The 9th Symposium on Accelerator Science and Technology, Tsukuba, Japan 1993

Operation with the Low Momentum Compaction Factor on an Electron Storage Ring
H. Hama, J. Yamazaki, E. Nakamura and G. lsoyama
UVSOR Facility, Institute for Molecular Science
Myodaiji, Okazaki 444, Japan
Abstract

where a is calculated by a formula

We have studied quasi-isochronous operation with thelow momentum compaction factor to reduce the bunch lengthof the electron beam on the UVSOR storage ring. Themomentum compaction factor a was reduced by changing thedispersion function in the bending magnets. Though effect ofthe second order a becomes dominant in the very low aregion, we could compensate it by reducing strength of thefocusing sextupole magnets. The momentum compaction
factor was reduced to less than one hundredth with respect tothe ordinary value. Using a streak camera, we measured thevery short bunch, and confirmed the storage ring wasoperated nearly isochronously. The beam current dependenceof the bunch length was also measured. The bunch
lengthening was interpreted by potential-well distortion
theory with a constant value of the effective longitudinal
coupling impedance over the wide range of a.
Introduction
A concept of the isochronous (a= 0) electron storage
ring was introduced to measure the speed of light with highaccuracy by Robinson in 19661). Deacon proposed to use theisochronous ring as a driver for a free electron laser (FEL)2>
with high output power. Recently Pellegrini and Robinpresented theoretical study of the single particle andcollective dynamics of a quasi-isochronous ring to reduce thebunch length and increase the peak current mainly forcolliders3>.
Since the beam bunch is very short when the storage ringis operated nearly isochronously, various applications can beforeseen in experimental study with synchrotron radiation.
For example, the study region of time resolved experimentwill be extended, and the gain of the FEL will be enhanced
because of the high peak current of the short bunch.
Coherent enhancement of synchrotron ra<iiation 4 > in thewavelength region of far infrared is possibly detected, if thebunch length shorter than a few mm is realized.
The fractional elongation of path length .1/ I l for an offmomentum particle is written astll = a t1 PIpa=~ J %d s ,and C, 7J and p denote the circumference of the ring, thedispersion function and the bending radius, respectively. The
longitudinal natural bunch length a 0 is proportional to thefractional energy spread <Ye I E 0 and to the square root of themomentum compaction a, and inversely proportional to thesquare root of the slope of the RF field VRF;

cro =Aa Eo/(3)<Ye •·y freve VRF EoSince the synchrotron frequency f. is also proportional to thesquare roo.t of a asIs= _1_/r-a-J,-re-ve-V-.RF-,(4)21t
Eoit is a good index for a as far as the RF voltage is kept
constantA·yExperimental
The UVSOR storage ring 5> consists of four units cells of
the Chasman-Green lattice, and is operated at an energy of
600 MeV for the beam injection. The beam is accelerated up
to 750 MeV for user experiment after the injection. The
momentum compaction factor is 0.035 at the regular
operating point for 600 MeV and the natural bunch length isapproximately 8 em. The dispersion function 7J of this typeof lattice can be varied while betatron wave numbers aremaintained at constant values.
Figure 1 shows beam optics calculated with the computercode LA TTICE6> for an extreme case close to a = 0. The
dispersion function changes its sign in the bending magnet.
The integral in eq. (2) cancels out, so that a becomes zero.
The experiment was performed at the energy of 600
MeV, and the single bunch mode was employed. The
1512(1),(2):[~Table 1. Basic parameters of the UVSOR ring at the regular
operating point for the beam energy of 600 MeV.

"cOSn..

~'' ·'

96,- ......
'a- 0.0
•\

/'.!

~yI

..' ' '!\.

/'/

.

·~

:,,.
'I/

cd: 3Circumference
Bending radius
RF frequency
Harmonic number

Peak RF voltage
Momentum compaction factor
Synchrotron frequency
Natural bunch length
Betatron tune

53.2m
2.2m
90.115 MHz
1646kV
0.035414.8 kHz258 ps
3.16
2.62

6.65
Path length (m)13.3

Fig. 1. Calculated betatron and dispersion functions in aunit cell for the extreme point of a - 0. The horizontal andthe vertical betatron wave numbers are maintained at 3.16 and2.62, respectively.

