Eulerian action principles for linearized reduced dynamical equations

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

DOI:https://doi.org/10.1063/1.870574· OSTI ID:7024950

Brizard, A ^[1]

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1. Lawrence Berkeley Laboratory, University of California, Berkeley California 94720 (United States)

New Eulerian action principles for the linearized gyrokinetic Maxwell--Vlasov equations and the linearized kinetic-magnetohydrodynamic (kinetic-MHD) equations are presented. The variational fields for the linearized gyrokinetic Vlasov--Maxwell equations are the perturbed electromagnetic potentials ([phi][sub 1],[bold A][sub 1]) and the gyroangle-independent gyrocenter (gy) function [ital S][sub gy], while the variational fields for the linearized kinetic-MHD equations are the ideal MHD fluid displacement [xi] and the gyroangle-independent drift-kinetic (dk) function [ital S][sub dk] (defined as the drift-kinetic limit of [ital S][sub gy]). According to the Lie-transform approach to Vlasov perturbation theory, [ital S][sub gy] generates first-order perturbations in the gyrocenter distribution [ital F][sub 1][equivalent to][l brace][ital S][sub gy], [ital F][sub 0][r brace][sub gc], where [ital F][sub 1] satisfies the linearized gyrokinetic Vlasov equation and [l brace] , [r brace][sub gc] denotes the unperturbed guiding-center (gc) Poisson bracket. Previous quadratic variational forms were constructed [ital ad] [ital hoc] from the linearized equations, and required the linearized gyrokinetic (or drift-kinetic) Vlasov equation to be solved [ital a] [ital priori] (e.g., by integration along an unperturbed guiding-center orbit) through the use of the normal-mode and ballooning-mode representations. The presented action principles ignore these requirements and, thus, apply to more general perturbations.

• DOE Contract Number: AC03-76SF00098
• OSTI ID: 7024950
• 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
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700340 -- Plasma Waves
Oscillations
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ACTION INTEGRAL
BOLTZMANN-VLASOV EQUATION
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
EQUATIONS
FLUID MECHANICS
FUNCTIONS
HYDRODYNAMICS
INTEGRALS
KINETIC EQUATIONS
MAGNETOHYDRODYNAMICS
MAXWELL EQUATIONS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
VARIATIONAL METHODS