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

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.
Authors:
 [1] ; ORCiD logo [2]
  1. Max-Planck-Institut fur Plasmaphysik, Garching (Germany)
  2. Saint Michael's College, Colchester, VT (United States)
Publication Date:
Grant/Contract Number:
SC0006721
Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 22; Journal Issue: 11; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Research Org:
Saint Michael's College, Colchester, VT (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
OSTI Identifier:
1469664
Alternate Identifier(s):
OSTI ID: 1226664

Tronko, Natalia, and Brizard, Alain J. Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories. United States: N. p., Web. doi:10.1063/1.4935925.
Tronko, Natalia, & Brizard, Alain J. Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories. United States. doi:10.1063/1.4935925.
Tronko, Natalia, and Brizard, Alain J. 2015. "Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories". United States. doi:10.1063/1.4935925. https://www.osti.gov/servlets/purl/1469664.
@article{osti_1469664,
title = {Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories},
author = {Tronko, Natalia and Brizard, Alain J.},
abstractNote = {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.},
doi = {10.1063/1.4935925},
journal = {Physics of Plasmas},
number = 11,
volume = 22,
place = {United States},
year = {2015},
month = {11}
}