Action principle and the Hamiltonian formulation for the Maxwell--Vlasov equations on a symplectic leaf

Journal Article · Mon Aug 01 04:00:00 EDT 1994 · Physics of Plasmas; (United States)

DOI:https://doi.org/10.1063/1.870569· OSTI ID:6930674

Fla, T ^[1]

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1. Institute of Mathematical and Physical Sciences, University of Tromso, N-9037 Tromso (Norway)

An action principle for the Maxwell--Vlasov (MV) equation is formulated in terms of the Maxwell fields and the generating function, [ital w]([ital z],[ital t]) for deviations from a reference distribution function, [ital f][sup 0]([ital z]), which labels a symplectic leaf. New formal fields suitable for variations are defined. These fields give rise to a symplectic and Poisson structure. The Hamiltonian formulation of the equations is found in terms of the new formal fields, and it is found how to derive Larsson's action principle [J. Plasma Phys. [bold 48], 13 (1992); [ital ibid]. [bold 49], 255 (1993)] and generalized versions of it on a Lagrangian constraint manifold in a double symplectic space. It is also shown how the relativistic Maxwell--Vlasov system and the Maxwell--Vlasov system with a time-dependent reference state can be formulated as an action principle and Hamiltonian system in terms of eight-dimensional particle phase space coordinates.

• OSTI ID: 6930674
• Journal Information: Physics of Plasmas; (United States), Journal Name: Physics of Plasmas; (United States) Vol. 1:8; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700330* -- Plasma Kinetics
Transport
& Impurities-- (1992-)
700340 -- Plasma Waves
Oscillations
& Instabilities-- (1992-)
ACTION INTEGRAL
BOLTZMANN-VLASOV EQUATION
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
EQUATIONS
FUNCTIONS
HAMILTONIAN FUNCTION
INTEGRALS
MATHEMATICAL SPACE
MAXWELL EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
PLASMA
RELATIVISTIC PLASMA
SPACE
VARIATIONAL METHODS