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preliminary results and the experimental details are reported
in ref. 7. Results of further investigation are described in thefollowings.
Compensation of a 2
We gradually reduced the momentum compaction a fromthe injection point using an accelerator control software8>.
The same procedure for the beam acceleration was employed
to synchronously change excitation currents of the Q-magnets
but the bending field was maintained. In the region of abelow 0.01, the effect of the second order term a 2 becamedominant for the off-momentum particle.
Taking into account a chromatic effect of the Q-magnet
for the dispersion function as1] =1]1 +1]2 L1 pp(5)'the momentum compaction factor should be redefined as)2

L1 + a2 (L1_p_ .
4.1 = a1 _p_(6)ppI
As reported previously7 >, the strength of the focusing
sextupole magnets for the chromaticity correction results inover correction for a 2 • Experimental values of a 2 were

0.2

rjNe

SF at o 1 • 0.0075

oSO at u, • 0.0075•SF at u I • 0.00097

derived from the RF frequency dependence of the measured
synchrotron frequency fitted with an analytical formula7>off.
including a 2 term. The magnitude of a 2 has linear.
dependence of the strength of sextupoles as shown in Fig. 2.
Since the value of 1] at the focusing sextupoles (SF-magnet) ismuch larger than that at the defocusing ones (SD-magnet), theSF-magnet is more effective to compensate a 2•
We systematically searched for suitable strengths of theSF-magnet for a 2 compensation at various operating points.
When the natural chromaticities are corrected with thesextupoles, the magnitude of a 2 increases gradually as a 1 islowered. However it can be seen in Fig. 3 that ~ is able to becompensated by slightly reducing the SF strength.
Bunch length measurement
The lowest a so far achieved with compensation of a2
was 0.0002, which is more than 150 times smaller than that of
the regular operating point. The bunch length was measured
using a streak camera at a low beam current less than 0.1 rnA.
The synchrotron frequency was also measured simultaneously
to make sure of the reduction of a. Streak time and aresponse function of a focused image were calibrated using asemiconductor laser. Figure 4 shows typical temporalprofiles of the bunch. When the bunch is very short, thebunch length was derived by taking into account the response
function of the detector because the focused image on thescreen of the streak camera has a finite width. The solid lines
indicate de-convoluted shapes of the time profile, while thedotted lines are raw spectra of the measured bunch profile.
Using eqs. (3) and (4), the bunch length can be expressed

0.0
Injection point.0.2~;:;.0.4 '--'--'~~.__._.__.__._....._._~._._.__._,_.._,_._._.~_._,_,

1.2

0.8

0.6

Realtive Sextupole strength~

300

1.00

••

..

0.95 Jl

•

!2.
ct.

•.!' -0.10

00

<'"

0.90 ~

0i

0-o.o50.00::JSF-strength to make a 2 = 00.85~

0.80
0.01

0.001

oOo
Channel Number

100 200 300 400
Channel NumbersooFig. 4. Time profiles of the bunch measured by the streak
camera at the injection point (left) and at the lowest a (right) .

a 2 at SF-strength = 1.0.15

900..!.
600~cFig. 2. Magnitude of a2 as a function of the relative
strength of sextupoles for operation points of different a 1.
Strengths of sextupoles are normalized to that for thechromaticity correction.
.0.20

a=D.0002
2o-.=15 ps

a1Fig. 3. Relative strength of SF-magnets to make ~ = 0 forvarious operating points. Measured values of a 2 at the SFstrength for the chromaticity correction are also plotted.

with the synchrotron frequency as(7)Ob = flit Eo eYe _h._ .
e VRF Eo/rev
The bunch length is plotted as a function of the synchrotron
frequency in Fig. 5. The bunch length is clearly proportional
to the synchrotron frequency. The time resolution of thestreak camera is estimated to be 15 ps, which is mainly due tostreak trigger jitters. The shortest bunch length was 20 ps (6mm) and a corresponding synchrotron frequency was 1.2 kHz
which is approximately l/12 of the normal value. Therefore
the momentum compaction factor was lowered to be 0.0002.
Though we could successfully reduce a to the very low value,
we lost the beam current from- 0.1 rnA down to a few JlA-469-

during the operation to further reduce a from a- 0.001. The
reason is not clear at the moment whether the control of thequadrupoles and the sextupoles was inappropriate or some

250

Injection point a= 0.034

200

results of the fit by eq. (8) with one free parameter of [Z/n]eff.
The bunch length measured at a very low beam current wasused as the natural bunch length o-0 • One can see that thebunch length converges upon the single line at higher beam
currents, which means the effective impedance is almostconstant. The derived value of [Z/n]eff was approximately
2.5 .a . The bunch lengthening is reasonably interpreted bypotential-well distortion theory over the wide range of a. A
similar result was obtained on the VUV-ring atNSLS 12l.

