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Title: Perturbative variational formulation of the Vlasov-Maxwell equations

Abstract

The perturbative variational formulation of the Vlasov-Maxwell equations is presented up to the third order in the perturbation analysis. From the second and third-order Lagrangian densities, the first-order and second-order Vlasov-Maxwell equations are expressed in gauge-invariant and gauge-independent forms, respectively. Upon deriving the reduced second-order Vlasov-Maxwell Lagrangian for the linear nonadiabatic gyrokinetic Vlasov-Maxwell equations, the reduced Lagrangian densities for the linear drift-wave equation and the linear hybrid kinetic-magnetohydrodynamic (MHD) equations are derived, with their associated wave-action conservation laws obtained by the Noether method. The exact wave-action conservation law for the linear hybrid kinetic-MHD equations is written explicitly. To conclude, a new form of the third-order Vlasov-Maxwell Lagrangian is derived in which ponderomotive effects play a crucial role.

Authors:
ORCiD logo [1]
  1. Saint Michael's College, Colchester, VT (United States)
Publication Date:
Research Org.:
Saint Michael's College, Colchester, VT (United States)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF)
OSTI Identifier:
1612062
Grant/Contract Number:  
SC0014032; PHY-1805164
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 25; Journal Issue: 11; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; physics

Citation Formats

Brizard, Alain J. Perturbative variational formulation of the Vlasov-Maxwell equations. United States: N. p., 2018. Web. doi:10.1063/1.5049570.
Brizard, Alain J. Perturbative variational formulation of the Vlasov-Maxwell equations. United States. doi:10.1063/1.5049570.
Brizard, Alain J. Mon . "Perturbative variational formulation of the Vlasov-Maxwell equations". United States. doi:10.1063/1.5049570. https://www.osti.gov/servlets/purl/1612062.
@article{osti_1612062,
title = {Perturbative variational formulation of the Vlasov-Maxwell equations},
author = {Brizard, Alain J.},
abstractNote = {The perturbative variational formulation of the Vlasov-Maxwell equations is presented up to the third order in the perturbation analysis. From the second and third-order Lagrangian densities, the first-order and second-order Vlasov-Maxwell equations are expressed in gauge-invariant and gauge-independent forms, respectively. Upon deriving the reduced second-order Vlasov-Maxwell Lagrangian for the linear nonadiabatic gyrokinetic Vlasov-Maxwell equations, the reduced Lagrangian densities for the linear drift-wave equation and the linear hybrid kinetic-magnetohydrodynamic (MHD) equations are derived, with their associated wave-action conservation laws obtained by the Noether method. The exact wave-action conservation law for the linear hybrid kinetic-MHD equations is written explicitly. To conclude, a new form of the third-order Vlasov-Maxwell Lagrangian is derived in which ponderomotive effects play a crucial role.},
doi = {10.1063/1.5049570},
journal = {Physics of Plasmas},
issn = {1070-664X},
number = 11,
volume = 25,
place = {United States},
year = {2018},
month = {11}
}

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