• A. Antoniazzi, D. Fanelli, A. Guarino, S. Ruffo
  Universita di Firenze, Florence
• G. De Ninno
  ELETTRA, Basovizza, Trieste

We discuss the analogies between two classical models of the single-pass free electron laser dynamics and of the beam-wave plasma instability. Moreover, a formal bridge between the two areas of investigation is established. This connection is here exploited to derive a reduced Hamiltonian formulation for the saturated regime of the free electron laser.A self consistent formulation of the parameters involved is proposed .

• A. Antoniazzi, D. Fanelli, S. Ruffo
  Universita di Firenze, Florence
• J. Barre'
  LANL, Los Alamos, New Mexico
• T. Dauxois
  ENS LYON, Lyon
• G. De Ninno
  ELETTRA, Basovizza, Trieste
• Y. Elskens
  Universite de Provence, Marseille

The non-linear dynamics of a single-pass, high-gain free-electron laser is analytically studied in the framework of the Vlasov-wave picture. A multiple time scale calculation is performed to derive the well known non-linear Landau equation for the complex amplitude of the unstable mode, which hence exhibits a limit cycle behaviour. The coefficients of the equation are analytically determined as function of a generic initial electron-beam distribution. Numerical results are presented. Possible extensions of this approach to the case of the Harmonic Generation are also discussed.

• A. Antoniazzi, D. Fanelli
  Universita di Firenze, Florence
• R. Bachelard, C. Chandre, M. Vittot
  CNRS/CPT, Marseille

We apply an innovative strategy to control chaotic diffusion in conservative systems to the case of a single pass Free Electron Laser. The core of our approach is a small apt modification of the system which channels chaos by building barriers to diffusion. By confining the electrons in phase space and limiting the oscillations of the dense core, we aim at stabilizing the laser intensity. Calculations are perfomed within the framework of a simplified Hamiltonian picture. Further extensions and future experimental applications are also discussed.

• S. Bielawski, C. Bruni, C. Szwaj
  PhLAM/CERCLA, Villeneuve d'Ascq Cedex
• M.-E. Couprie, D. Garzella
  CEA/DSM/DRECAM/SPAM, Gif-sur-Yvette
• G. De Ninno, B. Diviacco, M. Trovo
  ELETTRA, Basovizza, Trieste
• D. Fanelli
  Universita di Firenze, Florence
• M. Hosaka, M. Katoh, A. Mochihashi
  UVSOR, Okazaki
• G.L. Orlandi
  ENEA C.R. Frascati, Frascati (Roma)
• Y. Takashima
  Nagoya University Graduate School of Engineering, Nagoya

Dynamical instabilities lead to unwanted full-scale power oscillations in many classical lasers and FEL oscillators. For a long time, applications requiring stable operation were typically performed by working outside the problematic parameter regions. A breakthrough occurred in the nineties [1], when emphasis was made on the practical importance of unstable states (stationary or periodic) that coexist with unwanted oscillatory states. Indeed, although not observable in usual experiments, unstable states can be stabilized, using a feedback control involving arbitrarily small perturbations of a parameter. This observation stimulated a set of works leading to successful suppression of dynamical instabilities (initially chaos) in lasers, sometimes with surprisingly simple feedback devices [2]. We will review a set of key results, including in particular the recent works on the stabilization of mode-locked lasers, and of the super-ACO, ELETTRA and UVSOR FELs [3].

[1] Ott et al. Phys. Rev. Lett., 64, 1196 (1990). [2] Bielawski et al. Phys. Rev. A 47, 327 (1993). [3] Bielawski et al. Phys. Rev. E. 69, 045502 (2004), De Ninno & Fanelli, Phys. Rev. Lett. 92, 094801 (2004), Bruni et al., proc. EPAC 2004.

• E. Allaria, G. De Ninno
  ELETTRA, Basovizza, Trieste
• A. Antoniazzi, D. Fanelli
  Universita di Firenze, Florence
• F.T. Arecchi
  UNIFI, Sesto Fiorentino (FI)
• R. Meucci
  INOA, Firenze

We numerically investigate the effect of a delayed control method on the stabilization of the dynamics of the Elettra storage-ring free-electron laser in Trieste (Italy). Simulations give evidence of a significant reduction of the typical large oscillations of the laser intensity. Results are compared with numerical and experimental data obtained with a derivative feedback. The possibility of an experimental implementation of the proposed method is also discussed.

• G. De Ninno, B. Diviacco, M. Trovo
  ELETTRA, Basovizza, Trieste
• A. Antoniazzi, D. Fanelli
  Universita di Firenze, Florence
• R. Meucci
  INOA, Firenze

The possibility of establishing and maintaining a stable operation mode of a storage-ring free electron laser finally resides in a deep understanding of the strongly coupled laser-electron dynamics. Such a dynamics may be affected by electron-beam instabilities whose origin can be traced back either to electromagnetic wake fields or to "external" perturbations (e.g. line-induced modulations, mechanical vibrations, etc.). This is the case of the Elettra storage-ring free-electron laser which is significantly affected by a 50-Hz perturbation of the electron beam density. We have developed a simple theoretical model which has been proved to be able to provide insight into the evolution of the laser intensity. In this framework, we have also proposed the possibility of utilizing a derivative closed-loop feedback to create or enlarge the region of stable signal. A feedback of this type has been implemented on the Elettra storage-ring free-electron laser. The obtained results, which fully confirm our predictions, are discussed in this paper.