Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-01-17
European Physical Journal B 50 (2006) 603-611
Physics
Condensed Matter
Statistical Mechanics
European Physical Journal B in press (2006) in press
Scientific paper
10.1140/epjb/e2006-00175-0
A reduced Hamiltonian formulation to reproduce 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 $\omega\_+$ and $\omega\_-$. These quantities enter the model as external parameters, which can be self-consistently determined within the proposed theoretical framework. To this aim, we make use of a statistical mechanics treatment of the Vlasov equation, that governs the initial amplification process. Simulations of the reduced dynamics are shown to successfully capture the oscillating regime observed within the original $N$-body picture.
Antoniazzi Andrea
Elskens Yves
Fanelli Duccio
Ruffo Stefano
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