|approved||2016_sherwood_theory_conference.pdf||2016-03-19 12:46:18||Alain Brizard|
Author: Alain J Brizard
Requested Type: Poster
Submitted: 2016-02-08 07:04:25
Co-authors: N. Tronko
Saint Michael's College
One Winooski Park
Colchester, Vermont 05439
Equivalent guiding-center Hamiltonian theories are constructed based on higher-order Lie-transform perturbation methods . Higher-order guiding-center theories are distinguished on the basis of whether correction terms associated with magnetic-field nonuniformity appear either in the guiding-center symplectic (Poisson-bracket) structure, in the guiding-center Hamiltonian, or both. These theories are called equivalent - because they describe the same guiding-center magnetic-moment invariant.
Our work shows that the original guiding-center transformation derived by Littlejohn , which ignored first-order corrections in the guiding-center symplectic structure, is incomplete because it is unable to recover the standard guiding-center polarization . We show how equivalent guiding-center Hamiltonian theories can be constructed (through Lagrangian, Hamiltonian, and Jacobian constraints) with the necessary corrections that yield the standard guiding-center polarization. Lastly, the conservation law of guiding-center toroidal canonical angular momentum in axisymmetric tokamak geometry is derived explicitly.
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