An Action Principle for Magnetohydrodynamics

Calkin, M. G.

doi:10.1139/p63-216

Cited by 67 publications

(67 citation statements)

References 5 publications

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“…and yo(a) is not crucial; if they do not exist one simply thinks of 6 as an infinitesimal constant parameter.…”

Section: Relabeling Symmetry In Mhdmentioning

confidence: 99%

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Relabeling symmetries in hydrodynamics and magnetohydrodynamics

Padhye¹,

Morrison²

1996

113

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“…and yo(a) is not crucial; if they do not exist one simply thinks of 6 as an infinitesimal constant parameter.…”

Section: Relabeling Symmetry In Mhdmentioning

confidence: 99%

“…Prior to this work conservation of cross helicity was derived from a Lagrangian symmetry involving Clebsch potentials and the polarization in [6]. (See also [20].)…”

Section: Relabeling Symmetry In Mhdmentioning

confidence: 99%

Relabeling symmetries in hydrodynamics and magnetohydrodynamics

Padhye¹,

Morrison²

1996

113

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“…Similarly, in MHD, the variable conjugate to the magnetic field is the polarization; cf. Calkin (1963). However, the extra factor is a cyclic variable so one directly passes from (5A.2) to…”

Section: Commentsmentioning

confidence: 99%

The Hamiltonian structure of general relativistic perfect fluids

1985

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Abstract. We show that the evolution equations for a perfect fluid coupled to general relativity in a general lapse and shift,, are Hamiltonian relative to a certain Poisson structure. For the fluid variables, a Lie-Poisson structure associated to the dual of a semi-direct product Lie algebra is used, while the bracket for the gravitational variables has the usual canonical symplectic structure. The evolution is governed by a Hamiltonian which is equivalent to that obtained from a canonical analysis. The relationship of our Hamiltonian structure with other approaches in the literature, such as Clebsch potentials, Lagrangian to Eulerian transformations, and its use in clarifying linearization stability, are discussed.

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“…In 1963, CALKI~ [4] wrote the source equations of the electromagnetie field in a form suitable for ah action principle, by means of the so-called "polarization" P. Following CALKI~'S formulation, we showed [5] that the electromagnetic field E,B, interacting with a charged, moving fluid, can be described in terms of the "generalized electromagnetic antipotentials" M and E ] = 8~1 (8]k m Ok Mm --Pi),…”

Section: Basic Equationsmentioning

confidence: 99%

“…We therefore arrived at the source equations of the electromagnetic field [3], [4], a generalization of Ohm's law for infinite conductivity [7], and a generalization of the Clebsch's transformation in the presence of both the electromagnetic and "polarization" fields. The variation of ~ and S leads to the equations (13) and (14).…”

Section: Merchesmentioning

confidence: 99%

A Hamiltonian formulation in magnetofluid dynamics

Merches

1976

Acta Physica

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By using Clebsch representations for all necessary vector fields, an action principle for a compressible, inviscid, one-component magneto-fluid, undergoing isentropic motion in an electromagnetic field, is given. lntroductionThere are many papers regarding the derivation of the equations ofmagnetofluid dynamics from an action principle. One of the first and most important problems arising in such derivations is the construction of a Lagrangian density, suitable for the considered magnetofluid model.Regardless of the particular tases which are under discussion, there exist certain rules (or procedures) used in the derivation of the set of equations describing the behaviour of the magnetofluid system. One of tbese rules says that the electromagnetic field E, Bis expressed in terms ofeither the well-known potentials A, 9 [e.g. [1][2][3][4][5][6][7] or the so called "generalized antipotentials" [8]. On the other hand, the fluid velocity field vis usually represented in terms of a set of Clebsch potentials, and an interaction termas well. Both electromagnetic and Clebsch potentials are taken as variational parameters. But we should mention that this procedure is not compulsory: the Clebsch representation of the velocity field can be obtained asa result of the variation.The main purpose of the present paper is to give a variational principle for an inviscid, conducting fluid, and show that the representation of all vector fields in terms of Clebsch potentials is not only a possible, but also a useful method in the Lagrangian approach of magnetofluid dynamics. Construction of the Lagrangian densityLet our model of magnetofluid be an inviscid, one-component, compressible fluid, which undergoes isentropic motion in the electromagnetic field E, B. Ifwe denote by p and pe the mass and charge densities, and suppose that the particle number density Acta Physica Hungarica 54, 1983

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An Action Principle for Magnetohydrodynamics

Cited by 67 publications

References 5 publications

Relabeling symmetries in hydrodynamics and magnetohydrodynamics

Relabeling symmetries in hydrodynamics and magnetohydrodynamics

The Hamiltonian structure of general relativistic perfect fluids

A Hamiltonian formulation in magnetofluid dynamics

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