Hamiltonian description of a self-consistent interaction between charged   particles and electromagnetic waves
  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. 
Romain Bachelard (CPT), Cristel Chandre (CPT), Michel Vittot (CPT)