Lagrangian and Hamiltonian constraints for guidingcenter Hamiltonian theories
Abstract
In this paper, a consistent guidingcenter Hamiltonian theory is derived by Lietransform perturbation method, with terms up to second order in magneticfield nonuniformity. Consistency is demonstrated by showing that the guidingcenter transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new firstorder term appearing in the guidingcenter phasespace Lagrangian is identified through a calculation of the guidingcenter polarization. It is shown that this new polarization term also yields a simpler expression of the guidingcenter toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guidingcenter Lagrangian constraint on the guidingcenter Hamiltonian yields a natural interpretation for its higherorder corrections.
 Authors:

 MaxPlanckInstitut fur Plasmaphysik, Garching (Germany)
 Saint Michael's College, Colchester, VT (United States)
 Publication Date:
 Research Org.:
 Saint Michael's College, Colchester, VT (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 1469664
 Alternate Identifier(s):
 OSTI ID: 1226664
 Grant/Contract Number:
 SC0006721
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 22; Journal Issue: 11; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Citation Formats
Tronko, Natalia, and Brizard, Alain J. Lagrangian and Hamiltonian constraints for guidingcenter Hamiltonian theories. United States: N. p., 2015.
Web. doi:10.1063/1.4935925.
Tronko, Natalia, & Brizard, Alain J. Lagrangian and Hamiltonian constraints for guidingcenter Hamiltonian theories. United States. doi:10.1063/1.4935925.
Tronko, Natalia, and Brizard, Alain J. Thu .
"Lagrangian and Hamiltonian constraints for guidingcenter 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 guidingcenter Hamiltonian theories},
author = {Tronko, Natalia and Brizard, Alain J.},
abstractNote = {In this paper, a consistent guidingcenter Hamiltonian theory is derived by Lietransform perturbation method, with terms up to second order in magneticfield nonuniformity. Consistency is demonstrated by showing that the guidingcenter transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new firstorder term appearing in the guidingcenter phasespace Lagrangian is identified through a calculation of the guidingcenter polarization. It is shown that this new polarization term also yields a simpler expression of the guidingcenter toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guidingcenter Lagrangian constraint on the guidingcenter Hamiltonian yields a natural interpretation for its higherorder corrections.},
doi = {10.1063/1.4935925},
journal = {Physics of Plasmas},
number = 11,
volume = 22,
place = {United States},
year = {2015},
month = {11}
}
Web of Science
Works referenced in this record:
Variational principles of guiding centre motion
journal, February 1983
 Littlejohn, Robert G.
 Journal of Plasma Physics, Vol. 29, Issue 1
Beyond linear gyrocenter polarization in gyrokinetic theory
journal, September 2013
 Brizard, Alain J.
 Physics of Plasmas, Vol. 20, Issue 9
Regularization of HamiltonLagrangian Guiding Center Theories
journal, November 1985
 CorreaRestrepo, D.; Wimmel, H. K.
 Physica Scripta, Vol. 32, Issue 5
Hamiltonian theory of guidingcenter motion
journal, May 2009
 Cary, John R.; Brizard, Alain J.
 Reviews of Modern Physics, Vol. 81, Issue 2
Combined Maxwell and kinetic guidingcenter theory with polarization drift: Regularized variational formulation with local charge and energy conservation
journal, June 1986
 CorreaRestrepo, D.; Pfirsch, D.; Wimmel, H. K.
 Physica A: Statistical Mechanics and its Applications, Vol. 136, Issue 23
A guiding center Hamiltonian: A new approach
journal, December 1979
 Littlejohn, Robert G.
 Journal of Mathematical Physics, Vol. 20, Issue 12
Equivalence of two independent calculations of the higher order guiding center Lagrangian
journal, October 2014
 Parra, F. I.; Calvo, I.; Burby, J. W.
 Physics of Plasmas, Vol. 21, Issue 10
New Variational Formulation of MaxwellVlasov and Guiding Center Theories Local Charge and Energy Conservation Laws
journal, January 1984
 Pfirsch, D.
 Zeitschrift für Naturforschung A, Vol. 39, Issue 1
Selfconsistent equilibrium model of low aspectratio toroidal plasma with energetic beam ions
journal, August 2003
 Belova, E. V.; Gorelenkov, N. N.; Cheng, C. Z.
 Physics of Plasmas, Vol. 10, Issue 8
The electric dipole of a guiding center and the plasma momentum density
journal, January 1986
 Kaufman, Allan N.
 Physics of Fluids, Vol. 29, Issue 5
Hamiltonian formulation of guiding center motion
journal, January 1981
 Littlejohn, Robert G.
 Physics of Fluids, Vol. 24, Issue 9
On the gyrokinetic model in long wavelength regime
journal, June 2013
 Miyato, N.; Scott, B. D.; Yagi, M.
 Plasma Physics and Controlled Fusion, Vol. 55, Issue 7
Phasespace Lagrangian derivation of electrostatic gyrokinetics in general geometry
journal, February 2011
 Parra, Felix I.; Calvo, Iván
 Plasma Physics and Controlled Fusion, Vol. 53, Issue 4
Foundations of nonlinear gyrokinetic theory
journal, April 2007
 Brizard, A. J.; Hahm, T. S.
 Reviews of Modern Physics, Vol. 79, Issue 2
Automation of the guiding center expansion
journal, July 2013
 Burby, J. W.; Squire, J.; Qin, H.
 Physics of Plasmas, Vol. 20, Issue 7