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* Tel.: # 310-206-1677; fax: 310-206-5251. E-mail address: pellegrini @physics.ucla.edu (C. Pellegrini).

Nuclear Instruments and Methods in Physics Research A 445 (2000) 124 } 127

High power femtosecond pulses from an X-ray SASE-FEL

C. Pellegrini *

UCLA, Department of Physics and Astronomy, 405 Hilgard A venue, Los Angeles, CA 90095-1547, USA

Abstract

We discuss how to use the large-gain bandwidth of an X-ray SASE-FEL to produce femtosecond long pulses by

chirping and compressing the output FEL radiation. We consider the power level, spectral width, and intensity# uctuations of the compressed X-ray pulses, compared to the case with no compression. 2000 Elsevier Science B.V.All rights reserved.

PACS: 41.50; 78.47; 41.60C; 42.55

Keywords: Free-electron laser; Femtosecond; X-rays

1. Introduction

An FEL in the high-gain regime has a ratherlarge-gain bandwidth [1]. When starting fromnoise in a SASE-FEL, the gain bandwidth leads tothe presence of spikes in the temporal distributionof the ampli " ed radiation [2 } 4], if the electronbunch length is larger than the spike length. Theexistence of spikes and the statistical properties of the photons emitted in a SASE-FEL have beenrecently veri " ed experimentally in the infrared re-gion of the spectrum [5,6], with good agreementbetween theory and observations.

In a SASE-FEL operating at the wavelength ,the r.m.s. spike length at saturation is , the co-operation length, given by Refs. [2 } 4].

+4

(1)

where is the FEL parameter, related to the 1D

gain length by

%"

/2( 3 [1].The FWHM line width of a spike is

"2

. (2)

For a radiation pulse of r.m.s length . , the pulseconsists of a number of spikes, N 1 , each one occu-pying a length 2 . We evaluate the number of spikes by dividing the FWHM pulse length by2 .

N 1 +2.35 .2

. (3)

For a same pulse length FEL, not starting fromnoise, but from a coherent uniform signal longerthan the pulse length, the Fourier transform limitedline width would be

"2 .

(4)

0168-9002/00/$- see front matter 2000 Elsevier Science B.V. All rights reserved.PII: S 0 1 6 8 - 9 0 0 2 ( 0 0 ) 00 1 2 6 - 1

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smaller than Eq. (2) by a factor N 1 . Hence forexperiments needing high-frequency resolution, it isimportant to try to reduce the line width near tovalue (4), as proposed and discussed in Refs. [7,8].For other experiments, like pump } probe and/ornon-linear e ! ect studies, it would be convenient toreduce the pulse length to that of one spike. Achiev-ing this result isolating a single spike has two disad-vantages: (a) a reduction in the total intensity in thepulse; (b) a large intensity # uctuation, since theintensity in a single spike # uctuates as the negativeexponential distribution [2 } 4]. In this paper wepropose a method to reduce the pulse length to thatof a single spike by superimposing all the spikes.This system has the advantage that there is nointensity reduction, and the additional advantage

that the intensity # uctuation is still that of a SASE-FEL, of the order of the inverse of the square rootof the number of spikes.

The method we propose is based on chirping theradiation pulse, i.e. changing the frequency of eachspike by a quantity proportional to the spike longi-tudinal position inside the pulse, and compressingthe pulse using a pair of di ! raction gratings. Thepulse length can then be changed between . and

. In the case of an X-ray SASE-FEL like LCLS[9], this allows us to change the X-ray pulse lengthfrom about 200 fs to about 1 fs. The system peakpower is thus increased by a factor of about 200 tothe Terawatt level, while the intensity # uctuationsand the line width remain unchanged.

2. Chirping

The radiation wavelength of an FEL depends onthe beam energy, , measured in rest mass units as

"2

(1# K ) (5)

where and K are the undulator period and theaverage undulator normalized vector potential.A correlated frequency distribution along the radi-ation pulse chirping can be obtained by changingthe electron energy along the electron bunch, i.e.chirping the electron bunch energy before it entersthe undulator. This energy variation can be pro-

duced by accelerating the bunch in the full linac, orin part of it, at a RF phase di ! erent from 90 3. Byproperly choosing the RF accelerating phase, andcontrolling the wake " elds e ! ects, we can obtaintotal control of the electron energy chirping, andthus of the frequency distribution along the radi-ation pulse.

In what follows, we will make an initial estimateof the frequency chirping needed to compress thebunch, and of the grating pair needed to transformthe frequency chirping into a bunch length reduc-tion. For this initial evaluation we assume that thewavelength variation that we introduce is smallover a spike or

d

ds

; (6)

where is the spike line width (2). We can alsorewrite this condition, using (2), as

1 dds

;2 A

. (7)

We now assume that we produce a centralwavelength variation per spike, equal to a fraction

of the spike line width ( / ) " /2 , with( 1. We call the chirping parameter. The result-

ing total chirping, total wavelength variation alongthe bunch, is then

2" N

2(8)

with the chirping parameter ( 1.

