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Lectures Year : 2023

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

Abstract

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.
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Dates and versions

hal-03974974 , version 1 (06-02-2023)

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Attribution - NonCommercial - NoDerivatives - CC BY 4.0

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  • HAL Id : hal-03974974 , version 1

Cite

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