JAERI-Conf

95-021

PB35
Bunch Deformation of a Multi-Bunched Beamin TRISTAN Accumulation Ring
T. Obina*, Y. Funakoshi, M. Tobiyama K. Satoh and T. Kasuga*The Graduate University for Advanced Studies,
Oho 1-1, Tsukuba-shi, Ibaraki 305Japan
KEK:N ational Laboratory for High Energy Physics,
Oho 1-1, Tsukuba-shi, Ibaraki 305 Japan
Abstract
A remarkable bunch deformation has been observedin the TRISTAN Accumulation Ring (AR) during multibunch operations. When two bunches that have different
populations are stored in the ring, the bunch length ofthe smaller current bunch is larger than that of the larger
one. In some cases, longitudinal distributions of electrons
exhibit two peaks. These phenomenon can be explainedby an effect of wakefields due to higher order modes ofaccelerating cavities. We tried to determine the frequencyof the mode and the strength of the wakefield that is responsible for the phenomenon with a test bunch method.

I. Introduction
When an electron storage ring is operated in a single bunch mode, the current dependence of the bunch
length is explained by the potential well distortion andthe microwave instabilities. These theories were successfully applied to the bunch lengthening in the AR [1]. On
the other hand, a remarkable bunch deformation was observed when several bunches were stored in the AR [2].
In some cases the longitudinal distributions of electrons
exhibit two peaks or tabletop-like shape in four bunch oreight bunch mode operations. These phenomena were explained qualitatively with the potential well distortion due
to the long range wakefield, however, its source has not yet
been determined.
In this paper, the bunch deformation when two bunches
are stored in the ring is discussed. Because the deformation of each bunch was stable over the synchrotron oscillation period, it is quite natural to think that the deformation is caused by the potential well distortion due tohigh-Q components in the ring. In the AR, the higher
order modes (ROMs) of the accelerating cavities are oneof the candidates. We tried to determine the frequency of
the ROMs and the strength of the fields which induce thebunch deformations.
The machine parameters and the experimental conditions are listed in Table I.

II. Observation of Bunch Shape
There are two RF sections in the AR. Each section contains four APS (Alternating Periodic Structure) type cavities, each of which has 11 accelerating cells. It is reported
that the maximum beam current is limited by the coupled
bunch instabilities which arise from higher order modes(ROMs) of the cavities [3], we therefore drove only one
RF section to avoid the instabilities.
The longitudinal distributions of electrons were observed by focusing the visible light on a streak camera.
Synchrotron radiation (SR) from a bending section is led
to an optical stage located on a ground level and splitted

Table I
Main Parameters of the AR
Beam energy
Momentum compaction factor
Harmonic numberRF voltage
RF frequency
Energy loss
Nat ural bunch length
number of total cavity
number of operating cavity

EQ

hVo
fRF
Uouo

2.5 GeV0.01289640
1.0 ( ~ 2.0) MV
508.5808 MHz
0.1458 MeV /turn
1.4943 em
84

into two lines. One line of them is used for the streak
camera or a high speed photodiode, and the other is for aphoton counting system. In the multi-bunch operation, astreak camera detects the bunch shape while the photon
counting system measures the population of each bunch.
In the photon counting method, the flux of SR is attenuated down to a level at which the output of the photon
detector corresponds to one photon detection. The timedifferences between the arrival time of a photon at thedetector and the timing signal synchronized to the bunch
revolution are digitized and collected numerically.
Figure 1 shows an example of longitudinal beam profile of two bunches observed by the streak camera (Ramamatsu C1587 with M1955 synchroscan unit). The vertical-<E--- BunchFigure. 1. Longitudinal line density of two bunches. Thebunch current of number 1 and number 2 is 10 rnA and15 rnA, respectively.
axis represents the longitudinal distribution and the horizontal axis shows the vertical distributions of the bunches
in successive revolutions.

