JAERI-Conf 95-021

PB51
A Design Study of an FEL-SR at the FELl
Yasuyuki MIYAUCHI, Tohru TAK/1 and Takio TOMIMASUFree Electron Laser Research Institute, Inc. (FEU): 4547-44, Tsuda, Hirakata, Osaka 573-01, japan
Abstract
A compact, low emittance SR dedicated to both of FEL
and SOR is studied. The FEL wave length and small signal
gain are estimated using the emittance of the designed lattice.
Designing problem of the FEL- SR was also shown, and a
45 deg bending, modified DBA lattice was adopted. TheFEL wavelength, small signal gain, and output power areestimated.

1. Introduction
Considering the practical application of the short wave
length FEL, two types of facilities are promising: Linac typeand SR type. Linac can lase high power FEL, and SR canmake cw FELs with narrow spectrum bands. Considering theapplication of high peak power FEL, the FELl has adopted anS-band linac for its main accelerator system, and succeededin the lasing at two lasing sections (30 MeV and 70 MeV) for
middle and near infrared FEL longer than 1 f.1 m, and has
began the application study in the regions of solid statephysics and bio-sciences. In addition, we have constructed ahigh energy (160 MeV) beam line for the lasing of visibleand UV FELs with the wavelength of 1.2-0.35 f.1 m andobtained spontaneous emission of 0.5 f.1 m [1]. On the otherhand, aiming as a research and application center of FEL inJapan, the FELl has also considered the possibility of theconstruction of an SR for FEL and has prepared its space.
This paper reports a preliminary design study of an SR FEL
apparatus suitable for the FELl.
In the design of SRs, the selection of the lattice fromvarious candidates is most important. Most of SR FEL
experiments made use of existing machines such as ACO,VEPP-III, 1ERAS,. UV-SOR, and few SRs such as
super-ACO, Duke-SR, and NIJI-IV which were designed for
FEL lasing. Hence, we compared several achromatic, lowemittance lattices for a compact FEL SR suitable for theFELl, and chose a modified DBA lattice with eight 45 deg
bending magnets. We applied this lattice to the designed ofa 1 GeV SR for the application of SOR to say nothing ofFEL.

angle, respectively. In addition, the lattice of FEL SRs also
needs long straight sections for the installations of undulators.
Putting these conditions in mind, we compared fiveachromatic lattices shown in Fig. 1 using MAGIC, andobtained machine functions shown in Fig. 2.
Parameters including the emittance of 1 GeV of theselattices are listed in Table 1. We chose the betatron numbers
so as to make the emittance to be minimum, and adopted
edge angles so as to reduce the maximum values of verticalbetatron functions (3 1. The variation of the edge angle does
not affect the emittance. Table 1 shows that, there is noremarkable difference between three typical achromatic
lattices of DBA, TBA, and QBA.
Considering the diffraction limit of the lasing wave lengthof eq.(1), we adopted the 2-fold modified DBA lattice shownby Fig.1(e).

Table 1 Comparison of typical compact lattices
Lattice typeQBA
DBA*
DBATBA
DBA
Bending angle e (deg) 90
60
4545
45
Bending radius P (m)
2.3
2.3
2.3
2.3
2.3
Edge angle E (de g)
020
22.5
00Circumference C(m)41.95 43.46
45.75 68.05 52.46Long straight sec. L(m) 9.8
9.8
9.8
9.8
9.8
Periodicity N22242
Field gradient K • 11, ( 1/rn)(!:Length)(QC)
0.662 0.866
0.734
1.01
0.800
(QF)
1.15
1.04
0.938
1.11
1.18
(QD)
-1.08 -0.990 -0.900 -0.995 -1.14
(QF1)
0.752
(QD1)
-0.800
Betatron number ll x 2.75
2.75
2.75
3.25
3.25
J,! y
1.25
1.25
1.25
1.25
1.25
Emittance E (mm • rnrad) 0.90 7l 0.65 7l 0. 76 7l
0.29 7l 0.37 7l(1 GeV, MAGIC)
Betatron function (3 •. , (rn)1.06 2.54
2.51
11.8
1.76
(c:straight sec. center) 1l x, mox(rn) 23.6
12.0
12.1 13.8
15.4/l y, c(rn) 2.75 0.770 1.32 . 9.65
2.72/l y, m a x(rn) 27.1 77.5
45.8 23.0
27.5

