A new Hamiltonian method in nonlinear gyrokinetic theory

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Abstract
Nonlinear gyrokinetic theory for a general magnetic field in the low‐beta approximation is derived using a new Hamiltonian method. Gyroaveraged equations resulting from Hamiltonian procedures based on Darboux and Lie transform techniques [Phys. Fluids 2 4, 1730 (1981)] exhibit an unphysical dependence on the unit vectors used to describe the velocity perpendicular to the local magnetic field. The new method removes this unphysical dependence by modifying the Darboux algorithm and establishes the relationship between Hamiltonian gyrokinetic theory and the standard explicitly gyroaveraged theory.