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

Xavier Garbet (1, 2)

1 IRFM - Institut de Recherche sur la Fusion par confinement Magnétique
2 NTU - Nanayang Technological University

This 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.

Mots clés: Magnetic fusion energy; Plasma physics

Domaines: Physique [physics]

Xavier Garbet. Particle trajectories: equations of motion, canonical and non-canonical formulation. Doctoral. France. 2023. ⟨hal-03974974⟩