2. Comparison of lattices
Considering the limit of the available space, we wereinterested in so called compact rings. In these rings, bending
angles are large and corresponding changes of machinefunctions are also large. Therefore, making of dispersionfree straight sections is inevitable for the reduction of beam
diameter in the undulator section. For this reason, weconcentrated on achromatic lattice as DBA, TBA, and QBA.
As the small signal gain of FEL rapidly decreases below
the diffraction limited wave length, the lasing wave length A
should satisfy the following condition [2].
A >2 7l E ( E :emittance of the electron beam)(1)
Althogh, Einfeld and Plesko [3] and Wiedemann [4] proposed
equations for the estimation of emittance, their equations can
not be applied to large bending, compact lattices. In general,
there is a tendency Of E (m • rad)OC Y 2 () - 3 , where Y=1957E/GeV is the electron energy, () [rad] the bending-392-QD )F"'€{ I :§QOQF• Modified(a) 2xDBA"(" I:~(d) 4xDBA(b) 2xTBA(c) 2xQBA(e) 4xDBA (modified)Fig. 1 Achromatic lattices for compact rings

JAERI-Conf 95-021:L;ii;{-.. _ ·. . .

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20

15

1050

basic research of materials. In addition, as the length of
optical beam packet is proportional to the square root of thelength of electron bunches [5], the time fluency of FEL
increases according to the square root of the RF frequency.

--~~=-i:-:----OISTANCE [m](a)OBA LATTICE (8=90deg)
05Table 2 SR ring parameters
302!

20

15

10= ~li~'i'\ · '_· v,;ushv~~·.''''f.
;~~
~~0.5
50

Lattice parameters
Lattice type
Beam energy
Injection energy
Average current
CircumferenceLong straight section
Periodicity
Bending angle
Bending radius
Bending field
Field index
Edge angle
Focusing field gradient(Length 0.2 m)~·--5~~30

DISTANCE [m](b)TBA LATTICE (8=60deg)

0 I STANCE [m](c) OBA LA TTl CE (8=45deg)

f-,;ls·.··:. :-.1Vx"2 75/2, vr-!:-~5/2~/ ~..

::..

.

:~

Em ax
Einj

Ia vc
LNep

Bmax

nEK~

DISTANCE [m]RF parameters
Harmonic number
Frequency
Tube typeAce. Gap Voltage
Machine parameters
Betatron number(d)DBA LATTICE(8=45deg)•oo 0f---..;-~..c;-~-T-------'T--==l25 to
Vx:2J5/2,Vy:!1.25/2:"-~ 1---·~~8& ~:~20151050--oo-ca::-~~~-25

OISTANCE [m]h{RFVacc

Modified DBA
1 GeV
160 MeV
0.5 A (0.3 A*)
47.21 m8.78m
245 deg
2.3 m
1.45 T
00 deg5.628 m- 2 (QF1)-5.369 m- 2 (QD1)
4.000 m- 2 (QC)
-4.000 m - 2 (QD1)
7.344 m- 2 (QF1)
144915 MHz
CW Klystron
100 kV

3.25
1.25
0.0804aMomentum compaction
3.60x10- 7 7! m • rad(l GeV)
E
Emittance
CX,{31.52 m(straight section center)function
Betatron
14.2m/3x, max{3 y, c4.33 m(straight section center){3 y, max
21.4 m5.3x10- 4 (1 GeV)
t.E/E
Energy spreadax
0.71(1.46*)mm(1GeV,lO% coupling)
Bunch size
a,0.38(0.46*)mm(1GeV,lO% coupling)(Straight section center)a.
24.7 mm (1 GeV)
'Cx
11.1 ms
Damping time'Cy
8.2 ms'CE
3.6 ms
3.2x10 4 A· s
Touschek life time x Beam current
l.lx

l.l y(e)Modified DBA LATTICE(8=45deg)

Fig. 2 Machine functions of achromatic lattices

3. Design estimation of an FEL SRConsidering the limit of available space, we modified thelattice of Fig. 1(e) to resemble a race track shape anddesigned a ring shown in Fig. 3.
Its parameters are listed in Table 2, and the machinefunctions are shown in Fig. 4. The maximum energy is set
to be 1 GeV considering the application of SOR not only
FEL. The RF frequency is set to 915 MHz, and its powersource is supposed to be Toshiba cw klystron with highest
output power of 200 kW. Using this high frequency, we canmake short rnicropulse FELs which are convenient for theFig. 3 A layout plan of an FEL-SR at FELl-393-• used for FEL gain estimation

JAERI-Conf 95-021

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Vx=2. 75/2. Yy=J. 25/2

a 20~15:~20~

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~

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4. Conclusions and discussions

