Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

Natalia Tronko, Alain J. Brizard

2015 · Physics of Plasmas · vol. 22 · no. 11 · AIP Publishing · 10.1063/1.4935925

Abstract

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.

@article{Tronko_2015,
 title={Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories},
 volume={22},
 ISSN={1089-7674},
 url={http://dx.doi.org/10.1063/1.4935925},
 DOI={10.1063/1.4935925},
 number={11},
 journal={Physics of Plasmas},
 publisher={AIP Publishing},
 author={Tronko, Natalia and Brizard, Alain J.},
 year={2015},
 month=nov }