Hamiltonian description of a self-consistent interaction between charged particles and electromagnetic waves

Romain Bachelard (1, 2) , Cristel Chandre (1, 2) , Michel Vittot (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332

The Hamiltonian description of the self-consistent interaction between an electromagnetic plane-wave and a co-propagating beam of charged particles is considered. We show how the motion can be reduced to a one-dimensional Hamiltonian model (in a canonical setting) from the Vlasov-Maxwell Poisson brackets. The reduction to this paradigmatic Hamiltonian model is performed using a Lie algebraic formalism which allows us to remain Hamiltonian at each step of the derivation.

Mots clés: Hamiltonian dynamics; Maxwell-Vlasov equations; wave-particle interaction; Free Electron Laser

Domaines: Physique des plasmas [physics.plasm-ph]; Optique [physics.optics]

Romain Bachelard, Cristel Chandre, Michel Vittot. Hamiltonian description of a self-consistent interaction between charged particles and electromagnetic waves. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2008, 78 (3), pp.036407. ⟨10.1103/PhysRevE.78.03640⟩. ⟨hal-00257249⟩