25025

DISTANCE [m]Fig. 4 Machine functions of an FEL-SR
The FEL wave length is given by eq.(2).
A =(1+IK 2 12) A " 12 r 2(2)Here, A u[m] is the period length of the undulator,K=93.4B[TJA u[m], where B[T] is the peak value of theundulator magnetic field. The FEL wave length according tothe electron beam energy is shown in Fig. 5 with thediffraction limit of eq.{1). Here K is fixed to be v'2 forsimplicity. This value of K makes the small signal gain
almost maximum in many cases. Considering that themaximum average FEL out put power is proportional to thesynchrotron radiation (so called Renieri's limit)[6] which is
proportional to the fourth power of the electron beam energy
as eq.{3), the combination of a long period undulator andhigh energy electron beam is the answer to the demands ofhigh power FEL.
Pmax ={LlE/E)max8.86 X 10- 2 E 4 I I P{3)Here, t. E/E is the energy spread of the ring, I[ a] the average
current, and P [m] the bending radius, respectively. Figure 5
shows that the diffraction limit of 2 7l e is a very severe
restriction to high energy i.e. high output power operation ofFEL rings. In this figure, a moderate experimental limit suchas v' 2 7l e is also plotted.
The small signal gain of compton regime FEL can be
estimated by eq.(4) which uses a trivial arithmetic
deformation of the equation presented by Dattoli [7).
Go = 4.46x10- 3 {K 2 12) r - 3 [JJ) 2 {Lu 3 1 Au)·cl{(2 n fR F )(2 n a x a y a z)} • I • F 1(4)Here, Nu is the period number of undulator, Lu[m]=Nu Au[m] is the undulator length, [JJ) 2 ={Jo(f}-Jia-)}\f=K 2/(4+2K 2), fRF is the RF frequency of the accelerating cavity,
and a x, a y, a z are horizontal and vertical bunch radius andthe half of the bunch length, respectively. The factor F 1 =11
v' {(1 +wl2 a x) 2 +(l+wl2 a y) 2 } is the filling factor [8). Inaddition, maximum small signal gain using optical klystron(OK) can be estimated by the following equation [8,9).
GoK. max = 0.045 Go I {Nu{LlE/E)}{5)
Using the parameters listed in Table 2, we obtain thesmall signal gain with various period length according to theelectron energy shown in Fig. 6. Here, the undulator lengthLu is fixed to be 7 m considering the long straight section of
our lattice, and the filling factor is set to be 0.5 whichcorresponds that the optical waist size coincides with theelectron beam diameter, and K is v'2. This figure showsthat the small signal gain is large enough for the small period
length of 4 em, but, for larger period length, the gain
decreases due to the decrease of period number. In this case,the use of OK is necessary.
Figures 5 and 6 show that the combination of a small
undulator period length and the low electron energy issuitable for the lasing of short wavelength FEL, and thecombination of a large period length and the higher electronenergy is necessary for high power FELs.

We compared several achromatic lattices and adopted a 45
deg bending, modified DBA lattice as the lattice of acompact, low emittance SR for FEL. We estimated therelations between the electron beam energy, the period lengthof undulator, FEL wave length, and the small signal gain.
Our design needs further revising considering the available
space, estimated cost, and application plans.

FEL wave length and limit
1. 40~~ 0.80./'/c:/,//" / /"' 0. 60:>

~ 0. 40

mrad/

I

1. 00

11:~;,:;·:·.1I/

1. 20]

I--2nt:lllll·mrad-Q-).u=4CIII//~~AP12oml/-<)-J.U

1/= 16 Clllj

I-J.u=20ani~·""''"'l!-A.u=28cm;

1~'""""'1

L _______./

0.20

o.oo t::~~~~~m
200 300 400 500 600 700 800 900 1000

Electron energy [MeV]Fig. 5 FEL wavelength (K=I'"2)
0. 1~~-,~;,·=-4cmi7li~~.l.u=12cmj.-. 0. 08....!...
cj ~ ).u = 28"'cbDIIem I~~).u=36cml

1--Max. average j I
l__e~--- II/"'
J5 0. 02

Ij1·o·TOK·;;; 0. 04

I1--Au = 20 em 1

i~ 0.06

IJ

64

E:;;.
"'c.

3

"'bD"'.....

5 ....

2//0"'>"'x"'::!E/

00200 300 400 500 600 700 800 900 1000

Electron energy [MeV]Fig. 6 FEL small signal gain (K=I'"2, Ft=0.5)

References[1) T.Tomimasu, et. al., in this proceedings.
[2] J.B.Murphy and C.Pellegrini, Laser handbook
Vol.6 (1990) p.23
[3) D.Einfeld and M.Plesko, NIM, A335 {1993) 402[4) H.Wiedemann, J. de Physique {1983) C1-201[5) G.Dattoli, A.Renieri and A. Torre, Lectures on the Free
Electron Laser Theory and Related Topics(World Scientific, 1993) p.606[6] D.A.G.Deacon and J.M.Ortega, Laser Handbook
Vol.6 (1990) p.363[7] C.A.Brau, Free-Electron Lasers(Academic Press, 1990)
p.93[8) T.Tomimasu, Free Electron Laser and Its Applications(in Japanese, 1990) p.38
[9) D.A.G.Deacon and J.M.Ortega, Laser Handbook
Vol.6 (1990) p.359-394-I

I~Au=San i'