Eulerian action principles for linearized reduced dynamical equations
Abstract
New Eulerian action principles for the linearized gyrokinetic MaxwellVlasov equations and the linearized kineticmagnetohydrodynamic (kineticMHD) equations are presented. The variational fields for the linearized gyrokinetic VlasovMaxwell equations are the perturbed electromagnetic potentials ([phi][sub 1],[bold A][sub 1]) and the gyroangleindependent gyrocenter (gy) function [ital S][sub gy], while the variational fields for the linearized kineticMHD equations are the ideal MHD fluid displacement [xi] and the gyroangleindependent driftkinetic (dk) function [ital S][sub dk] (defined as the driftkinetic limit of [ital S][sub gy]). According to the Lietransform approach to Vlasov perturbation theory, [ital S][sub gy] generates firstorder 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 guidingcenter (gc) Poisson bracket. Previous quadratic variational forms were constructed [ital ad] [ital hoc] from the linearized equations, and required the linearized gyrokinetic (or driftkinetic) Vlasov equation to be solved [ital a] [ital priori] (e.g., by integration along an unperturbed guidingcenter orbit) through the use of the normalmode and ballooningmode representations. The presented action principles ignore these requirements and, thus, apply to more general perturbations.
 Authors:

 Lawrence Berkeley Laboratory, University of California, Berkeley California 94720 (United States)
 Publication Date:
 OSTI Identifier:
 7024950
 DOE Contract Number:
 AC0376SF00098
 Resource Type:
 Journal Article
 Journal Name:
 Physics of Plasmas; (United States)
 Additional Journal Information:
 Journal Volume: 1:8; Journal ID: ISSN 1070664X
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; MAGNETOHYDRODYNAMICS; ACTION INTEGRAL; VARIATIONAL METHODS; BOLTZMANNVLASOV 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 MaxwellVlasov equations and the linearized kineticmagnetohydrodynamic (kineticMHD) equations are presented. The variational fields for the linearized gyrokinetic VlasovMaxwell equations are the perturbed electromagnetic potentials ([phi][sub 1],[bold A][sub 1]) and the gyroangleindependent gyrocenter (gy) function [ital S][sub gy], while the variational fields for the linearized kineticMHD equations are the ideal MHD fluid displacement [xi] and the gyroangleindependent driftkinetic (dk) function [ital S][sub dk] (defined as the driftkinetic limit of [ital S][sub gy]). According to the Lietransform approach to Vlasov perturbation theory, [ital S][sub gy] generates firstorder 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 guidingcenter (gc) Poisson bracket. Previous quadratic variational forms were constructed [ital ad] [ital hoc] from the linearized equations, and required the linearized gyrokinetic (or driftkinetic) Vlasov equation to be solved [ital a] [ital priori] (e.g., by integration along an unperturbed guidingcenter orbit) through the use of the normalmode and ballooningmode 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 = {1070664X},
number = ,
volume = 1:8,
place = {United States},
year = {1994},
month = {8}
}