Particle trajectories: equations of motion, canonical and non-canonical formulation

DoctoralThis note presents different descriptions of the equations of motion of a charged particle subject to an electromagnetic field. Variational principles are given in their Lagrangian and Hamiltonian forms. A non-canonical form is determined in the special case of a strong magnetic guide-field. Conditions for integrability and existence of angle/action variables are derived and discussed. This methodology is applied to the tokamak magnetic configuration. Trajectories are explicitly calculated in the limit of small orbit width. Corresponding angle/action variables are constructed