Statistical mechanics and Vlasov equation allow for a simplified Hamiltonian description of Single-Pass Free Electron Laser saturated dynamics

A reduced Hamiltonian formulation which reproduces the saturated regime of a Single Pass Free Electron Laser, around perfect tuning, is here discussed. Asymptotically, N<Subscript>m</Subscript> particles are found to organize in a dense cluster, that evolves as an individual massive unit. The remaining particles fill the surrounding uniform sea, spanning a finite portion of phase space, approximately delimited by the average momenta ω<Subscript>+</Subscript> and ω<Subscript>-</Subscript>. We propose a theoretical framework in which the external parameters N<Subscript>m</Subscript>, ω<Subscript>+</Subscript> and ω<Subscript>-</Subscript> are self-consistently determined. To this aim, we make use of a statistical mechanics treatment of the Vlasov equation, that governs the initial field amplification process. Simulations of the reduced dynamics are shown to successfully capture the oscillating regime observed within the original N-body picture. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006