The lith Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

Longitudinal Beam Dynamics in Operation with Negative Momentum Compaction Factor
on the UVSOR Electron Storage Ring
Masahito HOSAKA, Jun-Ichiro YAMAZAKI, Toshio KINOSHITA and Hiroyuki HAMAUVSOR Facility, Institute for Molecular Science, 38 Nishigo-Naka, Myodaiji, Okazaki 444, Japan
Abstract
To investigate variations of the bunch length andthe energy spread of the electron beam on a storage
ring, we have measured longitudinal electron
distributions and spectra of spontaneous radiationfrom an optical klystron on the UVSOR storage ring
operated with both signs of negative and positive
momentum compaction factors.
Significant
differences in the bunch lengthening and the increaseof the energy spread with the beam current have beenfound between two operations.

=+ 0.0355

(a) a

..

, ,',

.. ''-~.

.. =- ...' ''(b) a,,

1 Introduction,,,0.0369'II\~

EnergyCircumference
Bending radius
Betatron tune
Momentum compaction a.
Harmonics
Main cavity RF frequency
Main cavity RF voltage
Energy spread
Natural emittanceOE=0.23MeV£o = 230 1t nm rad90 1t nm rad (positive a.}I...

,'-5 L.....~....L..........._,._j_~_,_j_~_,_jL....,_~...J......>.~._j_~

0

2

4

68

10

12Path Length (m)Fig.l Calculated Twiss parameters for one unit cellat positive a (a) and negative a (b) operations.

far as recent reports on relatively new machines, there
have been no dear evidence observed for the onset of
microwave instability [2]. On the UVSOR ring, wehave also observed no significant single bunch
instability up to the maximum beam current can bestored at present. Based on a low Q resonator
impedance model, Fang et. al. recently pointed out apossibility of which the threshold current for
microwave instability would be high and the bunch
lengthening would be not significant when a storage
ring is operated with a negative momentum
compaction factor [3].
2 Development of Lattice for Both Positive and
Negative Momentum Compaction Factors

E=600MeV
C=53.2mp=2.2mVx = 3.16 (horizontal)
Vv = 1.44 (vertical)
a.= I 0.0331
h=16fRF = 90.107 MHz
VRp=SOkV, --. I..

\ , ,.."'

Table 1
Basic Parameters of the UVSOR Storage Ring for
Negative a. Experiment.

,''•,',

In general, the single bunch dynamic behavior
such as lengthening of the bunched beam circulating
in a storage ring is governed by the electromagnetic
interaction between the impedance of the vacuum
chamber. On the way of development of third
generation synchrotron· radiation sources, they havemade effort to reduce the ring impedance employing
very smooth connections of vacuum pipes along with
development of a lattice for the very low beamemittance.
A longitudinal single bunch instability includingincrease of the energy spread of the beam due to highfrequency impedance of many parts of the vacuum
chamber, i.e., cavity, sudden change of pipes, groove,
low Q cavity-like structure, etc., is well known as
microwave instability [1]. On old machines, which weredesigned without deep consideration for theimpedance, both longitudinal and transverse single
bunch instability were often observed. However as,'' ... ,,,''\'\

Table 1 shows basic parameters of the UVSOR
storage ring for the negative a experiment. In thenominal operation for users of synchrotron radiation(SR), a bit of a positive dispersion remains in straightsections to minimize the effective emittance, and thenthe momentum compaction factor a is estimated to be+ 0.035. For the experiment with negative a, wedeveloped a new operating point, where a can betuned smoothly from positive to negative withoutchange of the betatron tunes. This operating point has-98-

The 11th Symposium on Accelerator Science and Technology, Harima Scienee Garden City, 1997

been also optimized to use of the helical opticalklystron with small gaps [4].
Calculated Twiss parameters of the lattice atpositive and negative a. operations are shown in Fig.
la and lb, respectively. At the positive a. lattice, thedispersion function is positive in the bending magnet.
On the other hand, at the negative a. lattice, thedispersion function alters from negative to positive inthe bend and a large negative dispersion function
makes the integral of the dispersion in the arc
negative.

300

250

0

S:
s:::.

'61

c:
Cll......
c::::1

cobO

bO

•

100.

a= -0.033

50

A dual-sweep streak camera is a powerful tool toobserve the electron distribution in the bunch and its
variation in a certain time range [5]. Since a slowsweep axis can be expanded up to 100 ms from theone turn period, we can not. only observe thecorrective longitudinal oscillation with thesynchrotron frequency of about 15kHz (see Table 1)
but also detect instabilities of which the electron
distribution is slowly varied.
Current dependent bunch lengthening has beenmeasured up to - 100 rnA with the single-bunch mode
for the almost same absolute values of the positive
and the negative momentum compaction factors (la.l =0.033). RMS bunch lengths were deduced fromspectra averaged over many turns in the twodimensional dual-sweep images of SR from a bending
magnet. Figure 2 shows variations of the bunch
length at a wide range of the single bunch current.
For the case of the positive a, the bunch lengthens
monotonously, which is in agreement with ourpervious measurements [6]. Based on potential-well
distortion theory with a broad band impedance model[7], the bunch length cr b at the average beam current I
is expressed asbO150s:::.
(,)

3 Measurement of Bunch Lengthening_(!!J,_) =ea. I [Zin]eff (..1L)3(!!J,_)30"0".f'1:it v,2 E 0"

200

(1)
I

where cr bO is the zero current (natural) bunch lengthand [Zin]eff is the effective longitudinal coupling.. impedance. By fitting the data for the positive a. witheq. (1), we obtained the effective impedance of 1.6 n,
where we assumed no frequency dependence for[Zin]eff· As shown in Fig. 2, the fitting quality is not sobad that there seems to be no significant frequency
dependence for [Zin]eff at the narrow region of which
the bunch length observed.
Since the bunch lengthening due to potentialwell distortion does not accompany increase of theenergy spread, the Keil-Schnell criterion for thethreshold condition of longitudinal microwave

