Canonical description of ideal magnetohydrodynamic flows and integrals of motion

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 69, Issue 4 2, 2004, Pages

  Kats, A V ^a  

^a A USIKOV INSTITUTE OF RADIO PHYSICS AND ELECTRONICS   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

CONFINED FLOW; CONSTRAINT THEORY; DIFFERENTIAL EQUATIONS; ENTROPY; FUNCTIONS; GAGES; HAMILTONIANS; INVARIANCE; MAGNETIC FIELD EFFECTS; PERTURBATION TECHNIQUES; PROBLEM SOLVING; THERMODYNAMIC STABILITY; VELOCITY MEASUREMENT;

BAROTROPIC FLOWS; CANONICAL DESCRIPTION; CLEBSCH VARIABLES; GAUGE TRANSFORMATIONS;

MAGNETOHYDRODYNAMICS;

EID: 42749105244     PISSN: 15393755     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

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31. This form of the action slightly differs from that proposed in Ref. [14], The main difference consists in introducing the vec tor potential for the magnetic field. Therefore, here the canonical pair is A, -M instead of H, S, where S=curlM. We do not consider the discontinuous flows and thus we omit the surface term in the action. But adding corresponding surface term we can easily take the breaks into account.
32. -1H + v × curlS+ ∇ψ, where ψ represents a scalar field respectful for the S gauge. This relation differs only by the S sign from Eq. (10.9) of reference [1] [or Eq. (7) in the original paper [22]].
33. tΛ, where Δ denotes the Laplace operator and Λ′ is arbitary solution of the Laplace equation.
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40. In terms of the differential forms α and I are scalar and vector 0 forms; L,J, and ρ and one-, two-, and three-forms, respectively.