Eur. Phys. J. B 50, 603-611 (2006)
https://doi.org/10.1140/epjb/e2006-00175-0

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

¹ Dipartimento di Energetica, Università di Firenze and INFN, via S. Marta, 3, 50139 Firenze, Italy
² Equipe Turbulence Plasma de l'UMR 6633 CNRS–Université de Provence, case 321, campus Saint-Jérôme, 13397 Marseille Cedex 13, France
³ Department of Cell and Molecular Biology, Karolinska Institute, 17177 Stockholm, Sweden

Corresponding author: ^a duccio.fanelli@cmb.ki.se

Received: 2 November 2005
Revised: 11 January 2006
Published online: 17 May 2006

Abstract

A reduced Hamiltonian formulation which reproduces the saturated regime of a Single Pass Free Electron Laser, around perfect tuning, is here discussed. Asymptotically, N_m 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₊ and ω_-. We propose a theoretical framework in which the external parameters N_m, ω₊ and ω_- 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.