~~150Conclusion

N10050210 12 14468
Synchrotron Frequency (kHz)

16Fig. 5. Measured bunch length plotted as a function of /smeasured simultaneously. The solid line is a result of the fit
including the detector resolution.
instability occurred.
Bunch lengthening
In a previous experiment, we observed the bunch
lengthening due to the potential-well distortion which does
not accompany with the increase of the energy spread9l. Thisis also supported by the result of the current dependence ofthe measured FEL gainlDl.
Based on potential-well distortion theory 11 >, the bunch
lengthening can be expressed as

I = ( 2 1t)- i e V RF
1
( 0' 3 _ 0' Ob 2) ,( 8)frevR 3 [z I n]etr
where <1 is the bunch length at the beam current /, R is themean radius of the ring, and [Z/n]eff is the effective
longitudinal coupling impedance. The bunch length wasmeasured at various operating points at beam currents ranging
from a few tens of rnA to less than 0.1 rnA. Figure 6 shows
the bunch length measured for three different values of a and1000 ,.......,-~....-..............-........................~....

•••

0:=0.034
0:=0.008
0:=0.003~
t>£g>100~..c:uc:~

Beam Current (mA)

Fig. 6. Current dependence of the bunch length at threedifferent values of a. The lines indicate the results of the fit
with eq. (8).

We have successfully shortened the bunch length down
to 20 ps by reducing the momentum compaction factor. The
effect of a 2 was compensated to a certain extent by reducing
the strength of the focusing sextupole magnets. The
estimated lowest momentum compaction factor wasapproximately 0.0002, which is 150 times smaller than thevalue of the regular operating point. The measured
synchrotron frequency was consistent with the bunch length,
and confirmed that the storage ring was operated nearlyisochronously.
The bunch lengthening was also measured at various
values of the momentum compaction factor. Based on
potential-well distortion theory, the effective longitudinal
coupling impedance was derived to be approximately 2.5 .Q,
which was almost independent of the bunch length and of themomentum compaction factor, over wide range of the beam
current.
Acknowledgements
We are grateful to the staff of the UVSOR facility for
their technical supports. One of the authors (H.H) wish tothank Dr. D. Robin for many variable discussions.

References
1) K.W. Robinson, Cambridge Electron Accelerator rep.
CEAL-1032 (1966).
2) D.A.G. Deacon, Phys. Rep. 76 (1981) 349.
3) .C. Pellegrini and D. Robin, Nucl. Instr. and Meth.
A301(1991) 27.
4) T. Nakazato et al., Phys. Rev. Lett 63 (1989) 1245.
5) G. lsoyama, Nucl. Instr. and Meth. A308 (1991) 31.
6) J. Staples, LATTICE, LBL rep. no. 23939 (Lawrence
Berkeley Laboratory, Berkeley, 1987).
7) H. Hama, S. Takano and G. Isoyama, Nucl. Instr. andMeth. A329 (1993) 29.
8) N. Kanaya, H. Hama, J. Yamazaki, 0. Matsudo and G.
Isoyama, IEEE Trans. Nucl. Sci. (in press).
9) A. Lin, H. Hama, S. Takano and G. lsoyama, Jpn. J.
Appl. Phys. 31 (1992) 921.
10) S. Takano, H. Hama and G. lsoyama, Jpn. J. Appl. Phys.
32 (1993) 1285.
11) B. Zotter, Proc. CERN Accelerator School, General
Accelerator Physics. Paris, 1984 (CERN, Geneva, 1985)
CERN 85-19, p. 415.
12) S. Krinksy et al., Storage Ring Development at theNational Synchrotron Light Source, BNL rep. no. 46615(Brookhaven National Laboratory, Upton, 1991).

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