets from canonical Lagrangian ones.

• OSTI ID: 22598965
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 6 Vol. 23; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
FLUIDS
HALL EFFECT
HAMILTONIANS
HELICITY
LAGRANGIAN FUNCTION
LANDAU LIQUID HELIUM THEORY
MAGNETIC FLUX
MAGNETOHYDRODYNAMICS
PLASMA
POTENTIALS
VECTORS