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.
Statistical theory of high-gain free-electron laser saturation / J. Barre; T. Dauxois; G. De Ninno; D. Fanelli; S. Ruffo. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - ELETTRONICO. - 69:(2004), pp. 0-0. [10.1103/PhysRevE.69.045501]
Statistical theory of high-gain free-electron laser saturation
FANELLI, DUCCIO;RUFFO, STEFANO
2004
Abstract
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.File | Dimensione | Formato | |
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