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Title: Eulerian action principles for linearized reduced dynamical equations

Abstract

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.

Authors:
 [1]
  1. Lawrence Berkeley Laboratory, University of California, Berkeley California 94720 (United States)
Publication Date:
OSTI Identifier:
7024950
DOE Contract Number:  
AC03-76SF00098
Resource Type:
Journal Article
Journal Name:
Physics of Plasmas; (United States)
Additional Journal Information:
Journal Volume: 1:8; Journal ID: ISSN 1070-664X
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; MAGNETOHYDRODYNAMICS; ACTION INTEGRAL; VARIATIONAL METHODS; BOLTZMANN-VLASOV EQUATION; DISTRIBUTION FUNCTIONS; KINETIC EQUATIONS; MAXWELL EQUATIONS; PERTURBATION THEORY; CALCULATION METHODS; DIFFERENTIAL EQUATIONS; EQUATIONS; FLUID MECHANICS; FUNCTIONS; HYDRODYNAMICS; INTEGRALS; MECHANICS; PARTIAL DIFFERENTIAL EQUATIONS; 700330* - Plasma Kinetics, Transport, & Impurities- (1992-); 700340 - Plasma Waves, Oscillations, & Instabilities- (1992-)

Citation Formats

Brizard, A. Eulerian action principles for linearized reduced dynamical equations. United States: N. p., 1994. Web. doi:10.1063/1.870574.
Brizard, A. Eulerian action principles for linearized reduced dynamical equations. United States. doi:10.1063/1.870574.
Brizard, A. Mon . "Eulerian action principles for linearized reduced dynamical equations". United States. doi:10.1063/1.870574.
@article{osti_7024950,
title = {Eulerian action principles for linearized reduced dynamical equations},
author = {Brizard, A},
abstractNote = {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.},
doi = {10.1063/1.870574},
journal = {Physics of Plasmas; (United States)},
issn = {1070-664X},
number = ,
volume = 1:8,
place = {United States},
year = {1994},
month = {8}
}