Validity of the guiding-center approximation in various mirror and toroidal magnetic geometries

We investigate the validity of the guiding-center approximation for the magnetic mirror geometry and the axisymmetric tokamak geometry. Particle and guiding-center orbits are compared on the basis of the conservation of the azimuthal canonical angular momentum for magnetic mirror geometry and the conservation of the toroidal canonical angular momentum for axisymmetric tokamak geometry.