III. Determination of the Higher Order Mode
A. Principle of Test Bunch Measurement
We found that longitudinal bunch shapes of the multibunched beam resembled a bunch shape with a double-347-JAERI-Conf 95-021

RF system proposed for the suppression of the longitudinal coupled bunch instabilities [4]. We consider a simple
model in which the bunch shape is determined by the accelerating rf and a higher order mode of a cavity. Thevoltage seen by the beam is expressed asV(¢) = Vo {sin(¢+ ..Ps) + ksin(n¢ + n..Pn)},(1)

where ..Ps is the synchronous phase, ..Pn the phase of theHOM field, kVo the peak voltage of the HOM, n¢ thephase of the HOM which has the frequency nfRF· For
any RF waveform, the electron line density is given by [5].( )~ ¢<X expandY 2 (¢,</>s) ={ -eVoY 2 (</>,..Ps) }2Jrhaj3 2 E(a; )2 '(2)~ 1<1> {V(¢)- Vr} d¢0

B. Experimental Setup(3)0where (";) is the rms momentum spre~d of the bunchand eVr is the energy loss per turn mamly due to thesynchrotron radiation.
In order to determine the frequency and the strength of
the wakefield, we thought up a test bunch measurement
method. We inject a large current bunch which generates awakefield and also inject a sufficiently small current bunch
whose wakefield is negligible. The shape of the small current bunch is deformed due to the wakefield, we therefore
can estimate the frequency of the mode by selecting thedistance between the two bunches. In the following partof this paper, we call the large current bunch the mainbunch, and the small current bunch the test bunch.
If we assign TM020 mode as a HOM field which affectthe bunch shape, !HoM = 1210 MHz and n = 2.381 is
obtained. We assume ..Pn = 0 to maximize the effect of theHOM and assume k = 0.1 as an example. Figure 2 shows
calculated bunch shapes of the test bunch in successive 10
rf buckets after the main bunch. The bucket number 0=z::s: ] 6f :=z:s;:]f :::z:s: j
2~:z::s:J~-0.1!1-(]_,0.2

Q

C.2

-0.11

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73

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-0.0.

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-0.2

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00.2:z:s: ]
-0.15

-0.2

05~:z:s:J-I:UI-O . .a0..2

00.2

Figure. 2. Simulation of the bunch shapes of the test
bunches with the bucket number 1 to 10. The bunchshapes are normalized with i( ¢ )d¢ = 1 . The abscissashows longitudinal position in units of radians.

Jmeans the position of main bunch and the bucket number
1 means the bucket is just after the main bunch, and soon.

There are two method to estimate the HOM frequency.
One of them is to measure the peak position of the bunch,and the other is to measure the bunch length. In bothmethods, the Fourier transform of the obtained data gives
us an information of the frequency of the mode. According to the sampling theorem, the highest frequency we candetermine is half of the rf frequency, and the higher frequency than that causes an aliasing. Therefore, we haveto determine the real frequency by any means.
We chose to measure the peak position of each bunch
because the simulation suggests that the effect of the HOM
appears more sensitively in the peak position than in thebunch length .

In the test bunch measurement, a large dynamic range
is required and the streak camera is not appropriate forthis purpose. We used a high speed PIN photodiode (AR82, Antronics Research) which has a rise time of 35 ps andthe photosensitive area of 0.01 mm 2 . The output of thephotodiode was fed to a digitizing sampling oscilloscope(Hewlett Packard HP54121 T). The trigger signal synchronized to the bunch revolution was generated by a circuit
which divides the RF signal by the harmonic number ofthe ring. The time jitters of the divider were measured
to be about 3 ps in standard deviation with a histogram
function of the oscilloscope. We also used a photon counting system to measure the bunch shape, however, it has andisadvantage that it needs long time about three minutes
in the measurement.
We injected the main bunch first, and injected the test
bunch into a selected bucket. The beam current of eachbunch is 20 rnA and 1 rnA, respectively. To avoid thecoupled bunch instabilities, both bunches were dumped bya stopper whenever before the measurement of the next
bucket. Because it is very time-consuming to measure allbuckets in AR, we only measured the successive 20 buckets
in 8 places in the ring.

