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arXiv · 1511.01005

Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

Natalia Tronko·Alain Brizard
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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. Lastly, an application of the guiding-center Lagrangian constraint on the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.

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Natalia Tronko, Alain Brizard. 2015-11-03. Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories. https://doi.org/10.1063/1.4935925

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