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Equivalent guiding-center Hamiltonian theories are constructed based onhigher-order Lie-transform perturbation methods. Higher-order guiding-centertheories are distinguished on the basis of whether correction terms associatedwith magnetic-field nonuniformity appear either in the guiding-centersymplectic (Poisson-bracket) structure, in the guiding-center Hamiltonian, orboth. These theories are called equivalent because they describe the sameguiding-center magnetic-moment invariant. The present work presents thedetailed derivations of results that were summarized in a recent paper byTronko and Brizard [Phys. Plasmas 22, 112507 (2015)].

Equivalent Higher-order Guiding-center Hamiltonian Theories