Statistical theory of high-gain free-electron laser saturation.
We propose an approach, based on statistical mechanics, to predict the saturated state of a single-pass, high-gain free-electron laser. In analogy with the violent relaxation process in self-gravitating systems and in the Euler equation of two-dimensional turbulence, the initial relaxation of the laser can be described by the statistical mechanics of an associated Vlasov equation. The laser field intensity and the electron bunching parameter reach a quasistationary value which is well fitted by a Vlasov stationary state if the number of electrons N is sufficiently large. Finite N effects (granularity) finally drive the system to Boltzmann-Gibbs statistical equilibrium, but this occurs on times that are unphysical (i.e., excessively long undulators). All theoretical predictions are successfully tested by means of finite- N numerical experiments.
Barré
Julien
J
Laboratoire de Physique, UMR-CNRS 5672, ENS Lyon, 46 Allée d'Italie, 69364 Lyon cédex 07, France.
Dauxois
Thierry
T
De Ninno
Giovanni
G
Fanelli
Duccio
D
Ruffo
Stefano
S