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Nuclear Instruments and Methods in Physics Research A 375 (1996) 67-70 NUCLEAR INSTRUMENTS

& METHOOS IN PHYSICS

ELSEYIER R~ZYH

Temporal and spectral evolution of a storage ring FEL source: experimental results on Super-AC0 and new theoretical approach

T. Haraa’b, M.E. Couprie”3b, M. Billardon”‘”

“Labormoire pour 1’CJtilisarion du Rayonnement ElectromagnPtique, Brit. 209D, Universite’ de Paris&d. 91 405 Orsay. France

hCEAIDSMIDRECAM, Service de Photon, Atomes et Moltkules. Saclay, 91 191 Gifsur-Ybjette, France

‘ESPCI. IO rue Vauquelin. 75231 Paris. France

Abstract Because of the complex interaction in a storage ring FEL system (SRFEL + storage ring), SRFELs show various

phenomena. Conventional theoretical models, such as the super-modes model, can not treat the dynamic behavior of the

SRFELs. or do not contain spectral effects. In this paper, a new simulation model is presented, which enables the study of temporal and spectral behavior of a SRFEL. Novel is that this model starts from the spontaneous emission spectrum, which is specially important for small gain FELs. The simulation results are compared with the experimental observations of the Super-AC0 FEL. We have also used the simulation code to study the response of the laser to perturbation on the beam.

These results provide meaningful aspects for designing new storage rings.

1. Introduction

The Super-AC0 FEL source in the UV (350 nm) is now used for user applications, such as a time-resolved fluores- cence experiment in biology [l] and two-color experi- ments, coupling FEL and synchrotron radiation (SR) [2,3].

For this, the stability of the FEL is a critical issue, and

hence, the detailed temporal and spectral studies of the Super-AC0 FEL [4,5] have been carried out. This has resulted in the development of a longitudinal feedback system [6] in order to maintain perfect synchronization between the laser micropulse and the positron bunch. Now this feedback system works effectively and intensity fluctuations are stabilized within a few %. The feedback

suppresses also the longitudinal micropulse jitter and spectral drift.

The thus stabilized laser has been used successfully for user applications. However, the feedback system, which is working currently at 50 Hz, can not react on the frequency components around the resonant frequency of the FEL system (-300 Hz at Super-ACO). Therefore, a better understanding of the SRFEL behavior is still necessary for further development of the laser.

Apart from the longitudinal jitter, we have also observed the various FEL dynamic behavior, such as chaotic mac- ropulses [7], laser wavelength drifts, spectral line width narrowing and deformation of micropulse temporal dis- tribution [4,5,8,9]. Some of these effects have been ob- served also at UVSOR, where a streak camera has been used to study the substructure and the evolution of the laser micropulse [lo]. These dynamic phenomena can not

be treated by previous models. such as the super-modes model [l I]. In this paper, a new theoretical model is presented to simulate the temporal and spectral dynamic behavior of the SRFEL.

2. Experimental observations at the Super-AC0 FEL

[4,51

With the Super-AC0 FEL, several fast detectors are employed to study the temporal and spectral characteris- tics. A streak camera and a dissector [12] are used for the temporal measurements and a scanning Fabry-Perot for the spectral measurements. The FEL behavior is very

sensitive to the detuning condition between the laser micropulse and the positron bunch [4,.5]. Naturally the laser micropulse is a reproduction of the bunched structure of the positron beam in the storage ring. Hence at Super- ACO, the laser is always pulsed with a period of 120ns, which corresponds to the period between the successive

bunches. Besides this, a macrostructure at ms scales, which depends on the detuning condition (Fig. la), can be observed. The RF frequency detuning of 1 Hz corresponds

to the cavity length change of 0.36 pm. When the optical cavity length is perfectly matched to the round trip time of the bunch in the ring (perfect synchronization), the laser is quasi-continuous except for the micropulse structure (zone 3). However, if the two pulses are slightly detuned at the order of lo-’ (detuning length/cavity length), the laser becomes pulsed (zones 2 and 4). The period (-3 ms) is determined by the laser gain and the energy damping time

0168-9002/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved

SSDI 0168-9002(95)01425-X Il. STORAGE RING BASED FELs

68 T. Ham et al. I Nucl. Instr. and Meth. in Phys. Res. A 375 (1996) 67-70

Ct3ltW

bunch

(4

(b)

