JAERI-Conf 95-021

PB33

Beam Test of the RF Feedback for KEKB in TRISTAN MR
S. Yoshimoto, E. Ezura, K. Akai, K. Ebihara and M. Suetake
KEK, National Laboratory for High Energy Physics
1-1, Oho, Tsukuba-shi, Ibaraki-ken, 305, Japan
Abstract
The RF feedback system for the KEK B-Factory(KEKB) has been tested using the beam of the TRISTAN Main Ring (MR). The coupled-bunch instabilityof the -1 mode was excited by intentionally detuning
the RF cavities; it was then successfully damped byreducing their impedance.s with the RF feedback.

I. Introduction
A luminosity goal of KEKB is 1 x 1034 cm- 2 s- 1 ,which requires the beam currents of 2.6 A for the 3.5
GeV positron ring and 1.1 A for the 8.0 GeV electronring. Under usual operation, the cavity is detuned
to present a matched load to the power source. ForKEKB, the detuning is very large due to the highbeam currents. The detuning gives the difference in.the real part of the cavity impedance at the upper andlower sideband for each mode, and causes the longitudinal coupled-bunch instability. One technique toavoid the instability is to use an RF feedback aroundthe cavity, which can reduce the cavity impedanceat the synchrotron sidebands [1]. We are developing
an RF feedback system using a parallel comb-filter,
which enables us to adjust the feedback phase at thesideband frequencies even if a frequency-dependentgroup delay is present around the feedback loop.
The parallel comb-filter feedback was tested
through a choke-mode cavity, and proved to be effective in reducing the cavity impedance [2]. Then, the ·feedback was tested using the beam of the TRISTAN
MR. The purpose of the beam test was to confirm
that a coupled-bunch instability caused by the cavity
impedance could really be eliminated by reducing itby means of RF feedback.

II. Excitation of Instability
Under usual MR operation, an amount of cavity
detuning is so small compared to the revolution frequency that the instability associated with the accelerating mode does not appear. One RF station wastherefore shut off from operation, and its idling cavities were substantially detuned to make the beam
unstable. An RF station has two accelerating units,each comprising a pair of nine APS (alternating periodic structure) cells. A total of thirty six cells weredetuned by -88 kHz (= /rev - Is) in order to set theresonant frequency of the cavities to the upper synchrotron sideband of the -1 mode. Fig. 1 shows themagnitude and real part of the cavity impedance for
detuned thirty six cells, with or without RF feedback.
The growth time of the -1 mode dipole oscillation
was calculated from the expression for equally spaced
rigid bunches [3], using the machine parameters given
in Table 1. The growth time due to the detuned cavities was 7. 7 ms and that due to the operating cavities
was 43.0 ms, giving the total growth time of 6.5 ms.
The radiation damping time was 20 ms. An estimatedgrowth time of any other mode was much slower than
20 ms.

-I

Frequency (f- frf)/frev

Fig. 1. Magnitude and the real part of the cavity
impedance for detuned thirty six cells, with or without
RF feedback.

Table 1
Machine parameters during the beam test.
e beam energy
e- beam current
Number of bunch
Momentum compaction
RF frequency
Revolution frequencySynchrotron frequency
Energy loss/turnCavity voltage
Unloaded Q
Shunt impedance/m
Coupling factor
Detuning frequency
Growth time of -1 mode
Radiation damping time

8.0
6.0
4
1.493 X 10- 3
508.6
99.3
11.6
7.4
90.0
39000
22.5
1.3
-87.7
6.5
20

GeV
rnAMHzkHzkHz
MeVMV
MO/m
kHz
msms

III. Feedback System
Fig. 2 shows a block diagram of the RF feedback
system used in the experiment. Since only the -1-341-

JAERI-Conf 95-021

mode could be unstable, only one channel of the parallel comb-filter was used. The RF switch was used toopen and close the feedback loop. In order to detect
the growth and damping of the -1 mode oscillations aspectrum analyzer was used in zero-scan mode. Since
there was no external signal to the system, only whenthe -1 mode was excited on the cavity, the system
operated so as to cancel it.

of about 80 ms. The beam thus survived in spite ofbeing unstable, though the life time was shortened toseveral tens of minutes from a normal value of several
hundred minutes.

BeamA~1.58MHzFig. 2. Block diagram of the RF feedback systemused in the beam test.

