Free Electron Lasers 2002 (eBook)

Proceedings of the 24th International Free Electron Laser Conference and the 9th FEL Users Workshop, Argonne, Illinois, U.S.A., September 9-13, 2002

E. Gluskin, K.-J. Kim, S.V. Milton (Herausgeber)

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2012 | 1. Auflage
726 Seiten
Elsevier Science (Verlag)
978-0-08-093042-8 (ISBN)

Infos

This book contains the Proceedings of the 24th International Free Electron Laser Conference and the 9th Free Electron Laser Users Workshop, which were held on September 9-13, 2002 at Argonne National Laboratory. Part I has been reprinted from Nucl. Instr. and Meth. A 507 (2003), Nos. 1-2.

Textauszug

Chaos studies on the super-ACO free electron laser

M.E. Couprieab*,     aService de Photons, Atomes et Molécules, CEA/DSM/DRECAM, 91 191 Gif-sur-Yvette, France; bLaboratoire pour l’Utilisation du Rayonnement Électromagnétique, Université Paris-Sud, Bât. 209D, BP 34, 91898 Orsay Cedex, France. E-mail address: [e-mail]

*Corresponding author. Laboratoire pour l’Utilisation du Rayonnement Électromagnétique, Université Paris-Sud, Bât. 209D, BP 34, Orsay Cedex 91898, France. Tel.: + 33-1-64-46-80-44; fax: [phone]. E-mail address: (M.E. Couprie).

A laser with parameters modulated at a frequency f may respond not only at f and its harmonics, but also at is sub-harmonic frequencies f/n. The laser behaviour can become irregular though remaining deterministic. A gain modulation has been applied on the Super-ACO Free Electron Laser close to its natural frequency, via a change of the synchronization between the electron bunch and the optical pulse (detuning). Different macrotemporal structures can be observed such as 1T regime in which the laser is pulsed at the modulation period, 2T, chaos and so on. Such transitions can also be measured on the Free Electron Laser pulse temporal position. Bifurcation diagrams and attractors have also been recorded. Comparisons with simulations will be also given.© 2003 Elsevier Science B.V. All rights reserved.PACS: 41.60.Cr; 42.65. Sf

Keywords

FEL

Chaos

Storage ring

1 Introduction

The emergence of lasers, being temporally and spatially coherent light sources, led to a wide variety of interest in many domains. The stability of a laser source is then a crucial element for fundamental applications in science and use in technology. The non-linearity of a laser gain system can nevertheless induce complex regimes, including stable period and harmonic regimes, limit cycles, and even chaotic regimes. Different analysis have been carried out on conventional laser sources, such as CO2 laser [1–3], He-Ne laser [4], Yag laser [5, 6], laser diode [7]. The gain modulation can be introduced by different means: electro-optical modulator [1], tilt of the resonator mirror [4], saturable absorber pressure or laser frequency [2]. Chaos can also appear in presence of an optical feedback [7]. Apart from the spiking structure of the Self-Amplified Spontaneous Emission (SASE) where chaotic polarized radiation has been observed [8], chaos has been studied on different Free Electron Lasers (FELs) sources, such as Raman devices [9], and Compton FELs. On infra-red LINAC based FELs, Hopf bifurcations and transition to chaos were reported on ELSA [10], limit cycles and period doubling versus cavity detuning were discussed for short pulse FELs such as FELIX [11], chaotic regimes were reported on the JAERI FEL for a modification of the detuning [12]. Sidebands generation and transition to chaos were seen on ELSA [13], on the Stanford FEL [14] with various modelisations [15]. First studies on chaos on a storage ring FEL on ACO and Super-ACO showed that the FEL macrotemporal structure in the millisecond time scale follows the laws of deterministic chaos [16]. Besides, it has often been observed on storage ring FELs that the macrotemporal structure could present a pulsed regime with random intensities [17, 18]. Further theoretical investigation carried out with a simplified model allowed the Lyapunov characteristic exponents to be determined [19]. More recent numerical analysis based on a complete modelisation of the longitudinal detuning of the FEL was performed and compared to experimental results [20]. New results obtained on the Super-ACO Free Electron Laser are here presented.