Fig. 1. Detuning curves obtained (a) experimentally and (b)

theoretically. The laser macrostructure is continuous in zones I, 3

and 5, and pulsed in zones 2 and 4. The top trace in (a) shows the micropulse position change in terms of the positron bunch.

of the ring. This macrostructure results from a kind of oscillation of relaxation of the beam energy spread excited

by the laser and damped by the radiation damping. If the detuning is further increased, the laser macrostructure

becomes continuous again (zones 1 and 5). The laser characteristics are different in each detuning

zone. In zone 3, maximum laser average power is obtained combined with the narrowest temporal and spectral widths (50~s and 0.3 A FWHM). However, significant longi- tudinal micropulse jitter around the positron bunch center

(up to 200 ps) is observed in this zone. In zones : and 4, the laser wavelength changes rapidly by a few A within less than a millisecond. The spectral line width tends to narrow as the laser intensity grows up. In zones 1 and 5, the laser is more stable in terms of the intensity fluctuation and the micropulse jitter. This is why we operated the laser in zone 1 or 5 for the first biology application [1], which was carried out before the feedback system was developed. But the average laser power in zone 1 or 5 is less than that of zone 3, and the temporal and spectral widths are wider.

These phenomena are closely related to the beam instability. For example, the wavelength drift becomes

significant when the collective bunch oscillations exist at high beam currents.

3. The storage ring FEL model

In storage ring FELs, the beam interaction with the laser field increases the beam energy spread, which leads to the gain reduction and laser saturation. In order to modelize the induced energy spread by the laser, we introduce the laser intensity 5, and the RMS beam energy spread gY_ at

the equilibrium [ 131, and we also define a synchronous particle, which circulates the ring with a constant period. The laser intensity of the (k + 1 )th pass, di,, , (w, T), at a

longitudinal position 7 from the synchronous particle can be deduced from the intensity of kth pass di,(w. 7). w represents the laser frequency. The laser intensities,

di,+, (w, 7) and di,(o, 7). are normalized to lc,. Then the basic equation set can be written as

X di,(w, 7 + ST, + , )

I = I

di,(w, 7) dw d7,

where R(o). G(o) and G,,(w) are the mirror reflectivity, the gain and the initial gain (G, (350nm) = 2% at Super- ACO), respectively. T<,~ and W, are the distances from the synchronous particle to the center of the bunch and to the

center of the laser micropulse at the kth pass. IdS,,,(w)/’ is the power spectrum of the spontaneous emission. (T,, cY and uYyo are the RMS bunch length, the energy spread and the initial energy spread, respectively. 7, is the damping time of the ring.

The power spectrum is obtained from the integration of Eq. (1) over x Integration over w gives the temporal distribution of the laser micropulse. The derivation of the temporal distribution is valid except for the situation close to the Fourier limit. The model starts from a spontaneous emission spectrum, and not from a white noise, which is an important hypothesis for small gain FELs since the experi-

T. Hara et al. I Nucl. Instr. and Meth. in Phys. Res. A 37.5 (1996) 67-70 69

ments indicate that the observed spectrum of the sponta-

neous emission is already expressed by the integrated

LiCnard-Wiechert equation. A detailed derivation of the equations is given in Ref. [4].

4. Simulation results

The experimentally obtained detuning curve is simulated numerically (see Fig. I), which shows the laser intensity and the macropulse structure as a function of the detuning. These curves in Fig. 1 match qualitatively. The simulation

results also indicate (not shown here) that the detuning curve extends in case of a small damping time and a large laser gain.

The evolution of the macropulse and the laser spectrum is calculated in each detuning zone. In zone 3, after the

intensity oscillations at the resonant frequency of the FEL

system (-300 Hz at Super-ACO), the laser reaches an equilibrium, and the macrostructure becomes continuous (Fig. 2a). The laser spectrum continues narrowing even after the equilibrium is reached (Fig. 2b). This is a kind of an “adiabatic” process. As shown in Fig. 3, the temporal and spectral widths narrow very slowly, and they finally

reach the Fourier limit after several seconds. However, the real storage rings are always under influence of various perturbation, so this “adiabatic” condition is generally

1 I , 1

P 0.0 0.2 0.4 0.6 0.6 1.0x106 Pass number

(a)

g 349.2 349.3 349.4 349.5 349.6 349.7x11YD

Wavelength [m]

@)

Fig. 2. The macrostructure and the spectral evolution of the laser in zone 3. (a) The laser intensity vs. pass number. (b) The spectral

line width after 80000 passes. 500000 passes and 1 000 000

passes.

