SEMINAIRE MERCREDI 15 DECEMBRE 2004
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Giovanni De Ninno
Sincrotrone Trieste

Title: Non-linear dynamics of a Storage-Ring Free-Electron Laser:
Hopf bifurcation and stabilization

Abstract: In a Free Electron Laser (FEL) a relativistic electron beam interacts
with an electromagnetic field as it passes through a periodic magnetic structure
(e.g. an undulator) forcing particles to move along sin-like trajectories and,
consequently, to emit radiation. The term FEL covers a wide variety of
configurations. A Storage-Ring FEL (SRFEL), on which attention will be here
concentrated, provides intense, tunable, monochromatic and fully coherent radiation
in the range from the visible to the UV/VUV. In a SRFEL the light emitted by
electrons is stored in an optical cavity and amplified during successive
interactions with the electron beam. The amplification is obtained to the detriment
of the electron-beam energy, whose spread increases with the growth of the
intra-cavity power. This heating effect leads to the reduction of the amplification
gain until when the latter reaches the level of the cavity losses (laser
saturation).

The dynamics of a SRFEL depends strongly on the light-electron synchronism, i.e.
the difference between the electron beam revolution period and the round trip of
the photons in the cavity. For a small detuning, the laser intensity displays a
"continuous wave" ("cw") behaviour, while regular oscillations are found for larger
detuning amounts. If an external modulation is applied to the detuning parameter
the system is shown to produce chaotic regimes. Given this setting and aiming at
improving the performance of the device, it is of paramount importance to
investigate the non-linear dynamics of the system and achieve a comprehensive
understanding of the mechanism of saturation. In particular, it is crucial for user
applications to obtain a stable and extended "cw" region.

In [1] a new model for the longitudinal dynamics of a SRFEL was introduced and
shown to be particularly suitable for analytic calculations. Within this framework
explicit expressions for the asymptotic values of the main statistical parameters
of the laser distribution are provided as function of the detuning amount.
Moreover, the transition between stable and unstable regimes is characterized as a
Hopf bifurcation and an explicit expression for the critical detuning is given.
These findings open up the perspective of using a derivative closed-loop feedback
to enlarge the region of stable signal. A feedback of this type has been
implemented on the Elettra SRFEL.

In this talk, we will first give a general overview of the principle and the
performance of an FEL. Then, we will review the theoretical approach which allowed
us to propose a control strategy for improving the stability of a SRFEL. Finally,
we will show that predictions are in a very good agreement with experimental
results.

[1] G. De Ninno, D. Fanelli, Phys. Rev. Lett. 92, 094801 (2004).