Canonical Hamiltonian gyrocenter variables and gauge invariant representation of the gyrokinetic equation.

Abstract

By using the extended phase space Hamiltonian Lie-transform perturbation method, Hamiltonian canonical variables have been found to describe the motion of gyrocenters. A representation of the gyrokinetic equation has been established in terms of the magnetic moment M, the total energy U, and the canonical toroidal momentum P of the particle. This representation of the gyrokinetic equation is invariant with respect to the gauge transformation of perturbation fields. It explicitly reveals the effects of toroidal symmetry breaking, and it indicates the role that the perturbed canonical toroidal momentum plays in the gyrokinetic theory. In particular, it is found that the free energy associated with partial differential(P)f(0)(M,U,P) [here f(0)(M,U,P) is the equilibrium distribution function] does not have any nonadiabatic linear driving to the axisymmetric modes.