Hamiltonian guiding center equations in toroidal magnetic configurations

Guiding center equations for particle motion in a toroidal magnetic configuration are derived using general magnetic coordinates. For the case of axisymmetry, the explicit transformation to exact Hamiltonian canonical variables is presented for the first time. Approximate canonical coordinates are introduced also for three-dimensional configurations with strong toroidal magnetic field. Previous derivations made use of so-called Boozer equilibrium coordinates, which are highly nonuniform and are canonical only in the exceptional case of low beta, up–down symmetric configurations. The present formalism is valid for arbitrary, spatially well distributed magnetic coordinates, greatly increasing the accuracy of calculations. Magnetostatic equilibrium is not assumed in the present formalism, the analysis holds for any configuration with nested flux surfaces.