I- 0 10

l_asZ evoGn time ‘i@ 50 60X10“

(b)

Fig. 3. “Adiabatic” narrowing of the temporal and spectral width

of the laser micropulse in zone 3. (a) The temporal width

narrowing. (b) The spectral line narrowing.

broken before reaching the Fourier limit. Hence, the observed spectral line width depends a lot on the ring

stability in the experiments. The observed line width is smaller when the ring is stable.

The laser intensity and the spectrum evolve differently

in zones 1 and 5. As shown in Fig. 4a. the laser reaches

p_/;;

0.0 0.2 0.4 0.6 0.8 1.0x10”

Pass number

(a)

,x ‘Zo.12

z?

-1

.ro.os

xl

Eo.04

~o.oojn 5 320 330 340 350 360 370 380x10-

Wavelength [m]

(h)

Fig. 4. The macrostructure and the spectral evolution of the laser

in zones 1 and 5. (a) The laser intensity vs. pass number. (b) The

~ spectral line widths at 500 000th pass and 1 000 000th pass.

II. STORAGE RING BASED FELs

70 T. Hara et al. I Nucl. Instr. and Meth. in Phyr. Res. A 375 (1996) 67-70

rapidly the equilibrium and there is no large intensity oscillation. The spectral width is much larger and several spectral lines can appear (Fig. 4b). Since the micropulse always changes its position on the bunch due to the detuning, the “adiabatic” spectral line narrowing does not occur in the equilibrium state.

In Fig. 5, the experimentally observed macrostructure and the simulated one are compared in zones 2 and 4. The

difference of the shapes originates from the linear approxi-

mation of the beam energy spread model [4]. The responses of the FEL to various perturbation on the

beam (such as beam orbit change and a beam energy jump) are also investigated. The results show that the laser in

0 5 10 Tiie [rnsj’

(4

(b)

Fig. 5. Comparison of the macropulse in zones 2 and 4 between

(a) the experiment and (b) simulation.

zone 3 is generally more sensitive to such perturbation than the laser in zone 1 or 5 [5]. This agrees with the experimental facts.

5. Discussion

A newly developed simulation model can treat the temporal and spectral dynamic evolution starting from the

spontaneous emission. The results are in agreement with the Super-AC0 experiments. The simulation indicates that

the temporal and spectral “adiabatic” narrowing to the

Fourier limit is possible at the perfect synchronization (zone 3) on an ideally stable ring. The model presented here is also applicable to study the origin of the jitter, the

effects of the collective oscillations of the bunch etc. There are still some points to improve, such as the linear approximation of the laser beam heating. nevertheless, the model may be useful to examine the characteristics of new

SRFELs before designing them.

References

[I] M.E. Couprie, F. Merola, D. Garzella. A. Delboulbt, T. Ham

and M. Billardon, Rev. Sci. Instr. 65 (1994) 1485.

[2] D. Garzella, L. Nahon, T. Hara, M.E. Couprie. M. Billardon.

M. Meyer and P. Morin. 1st FEL user workshop. Stanford.

CA. USA. Aug. 1994.

[3] M. Marsi, R. Bakker. M.E. Couprie, A. Delboulbe, D.

Garzella. T. Hara. L. Nahon, M. Billardon. G. Indlekofer and

A. Taleb-Ibrahimi. 2nd FEL user workshop. New York, NY,

USA, Aug. 1995.

[4] T. Hara, Ph.D. dissertation, Universite de Paris XI ( 1995).

[5] T. Hara, M.E. Couprie. A. Delboulbe, D. Garzella. L. Nahon

and M. Billardon, Nucl. Instr. and Meth. A 358 (1995) 341.

[6] M.E. Couprie, D. Garzella, T. Hara, J.H. Codarbox and M.

Billardon. Nucl. Instr. and Meth. A 358 (1995) 374.

[7] M. Bihardon, Phys. Rev. Lett. 65 (1990) 713.

[S] M.E. Couprie. D. Gontier, P. Toussel. T. Hara, A. Delboulbe

and M. Billardon, Rapport d‘experience. Ref. CEA/DSM/

DRECAMfSPAM-931377 (CEA, 19931.

[9] T. Hara. M.E. Couprie, A. Delboulbe, P. Troussel, D. Gontier

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[lo] H. Hama, J. Yamazaki, T. Kinoshita, K. Kimura and G.

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