Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

Tronko, Natalia; Brizard, Alain J.

doi:10.1063/1.4935925

Title: Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

Journal Article · Thu Nov 19 00:00:00 EST 2015 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4935925· OSTI ID:1469664

Tronko, Natalia ^[1];

^[2]

Max-Planck-Institut fur Plasmaphysik, Garching (Germany)
Saint Michael's College, Colchester, VT (United States)

In this paper, a consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guiding-center Lagrangian constraint on the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.

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Research Organization:: Saint Michael's College, Colchester, VT (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0006721

OSTI ID:: 1469664

Alternate ID(s):: OSTI ID: 1226664

Journal Information:: Physics of Plasmas, Vol. 22, Issue 11; ISSN 1070-664X

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

Country of Publication:: United States

Language:: English

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Cited by: 20 works

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References (16)

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Cited By (12)

Second-order nonlinear gyrokinetic theory: from the particle to the gyrocentre Tronko, Natalia; Chandre, Cristel Journal of Plasma Physics, Vol. 84, Issue 3 https://doi.org/10.1017/s0022377818000430	journal	June 2018
Second order gyrokinetic theory for particle-in-cell codes Tronko, Natalia; Bottino, Alberto; Sonnendrücker, Eric Physics of Plasmas, Vol. 23, Issue 8 https://doi.org/10.1063/1.4960039	journal	August 2016
Verification of Gyrokinetic codes: Theoretical background and applications Tronko, Natalia; Bottino, Alberto; Görler, Tobias Physics of Plasmas, Vol. 24, Issue 5 https://doi.org/10.1063/1.4982689	journal	May 2017
Gyrokinetics from variational averaging: Existence and error bounds Possanner, Stefan Journal of Mathematical Physics, Vol. 59, Issue 8 https://doi.org/10.1063/1.5018354	journal	August 2018
Hierarchy of second order gyrokinetic Hamiltonian models for particle-in-cell codes Tronko, N.; Bottino, A.; Chandre, C. Plasma Physics and Controlled Fusion, Vol. 59, Issue 6 https://doi.org/10.1088/1361-6587/aa68af	journal	May 2017
Conservative magnetic moment of runaway electrons and collisionless pitch-angle scattering Liu, Chang; Qin, Hong; Hirvijoki, Eero Nuclear Fusion, Vol. 58, Issue 10 https://doi.org/10.1088/1741-4326/aad2a5	journal	August 2018
Orbit-modulated plasma transport and sources Stoltzfus-Dueck, T. Nuclear Fusion, Vol. 60, Issue 1 https://doi.org/10.1088/1741-4326/ab5339	journal	December 2019
Second order Gyrokinetic theory for Particle-In-Cell codes Tronko, Natalia; Bottino, Alberto; Sonnendruecker, Eric arXiv https://doi.org/10.48550/arxiv.1604.03538	text	January 2016
Hierarchy of second-order gyrokinetic Hamiltonian models for particle-in-cell codes Tronko, Natalia; Bottino, A.; Chandre, Cristel arXiv https://doi.org/10.48550/arxiv.1703.05095	text	January 2017
Verification of Gyrokinetic codes: theoretical background and applications Tronko, Natalia; Bottino, Alberto; Goerler, Tobias arXiv https://doi.org/10.48550/arxiv.1703.07582	text	January 2017
Gyrokinetics from variational averaging: existence and error bounds Possanner, Stefan arXiv https://doi.org/10.48550/arxiv.1711.09620	text	January 2017
Lifting of the Vlasov-Maxwell Bracket by Lie-transform Method Brizard, A. J.; Morrison, P. J.; Burby, J. W. arXiv https://doi.org/10.48550/arxiv.1606.06652	text	January 2016

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