A Hamiltonian and geometric formulation of general Vlasov-Maxwell-type models

William Barham; Philip J. Morrison; Eric Sonnendrücker

doi:10.1016/j.fpp.2023.100016

A Hamiltonian and geometric formulation of general Vlasov-Maxwell-type models

William Barham
, Philip J. Morrison
, Eric Sonnendrücker

Chair of Numerical Methods in Plasma Physics

Oden Institute for Computational Engineering and Sciences
University of Texas at Austin
Max Planck Institute for Plasma Physics

Research output: Contribution to journal › Article › peer-review

Abstract

Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L² duality, and one utilizing an abstract notion of duality. The final of these is used to express the geometric and Hamiltonian structure of kinetic theories in general media. The Poisson bracket so stated is explicitly metric free. Finally, as a special case, the Lorentz covariance of such kinetic theories is investigated. We obtain a Lorentz covariant kinetic theory coupled to nonlinear electrodynamics such as Born-Infeld or Euler-Heisenberg electrodynamics.

Original language	English
Article number	100016
Journal	Fundamental Plasma Physics
Volume	5
DOIs	https://doi.org/10.1016/j.fpp.2023.100016
State	Published - Jun 2023

Keywords

Geometric mechanics
Hamiltonian field theory
Relativistic plasma
Vlasov-Maxwell equation

Access to Document

10.1016/j.fpp.2023.100016

Cite this

@article{8cfca91dd5904866bc5d9007e49a227a,

title = "A Hamiltonian and geometric formulation of general Vlasov-Maxwell-type models",

abstract = "Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L2 duality, and one utilizing an abstract notion of duality. The final of these is used to express the geometric and Hamiltonian structure of kinetic theories in general media. The Poisson bracket so stated is explicitly metric free. Finally, as a special case, the Lorentz covariance of such kinetic theories is investigated. We obtain a Lorentz covariant kinetic theory coupled to nonlinear electrodynamics such as Born-Infeld or Euler-Heisenberg electrodynamics.",

keywords = "Geometric mechanics, Hamiltonian field theory, Relativistic plasma, Vlasov-Maxwell equation",

author = "William Barham and Morrison, \{Philip J.\} and Eric Sonnendr{\"u}cker",

note = "Publisher Copyright: {\textcopyright} 2023 The Authors",

year = "2023",

month = jun,

doi = "10.1016/j.fpp.2023.100016",

language = "English",

volume = "5",

journal = "Fundamental Plasma Physics",

issn = "2772-8285",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - A Hamiltonian and geometric formulation of general Vlasov-Maxwell-type models

AU - Barham, William

AU - Morrison, Philip J.

AU - Sonnendrücker, Eric

PY - 2023/6

Y1 - 2023/6

N2 - Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L2 duality, and one utilizing an abstract notion of duality. The final of these is used to express the geometric and Hamiltonian structure of kinetic theories in general media. The Poisson bracket so stated is explicitly metric free. Finally, as a special case, the Lorentz covariance of such kinetic theories is investigated. We obtain a Lorentz covariant kinetic theory coupled to nonlinear electrodynamics such as Born-Infeld or Euler-Heisenberg electrodynamics.

AB - Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L2 duality, and one utilizing an abstract notion of duality. The final of these is used to express the geometric and Hamiltonian structure of kinetic theories in general media. The Poisson bracket so stated is explicitly metric free. Finally, as a special case, the Lorentz covariance of such kinetic theories is investigated. We obtain a Lorentz covariant kinetic theory coupled to nonlinear electrodynamics such as Born-Infeld or Euler-Heisenberg electrodynamics.

KW - Geometric mechanics

KW - Hamiltonian field theory

KW - Relativistic plasma

KW - Vlasov-Maxwell equation

UR - https://www.scopus.com/pages/publications/85204889210

U2 - 10.1016/j.fpp.2023.100016

DO - 10.1016/j.fpp.2023.100016

M3 - Article

AN - SCOPUS:85204889210

SN - 2772-8285

VL - 5

JO - Fundamental Plasma Physics

JF - Fundamental Plasma Physics

M1 - 100016

ER -

A Hamiltonian and geometric formulation of general Vlasov-Maxwell-type models

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this