IV. Results and Discussion
Figure 3 shows the peak position of the test bunches.
The abscissa shows the bucket number from 1 to 640 andthe ordinate represents the peak position in units of picoseconds. The peak positions vary depending on thebucket number due to the transient beam loadingeffectof the main bunch. The calculated difference in the synchronous phases between just after and before the mainbunch was 128 ps which is consistent with the measurement.
We subtract the offset due to the beam loading and calculated the Fourier transform of the variations of the peakposition. Peak positions of the unmeasured buckets wereassumed to be zero. The result is shown in Fig. 4. There
are sharp peaks in every 6.36 MHz. These peaks arise
from the fact that we could not measure the all buckets
but only eight places were measured.
Two large peaks are recognized at 189.1 MHz and241.6 MHz. From a measurement of cavity higher ordermodes, several modes can be listed up as candidates. In
the single bunch operation, we measured the beam spectrum of a cavity with a pickup located on its end plate.
The resonant frequency of the TM020 mode is ranged fromabout 1206.3 MHz to 1211.9 MHz because the APS cavity has 11 cells in it. These frequency will be observed

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Time [ps]Figure. 3. Peak position ofthe test bunchs. The measured
bucket number is 0±20, 80±10, 160±10, · · · , 480±10 and560±10.

Figure. 5. Longitudinal line density of two bunches measured by the streak camera. The beam current of thelarge peak is 15 rnA and the small peak is 10 rnA, and themeasured bunch length was 250 ps and 375 ps in FWHM,respectively. The total RF voltage was 2.3 MV.

0.6

by calculations and compared with the measurements.
The impedance of the APS cavity was calculated with thecomputer code URMEL [7]. The higher order mode which
has the highest shunt impedance is the TM012 mode that
could produce a wake voltage of 34 kV at h = 25.7 rnA.
It corresponds to k = 0.015 and is ten times smaller thanthe measurement. If we consider the TM020 and TM022
modes, the difference of the calculations and the measurements are in the same order. However, the impedance iscalculated for only one cavity in the AR. If we take eightcavities into account, the difference will become small.

0.2

50100150

200250Frequency [MHz]Figure. 4. Fourier transform of the peak position.

from 189.1 MHz to 194.7 MHz which is consistent with
the Fourier transform of the test bunch measurement. In
the same way, TM022 mode which has the resonant frequency from 1788.8 MHz to 1798.3 MHz will appear as236.0 MHz to 245.6 MHz. We have not measured thecharacteristics of the other seven cavities in detail, however, the two modes are thought to be the main source ofthe bunch deformation.
In the rest part of the paper, we will discuss the bunch
deformation in the two bunch operation.
At first, we measured the bunch length under the single
bunch condition. The bunch was lengthened in accompany
with the increase of bunch current, which is well matchedwith the scaling low above threshold [6]. Next, we stored
two bunches in the ring. When the bunch currents of thetwo bunches were equal, the bunch lengths were equal toeach other and the length was slightly longer than thatof the single bunch if we compare with the same bunch
current. However, if the bunch currents are not equal, thebunch length of the smaller one becomes much longer thanthat under a single bunch condition, and the bunch lengthof the larger one becomes shorter as shown in Fig. 5. We
fit the bunch shape using the eq. 2 with the least-squares
method. The solid line in the figure shows the fitted result. We assumed that the field of two higher order modes,
TM020 and TM022, affect the bunch shape. To estimate
the strength of the long-range wakefield only, we used thebunch length of the single bunch condition instead of thenatural bunch length in the equation. Rough estimationof the k value from the bunch shape was k = 0.1 rv 0.25.
If we assume k = 0.1 in both modes, the maximum peakvariation of the test bunch was calculated to be about
100 ps. This value is well matched to the measured peakvariation in Fig. 3.
At last, we estimated the induced voltage of the HOMs

V. Summary
The bunch deformation in the AR during the multibunched beam operation was measured and explainedwith the higher order modes of the cavities qualitatively.
We thought up the test bunch measurement method andconcluded that the two modes, TM020 and TM022, arecandidates for the source of the deformation. The fieldstrength estimated from the test bunch method is consistent with the strength which produces the deformation of
the two bunches, however, the calculated impedance of acavity is ten times smaller to explain it. Further analysis
and measurements are now in progress.

Acknowledgments
The authors wish to thank Dr. K. Akai and Dr. Y. Morozumi who have been kindly supporting the experimentand the calculations of the cavity HOMs.

References
[1]
[2]
[3]
[4]
[5]
[6]
[7]

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