2 The Longitudinal Dynamics of a Storage Ring FEL

In addition to the microtemporal structure reproducing the recurrence of the electron bunches in the ring at a high repetition rate (8 MHz for Super-ACO), the FEL exhibits a macrotemporal structure at the millisecond time scale [21, 22]. Depending on the gain and of the losses of the laser system, this regime appears systematically for given values of the synchronisation between the optical wave in the optical resonator and the electron bunches stored in the ring. The detuning Δ is defined as Δ = Tel - Tph where Tel is the time interval between two adjacent electron bunches and Tph is the round-trip time of the light wave in the optical cavity. “CW” regimes at the millisecond time scale are observed around perfect tuning and for large detunings, as shown in Fig. 1a. Pulsed regimes appear for intermediate detunings, as illustrated in Fig. 1b.

Fig. 1 (a) FEL Intensity, Measured with a Photomultiplier, Versus the Tuning Condition, Modified by a sweep of the RF frequency of Super-ACO. 1 Hz frequency change corresponds to 1.2 fs detuning change. (b) Intensity versus time for a pulsed FEL, exhibiting a natural frequency of 200 Hz. Case of Super-ACO operated at 800 MeV, with 38.2 mA, the FEL being at 350 nm, with a gain of 1.5% and cavity losses of 0.8%. (c) Simulations of the FEL evolution for different detunings. Parameters of the simulation: 800 MeV, 40 mA, gain of 2%, cavity losses of 0.5%.

This behaviour can be described by a phenomenological model, following the evolution of the FEL intensity profile yn(t) at each pass n [23, 24]. The spontaneous emission is is represented as a monochromatic wave and the optical wave is assumed to be sharply centered on the resonant wavelength. At each pass n, the light wave is amplified according to the gain term g(t), reflected on the cavity mirror of reflectivity R, and the spontaneous emission from the undulator adds up. The slippage being extremely small, it is here neglected. It comes [21]:

(1)

(2)

where In is the total laser intensity and Ieq the FEL equilibrium intensity and τ the longitudinal coordinate. Because of the FEL “heating”, the normalised electron bunch energy spread at pass n evolves as

(3)

where τs is the synchrotron damping time, ∑n = ()/(), σγn being the energy spread at pass n, σγoff laser off, and σγeq at equilibrium (∑ = I = 1). The FEL saturation leads to a reduction of the gain at pass n gn,0 for the centre of the bunch distribution, according to [20]:

(4)

where goff the is the gain at the laser start-up, P are the cavity losses. The gain dependence versus τ can be written as g(τ) = g0e−τ2/2σ2ln, assuming a Gaussian distribution of RMS dimension σln, go being the maximum gain for τ = 0. For Δ = 0 and considering a small perturbation to the equilibrium state, the energy spread evolution reduces to a second-order differential equation [25], allowing to understand the pulsed regimes of the FEL. The insertion of the detuning [23–26] in the model showed “CW” regimes at the millisecond time scale around perfect tuning whereas pulsed regimes are obtained for intermediate detunings. For larger desynchronisation between the electron bunches circulating in the ring and the optical pulses in the resonator, the FEL is again “CW”, but with larger temporal and spectral distributions. The model can properly reproduce the experimental behaviour of the FEL intensity versus detuning, as shown in Fig. 1c.

An external modulation of the tuning condition can be added to the model, such as

(5)

where f and a are the frequency and the amplitude of the modulation, and b is the detuning around which the modulation is performed. f and a are the control parameters of the system in our experiment.

3 The Response of the Super-ACO FEL to a Detuning Modulation

The Super-ACO FEL presents a stable “CW” regime around perfect synchronism. Various studies on the different sources of perburbations have been extensively carried out in order to provide a source as stable as possible for the users [27]. A longitudinal feedback system has been developed in order to compensate drifts in synchronisation [28]. An external modulation can be experimentally applied to the RF frequency pilot generator, allowing a controlled change of the FEL detuning.

The FEL intensity, measured with a photomultiplier, is recorded for different values of the amplitude and the frequency of the modulation. When the amplitude of the applied modulation is increased, in the case of a modulation at 660 Hz presented in Fig. 2a, the FEL still adopts a pseudo “CW” regime for very low...

Produkt-Details

• Erscheint lt. Verlag: 2.12.2012
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Optik
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-08-093042-5 / 0080930425
• ISBN-13: 978-0-08-093042-8 / 9780080930428