01020

30

40

50

60

7080

Beam Current (mA)

Fig. 2 Measured bunch lengths plotted as a function of
the beam current.

instability is able to be modified by replacing the peakcurrent of the lengthened bunch [8].
The peak current for the Gaussian particle
distribution is written as I C I {.f'1:it crb), the KeilSchnell stability criterion is rewritten as(2)where cr EIE is the relative energy spread of the beam,respectively. A form factor of the particle distribution
in the momentum space F is approximately the unity
for bell-shape distributions.
Using the ringparameters shown in Table 1 and the deduced valueof 1.6 n for [Zin]eff' a threshold bunch length formicrowave instability estimated from eq. (2) isapproximately 47 ps/mA. The beam with the bunch
length below this line would be longitudinallyunstable. However this threshold condition isobviously over estimated, because we have notobserved clear evidence of instability even at thehigher beam current of 100 rnA with the positive a.
Since the Keil-Schnell stability criterion is for the worst
case and the threshold condition should be varied by
a combination of actual resistive and reactiveimpedances.
The bunch lengthening with the negative a. wasdrastically changed. As one can see, the bunch
shortening was observed up to - 15 rnA, and then thebunch lengthened with the current. We confirmed thepoint of discontinuity around 15 rnA as an onset of
longitudinal microwave instability by the 2dimensional streak camera image.
The bunch shortening can be simply explained
assuming the wake field generated by an inductive (L)-99-The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

impedance as Vwa~ce=-L(dlldt).
Since thesynchronous phase of the beam with the negative a. ist~e opposite side of the slope of the accelerating RF
fteld, a combined field with the RF field and the wakefield becomes steep if the other is gently-sloping.
4 Measurement of Energy Spread
Radiation spectrum from the optical klystron isvery sensitive to the beam energy spread. A~adulation factor, which indicates degree ofmterference between two radiations from undulators
separated by a dispersive section, defined as!mod= (S+- S_) I (S+ + S_), where S+ and S_ are themaximum and the minimum intensities of a jagged~tructure spectrum, respectively.
Completemterference m both spatial and frequency demains
makes !mod =1. An actual modulation factor may beseparated into two terms as !mod =h fy where h and /yare the modulation factors originated from theemittance and the energy spread, respectively. The
analytical formula of /y is written as

where N u and N d are the period number of one
undulator and the interference order of the radiation.
We chose a resonant wavelength of 355. nm tomeasure the modulation factor, and Nd at thewavelength was 130. Results of the measurement of
the energy spread are plotted as a function of thebeam current in Fig. 3. One can apparently notice thethreshold beam current around 15 rnA exists for the(X=- 0.033~0.3~~/lio_.--'-g____ ..£- ___ _-£-""-...i;i----'2--- ~0.2(X=+ 0.0'35e;Q)

c:w

0.1

0 ~~~~~~~~~~~~~~
01020

30405060

7080

Beam Current (mA)

Fig. 3 Deduced energy spread from the modulation factor
oHhe spontaneouse spectra. Lines are drawn by eyes.

increase of the energy spread in the negative a.
operation, which corresponds with the result of thebunch length measurement. Meanwhile there seems
to be no clear indication of the onset of microwave
instability in the positive a operation. Although there
is a small discontinuity seen around the beam currentof 50 rnA, the increase rate of the energy spread at thehigher beam current is slow. We have not identified
whether microwave instability occurred in thepositive a. operation.
5 SummaryThe normalized effective longitudinal impedanceof 1.6 n was deduced from the bunch lengthening
with the positive a.. The reason why the instability
was occurred only in the negative a. operation is thatthe potential-well distortion due to the impedanceacts to shorten the bunch length for the negative a.
and the peak current reaches the threshold ofinstability at the lower beam currentthan the positivea.. The averaged bunch length with the negative a. isshorter than that with the positive a. at the wide rangeof the beam current. Nevertheless the negative a.
operation has no advantage because of the lower
threshold current of microwave instability. As far as
the UVSOR ring, the suggestion of Fang et. al. is notrealized. Probably the impedance model of a low Q
resonator is not suitable for the UVSOR ring. As
mentioned previously, the interaction between theelectron bunch and the impedance of the chamber
depends upon properties of the impedance, such as
the combination of inductive and resistivecomponents and the frequency dependence.
References[1] for example; A. W. Chao, AlP Proc. No. 105(American Institute of Physics, New York, 1983) 353.
[2] A. H. Lumpkin et. al., Proc. 18th Int. Free
Electron Lasers Conf., Rome, Italy, 1996.
[3] S. X. Fang et. al., KEK Preprint 94-190 (NationalLaboratory for High Energy Physics, Tsukuba 1995).
[4] H. Hama et. al., Proc. 3rd Aisan Symp. on Free
Electron Laser (IONICS Publishing Co. Ltd., Tokyo1997) 17.
[5] H. Hama et. al., Nucl. Instr. and Meth. A375
(1996) 32.
[6] H. Hama et. al., Proc. 9th Symp. on Accelerator
Science and Technology, Japan (1993) 468.
[7] B. Zotter, Proc. CERN Accelerator School, Paris
1984, CERN report 85-19 (CERN, Geneva, 1985) 415; JL. Laclare, CERN Report 87-03 (CERN, Geneva, 1987)
264.
[8] E. Keil and W. Schnell, CERN report ISR-THRF I 69-48 (CERN, Geneva, 1969).

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