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Charged particle motion in axisymmetric toroidal magnetic fields is analyzedwithin the context of the canonical Hamiltonian Guiding Center theory. Acanonical transformation to variables measuring the drift orbit deviation froma magnetic field line is introduced and an analytical transformation toAction-Angle variables is obtained, under a zero drift width approximation. Thelatter is used to provide compact formulas for the orbital spectrum of thedrift motion, namely the bounce/transit frequencies as well as thebounce/transit averaged toroidal precession and gyration frequencies. Theseformulas are shown to have a remarkable agreement with numerically calculatedfull drift width frequencies and significant differences with standardanalytical formulas based on a pendulum-like Hamiltonian description. Theanalytical knowledge of the orbital spectrum is crucial for the formulation ofparticle resonance conditions with symmetry breaking perturbations and thestudy of the resulting particle, energy and momentum transport.

Analytical Calculation of the Orbital Spectrum of the Guiding Center Motion in Axisymmetric Magnetic Fields