3. The grating compressor

In this Section we discuss the characteristics of the grating compressor. The geometry of the com-pressor is shown in Fig. 1. The incidence angle, ,is assumed to be smaller than unity, but largercompared to the angular spread in the radiationbeam. The grating lines are separated by the dis-tance a , and the two gratings are separated by d .

Considering " rst-order di ! raction, the scatteringangle, , is related to the incident angle, , by

a (cos ! cos )" . (9)

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Fig. 1. Schematic representation of the compression system.

Fig. 2. Compression factor versus grating separation d for" 0.5 (solid line), " 0.05 (dotted line), " 0.025 (dashed line).

The angle is a function of the incident angle andof the ratio /a . For two rays with wavelength ,and # , corresponding to the angles and

# , the di ! erence in path length is AC !AB ! BC cos . We de " ne the compression factor,F , as the di ! erence in path length divided by therms pulse length, . . We also de " nex " /a , x # " ( # )/a . Let AC " s , AD " ,BC " l. Then

s (x , , d )"d

sin (x , )(10)

(x , , d )"d

tan (x , ). (11)

The distance BC " l, giving the minimum grating

length, isl(x , , , d )" (x , , d )! (x # , , d ). (12)

The compression factor is then given by

F (x , , , d , )" +s(x , M , d )! s(x # , M , d )

! l(x , , M , d ) cos M , / . . (13)

4. The LCLS case

We consider now an example similar to theLCLS [6], with " 1.5; 10 \ m, " 2.4; 10 \ ,

. " 2; 10\ m. We then have & 5; 10 \ m,N 1 & 150. The spike line width is then

/ & 5; 10\ . The Fourier transform limit of the line width is about 10 \ . We assume for thegrating a " 10 \ m, and evaluate the X-ray energydensity incident on the " rst grating, and the separ-ation of the two gratings for di ! erent values of chirping and compression. The power density in

the incident beam is reduced by the factor .Respect to the normal incidence case. To estimatethe energy density at the compressor we assumethat the spot size is increased from the original 30to 100 m, by proper choice of the distance of theundulator exit to the " rst grating. The LCLS peakpower is about 10 GW, corresponding to an energyper pulse of 3 mJ, and an energy density of 10 J/cmfor normal incidence. The energy density incidenton the grating is then 10 J/cm . For ( 0.1 theincident energy density is smaller than 1 J/cm ,

small enough to avoid damaging the grating. Sincethe X-ray pulse is di ! raction limited, its angularspread is about 4 ; 10 \ rad, so any value of lar-ger than 10 \ is acceptable. For what follows, wewill assume as an example " 0.05. The corre-sponding value of is " 0.07.

In Fig. 2 we plot the compression factor versusthe separation of the two gratings, d , for di ! erentvalues of the wavelength chirping introduced in theX-ray pulse, 2 (8). The three curves in Fig. 2 cor-respond to a value of the chirping parameter

" 0.5, 0.05, 0.025, full, dotted and dashed lines,

respectively. A full compression to a bunch lengthequal to the spike length is obtained for F "! 1.For the LCLS case we have N 1 / " 150;

5; 10\ " 7.5; 10\ . To obtain this chirping wewould need a 3.7% energy chirping in the electronbunch, too large to avoid electron phase-space dilu-tion due to chromatic e ! ects. A value one tenth of that corresponding to the dotted line, is acceptable.From Fig. 2 we see that to obtain full compressionwe need d & 1.2 m, a value leading to a possible,practical design.

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The value of l, the grating minimum length, forthe case of " 0.05, d " 1.2 m, is l& 15 cm, againan acceptable value.

5. Conclusions

We have shown that by chirping the electronbunch longitudinal energy distribution in the linacit is possible to correlate the frequency with thelongitudinal position of the spikes in a SASE-FEL.Using the line-width of a single spike we can com-press the X-ray pulse with a pair of di ! ractiongrating, and reduce the length of the LCLS X-raypulse to about 1 fs, increasing the peak power tomore than 1 TW.

Acknowledgements

The author wishes to thank H.-D. Nuhn formany useful discussions. This work was supported

by the US Department of Energy under Grant ERNo. DE-FG03-92ER40793.

References

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Report No. TESLA-FEL 97-02, 1997.[4] K.J. Kim, in: Proceedings of the ICFA Workshop in Non-

linear Dynamics, AIP Conference Proceedings Vol. 395,1996.

[5] M. Hogan et al., Phys. Rev. Lett. 80 (1998) 289.[6] M. Hogan et al., Phys. Rev. Lett. 81 (1998) 4867.[7] J. Feldhaus et al., Opt. Commun. 140 (1997) 341.[8] L.H. Yu, Phys. Rev. A 44 (1991) 5178.

[9] Linac Coherent Light Source Design Study Report, LCLSDesign Study Group, SLAC-Report, 1998.

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