IV. Experimental Results
The experiment was carried out at 8 GeV withfour equally spaced electron bunches, which make thebeam current of about 6 rnA. Although it could be
increased to over 10 rnA, the -1 mode oscillation was
most severe around 6 rnA. Fig. 3 shows the spectraof the beam-induced cavity voltages. The revolution
harmonics of the beam current are shown in Fig. 3 (a),where the highest peak results from the impedance ofthe cavities tuned at the RF frequency. Fig. 3 (b), (c)and (d) show the signals around frJ -!rev = 508.48
MHz. When the cavities were not detuned, only thesteady spectrum of the revolution harmonic was seenat 508.48 MHz (Fig. 3 (b)). When the cavities weredetuned by -88 kHz, the instabilities, especially of
the -1 mode, appeared as shown in Fig. 3 (c). The
spectrum disappeared after the feedback loop wasclosed (Fig. 3 (d)). With the feedback, however, thereappeared the bump between the revolution harmonic(/r J - !rev) and its upper sideband (/r J - /rev + Is),a cause of which is not clear yet. One may also note
that, when the loop was closed, the noise floor wasraised due to the noise amplification around the loop.
Fig. 4 shows the amplitude versus the time of the-1 mode oscillation, which was excited by detuning
the cavities without feedback. The increase of the amplitude was limited by some unknown damping mechanism, and turned to the decrease. Then, at a certain small amplitude, where a growth rate exceededa decreasing damping rate, the amplitude began toincrease again. This behavior repeated with a period

Fig. 3. Spectra of the beam-induced cavity voltages.

Fig. 4. Amplitude versus time of the -1 mode oscillation excited by the detuned cavities without RFfeedback.
The damping rate of the -1 mode, (L 1, and thedamping time r_ 1 ( = 1/ cL 1 ) are given by
a-1 = arad + a;mp + aps,

(1)

1/;_1 = 1/Trad + 1/Timp + 1/TFB,(2)

where arad is the radiation damping rate, a;mp thedamping rate due to cavity impedance and aps the-342-

JAERI-Conf 95-021

damping rate due to RF feedback. Trad, Timp andTFB are the damping time due to radiation, cavity
impedance and RF feedback respectively. A negative
Timp indicates the excitation of instability, and an unstable oscillation will occur when-Timp< Trad + TFB·(3)The idling cavities were detuned by -88 kHz
throughout the feedback experiment. Fig. 5 showsa typical amplitude. behavior of the -1 mode oscillation. The amplitude began to increase exponentiallywhen the loop was opened at 0 ms, and turned todecrease when the loop was closed at about 90 ms.
This figure clearly shows the effectiveness of the RF
feedback .. The bottom figures show expanded views
just after the loop off and on.

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180 ........

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: -~-~~~.t-~.~:~.1~:~.~-~~:t:~.~~-~-~t.~.~--~-j_t~-~-~:1.~:~12141618111

Loop Gain [dB]Fig. 6. Measured and estimated damping times as afunction of the loop gain.

lb = 6.21 rnA, Gain= 13.3 dB-70'a~-80

V. Discussion....... -~· .. ... -~ .. .. --~ ........ -~ ....... --~ ....... ··:·· ....... :· ........ ~- ........ ~-- ..... .
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::~~~~~~~~~Time[ms)Bltimatcd GrOW1b. Time • 9.7 1D1llllimar.dDampiagTUDO•IBI.Ima.

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·=·····~T1Dl0•4i•36mt····20406080Time[ms)Fig. 5. Amplitude versus time of the -1 mode oscillation when the feedback loop was opened, and thenclosed after a short period of time.
The growth time was measured from the initialslope of the increasing amplitude when the feedback
loop was opened. The measured growth time was 9.9
ms on the average of ten measurements, and varied
between 9.1 ms and 11.0 ms. The growth time, obtained from the estimated Trad and Timp, was 9.7 ms,
which agreed well with the measured value.
The damping time was measured from the initialslope of the decreasing amplitude when the feedback
loop was closed. In order to exclude any nonlinear effect from the measurements, the loop was closed while
an amplitude was still very small. The measurement
was repeated two or three times for each loop gain of
13.3, 15.3, 17.3 and 22.3 dB. Fig. 6 shows the measured and estimated damping times as a function of
the loop gain. The crosses show the measured points,
while the solid line represents the damping time derived from the estimated Trad, Timp and Tp B. The
broken line represents the estimated minimum damping time, which would be obtained with an infinite
loop gain.

A threshold gain is defined here as a loop gain at
which a combined damping time of Trad and TFB isequal to a growth time, -Timp. The measured threshold gain was about 12 dB, which was in good agreement with the estimated threshold of 12.5 dB. However, in the region above the threshold, the measured
damping times were much shorter than the estimatedones. Besides, some of the measured points are foundbelow the broken line. This may suggest that the experiment included some factor which we did not take
into account.
Since the measured damping time varied more than
we had expected, we felt concern about the stabilityof the feedback system operating at a very low RF
power. If the gain fluctuation was the only cause of
the measured damping time variation, a range of fluctuation would be about 10 dB. Later we measured thesystem stability under very low power operation, andfound out that either the frequency converter or theparallel comb-filter had a rather large phase fluctuation. Though we have not yet evaluated its effecton the gain variation, it may be responsible to someextent for the measured damping time variation.

VI.. Acknowledgments
We would like to thank the members of the operating group for their help in carrying out the beam
test.

References[1] D. Boussard et al. , IEEE Trans. Nucl. Sci. Vol.
NS-30, No.4, p. 2239, (1983).
[2] S. Yoshimoto et al. , contributed to 1995 IEEE
PAC and Int. Conf. High Energy Accelerators,Dallas, Texas, 1995.
example, C. Pellegrini et al. , PEP-258, Oct.
for[3]
1977.

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