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Title: Hamiltonian formulations for perturbed dissipationless plasma equations

Abstract

The Hamiltonian formulations for the perturbed Vlasov–Maxwell equations and the perturbed ideal magnetohydrodynamics (MHD) equations are expressed in terms of the perturbation derivative ∂ F / ∂ ϵ ≡ [ F , S ] of an arbitrary functional F [ ψ ] of the Vlasov–Maxwell fields ψ = ( f , E , B ) or the ideal MHD fields ψ = ( ρ , u , s , B ) , which are assumed to depend continuously on the (dimensionless) perturbation parameter ϵ. In this study, [ , ] denotes the functional Poisson bracket for each set of plasma equations and the perturbation action functional S is said to generate dynamically accessible perturbations of the plasma fields. The new Hamiltonian perturbation formulation introduces a framework for functional perturbation methods in plasma physics and highlights the crucial roles played by polarization and magnetization in Vlasov–Maxwell and ideal MHD perturbation theories. One application considered in this paper is a formulation of plasma stability that guarantees dynamical accessibility and leads to a natural generalization to higher-order perturbation theory.

Authors:
ORCiD logo [1]; ORCiD logo [2]
+ Show Author Affiliations
  1. Saint Michael's College, Colchester, VT (United States). Dept. of Physics
  2. Aix-Marseille Univ., Marseille (France). Centre National de la Recherche Scientifique (CNRS)
Publication Date:
Research Org.:
Saint Michael's College, Colchester, VT (United States)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF); European Atomic Energy Community (Euratom)
OSTI Identifier:
1851859
Alternate Identifier(s):
OSTI ID: 1742060
Grant/Contract Number:  
SC0014032; PHY-1805164; 633053
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 27; Journal Issue: 12; 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; Hamiltonian mechanics; Maxwell equations; calculus of variations; magnetohydrodynamics; perturbation theory; Vlasov equation; electromagnetism; vector fields; magnetization

Citation Formats

Brizard, A. J., and Chandre, C. Hamiltonian formulations for perturbed dissipationless plasma equations. United States: N. p., 2020. Web. doi:10.1063/5.0028471.
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Brizard, A. J., & Chandre, C. Hamiltonian formulations for perturbed dissipationless plasma equations. United States. https://doi.org/10.1063/5.0028471
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Brizard, A. J., and Chandre, C. Wed . "Hamiltonian formulations for perturbed dissipationless plasma equations". United States. https://doi.org/10.1063/5.0028471. https://www.osti.gov/servlets/purl/1851859.
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@article{osti_1851859,
title = {Hamiltonian formulations for perturbed dissipationless plasma equations},
author = {Brizard, A. J. and Chandre, C.},
abstractNote = {The Hamiltonian formulations for the perturbed Vlasov–Maxwell equations and the perturbed ideal magnetohydrodynamics (MHD) equations are expressed in terms of the perturbation derivative ∂ F / ∂ ϵ ≡ [ F , S ] of an arbitrary functional F [ ψ ] of the Vlasov–Maxwell fields ψ = ( f , E , B ) or the ideal MHD fields ψ = ( ρ , u , s , B ), which are assumed to depend continuously on the (dimensionless) perturbation parameter ϵ. In this study, [ , ] denotes the functional Poisson bracket for each set of plasma equations and the perturbation action functional S is said to generate dynamically accessible perturbations of the plasma fields. The new Hamiltonian perturbation formulation introduces a framework for functional perturbation methods in plasma physics and highlights the crucial roles played by polarization and magnetization in Vlasov–Maxwell and ideal MHD perturbation theories. One application considered in this paper is a formulation of plasma stability that guarantees dynamical accessibility and leads to a natural generalization to higher-order perturbation theory.},
doi = {10.1063/5.0028471},
journal = {Physics of Plasmas},
number = 12,
volume = 27,
place = {United States},
year = {Wed Dec 23 00:00:00 EST 2020},
month = {Wed Dec 23 00:00:00 EST 2020}
}
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https://doi.org/10.1063/5.0028471
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