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approved2016_sherwood_theory_conference.pdf2016-03-19 12:46:18Alain Brizard


Author: Alain J Brizard
Requested Type: Poster
Submitted: 2016-02-08 07:04:25

Co-authors: N. Tronko

Contact Info:
Saint Michael's College
One Winooski Park
Colchester, Vermont   05439
United States

Abstract Text:
Equivalent guiding-center Hamiltonian theories are constructed based on higher-order Lie-transform perturbation methods [1]. 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 [2]-[4] because they describe the same guiding-center magnetic-moment invariant.

Our work shows that the original guiding-center transformation derived by Littlejohn [5], which ignored first-order corrections in the guiding-center symplectic structure, is incomplete because it is unable to recover the standard guiding-center polarization [6]. 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.

[1] N. Tronko and A.J. Brizard, Phys. Plasmas 22 (2015) 112507.
[2] F. I. Parra and I. Calvo, Plasma Phys. Controlled Fusion 53 (2011) 045001.
[3] J. W. Burby, J. Squire, and H. Qin, Phys. Plasmas 20 (2013) 072105.
[4] F.I. Parra, I. Calvo, J. W. Burby, J. Squire, and H. Qin, Phys. Plasmas 21 (2014) 104506.
[5] R. G. Littlejohn, J. Plasma Phys. 29 (1983) 111.
[6] D. Pfirsch, Zeitschrift Naturforschung Teil A 39 (1984) 1.