Hamiltonian structure of the guiding center plasma model

Burby, J. W.; Sengupta, W.

doi:10.1063/1.5016453

Title: Hamiltonian structure of the guiding center plasma model

Journal Article · Wed Feb 14 00:00:00 EST 2018 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.5016453· OSTI ID:1540153

^[1]; Sengupta, W. ^[1]

New York Univ. (NYU), NY (United States). Courant Inst. of Mathematical Sciences

The guiding center plasma model (also known as kinetic MHD) is a rigorous sub-cyclotron-frequency closure of the Vlasov-Maxwell system. While the model has been known for decades and it plays a fundamental role in describing the physics of strongly magnetized collisionless plasmas, its Hamiltonian structure has never been found. We provide explicit expressions for the model's Poisson bracket and Hamiltonian and thereby prove that the model is an infinite-dimensional Hamiltonian system. The bracket is derived in a manner which ensures that it satisfies the Jacobi identity. We also report on several previously unknown circulation theorems satisfied by the guiding center plasma model. Without having knowledge of the Hamiltonian structure, these circulation theorems would be difficult to guess.

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Research Organization:: New York Univ. (NYU), NY (United States); Oak Ridge Associated Univ., Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-86ER53223; AC05-06OR23100

OSTI ID:: 1540153

Journal Information:: Physics of Plasmas, Vol. 25, Issue 2; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 9 works

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References (33)

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A low-frequency variational model for energetic particle effects in the pressure-coupling scheme Close, Alexander R. D.; Burby, Joshua W.; Tronci, Cesare arXiv https://doi.org/10.48550/arxiv.1802.00978	text	January 2018
Energy and momentum conservation in the Euler–Poincaré formulation of local Vlasov–Maxwell-type systems Hirvijoki, Eero; Burby, Joshua W.; Pfefferlé, David Journal of Physics A: Mathematical and Theoretical, Vol. 53, Issue 23 https://doi.org/10.1088/1751-8121/ab8b38	journal	May 2020
General formulas for adiabatic invariants in nearly-periodic Hamiltonian systems Burby, J. W.; Squire, J. arXiv https://doi.org/10.48550/arxiv.2005.00634	text	January 2020

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