Hamiltonian formulation of guiding center motion and of the linear and nonlinear gyrokinetic equation

This derivation of the gyrokinetic equations is based on the Hamiltonian formulation of the guiding center motion. The transformation to guiding center variables is accomplished by a sequence of canonical transformations. The kinetic equation is determined by Liouville’s equation. This equation is then ordered in accordance with the gyrokinetic ordering, and analyzed order by order to obtain the linear and nonlinear gyrokinetic equations.