The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

THE -1 MODE DAMPING SYSTEM FOR KEKB
S. Yoshimoto, K. Akai and E. Ezura
KEK, High Energy Accelerator Research Organization
1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan
Abstract
We have developed the -1 mode damping system forKEKB. It was tested using the beam of KEKB LER, andproved to be effective in damping the coupled-bunch instability of the -1 mode associated with the accelerating mode.
This system was incorporated into the RF system and has
been stably operating in LER. The instability is suppressedby the damper and the beam current has been increased up
to 1.86 A. We also discuss the requirements for the damper
for upgrading to SuperKEKB.

up-converted to the RF frequency and adjusted in phase, it
is fed back to the RF signal path to the cavity.

INTRODUCTION

The feedback is carried out only in the lower side of theRF frequency by using a single-side-band (SSB) filter thatcuts the signal in the upper side of the RF frequency. The
advantage of the SSB method is that the impedance at theupper side of the RF frequency that contributes to damp the-1 mode is not affected by the feedback. Figure 2 shows
the measured transfer function of the SSB filter. It is seenthat the filter rejects the signal in the upper side of the RFfrequency.
0Amplitude [dB]-10-20-30-40-50-60-70-100

5Frequency ∆ƒ/ƒrev

10Figure 2: Measured transfer function of the SSB filter.
We have developed a new digital filter and replaced theanalog one [3]. Figure 3 shows the measured transfer function of the digital filter. In order to adjust the center frequency of the filter to the synchrotron upper sideband, thefrequency offset relative to the revolution frequency (99.4kHz) can be changed from 0 to -3 kHz by a 20 Hz step.
5ƒoffset = 0 kHz (= ƒrev)ƒoffset = -1.5 kHzƒoffset = -3.0 kHz

0-5-1090450-15-45-20-25Figure 1 shows the block diagram of the -1 mode damping system. A beam signal from a pickup electrode isdown-converted to the baseband frequency, then filtered topick up the -1 mode signal using a digital filter. After being-5

Phase [deg]

SYSTEM DESCRIPTION

Figure 1: Block diagram of the -1 mode damping system.

Amplitude [dB]

In electron storage rings, resonant frequency of the fundamental cavity mode should be detuned downwards fromthe RF frequency in order to compensate for the reactive
component of the beam loading. Since the amount of thedetuning is proportional to the beam current, it can exceed
the revolution frequency in a large storage ring with a highbeam current such as B-factories. The growth rate of theinstability can be much larger than the radiation damping
rate. One of the key issues for the B-factory RF system ishow to avoid this instability.
PEP II and KEKB have chosen different approaches tosolve the problem. PEP II uses a combination of feedback
loops that reduces the impedance seen by the beam. KEKB,
on the other hand, uses innovative normal-conducting cavities called ARES [1] and single-cell superconducting cavities (SCC) [2]. High stored energy in these cavities reduces
the detuning frequency and thus suppresses the instability.
During the operation of KEKB, the instability is sufficiently suppressed in HER up to the design beam currentof 1.1 A. In LER, however, it turned out that the instability is not cured only by the ARES scheme. The instability
occurred at 1 A, much lower than the design beam current.
We have developed the -1 mode damping system to curethe problem. After being tested in LER, it began operating
for physics run.
In this paper we describe the -1 mode damping system,
the beam test results and the operating status. We also discuss requirements for the damper for future upgrade toward
SuperKEKB.

-90
0.94

0.96

0.98
Frequency ƒ/ƒrev

11.02

Figure 3: Measured transfer function of the digital filter.

The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

OPERATION OF THE -1 MODE DAMPER

Beam Test Results
A preliminary experiment of the -1 mode damping system was carried out in LER in December 2001. The instability was excited by intentionally detuning two ARES
cavities by -60 kHz. The -1 mode damper was implemented
in one of eight RF stations. The experimental procedure isas follows:• The synchrotron upper sideband frequency is measured by a spectrum analyzer.
• The center frequency of the filter is adjusted to theupper synchrotron sideband.
• The feedback phase is adjusted using a phase shifter
so as to minimize the amplitude of the -1 mode.

Figure 4 shows the measured spectrum of the -1 mode withand without the feedback. The amplitude of the -1 mode
upper synchrotron sideband decreased by 15 dB when thefeedback loop was closed. Figure 5 shows the change ofthe measured amplitude of the -1 mode oscillation when thefeedback is switched off. The amplitude rapidly increases
until the beam is finally lost. Thus the effectiveness of thedamper was demonstrated.
Beam Curent = 890 mA= 2.09 kHz
without feedback ƒswith feedback
Detuning= -60 kHz
Filter BW= 1 kHz

Amplitude [dBm]

Amplitude [dBm]-80

Feedback on-120

01Feedback off
234

Time [sec]Figure 5: The change of the amplitude of the -1 mode oscillation when the feedback is switched off.
Figure 6 shows the effect of the feedback during a beam
injection. When the feedback is off, the beam current issaturated at 1 A and even the beam loss occurs. After thefeedback is switched on, the beam current can be increased.
Figure 7(a) and (b) show measured spectrum of the -1 mode
without and with the feedback. When the feedback is off
at 1 A, the amplitude at the upper synchrotron sideband of
the -1 mode is about the same as that of the revolution harmonic frequency (Figure 7(a)). Thus a strong oscillation
is excited. With the feedback on, the oscillation is sufficiently damped (Figure 7(b)) and the beam current can beincreased up to 1.86 A. It means that the feedback damping
time is faster than 8.5 ms.
The present limitation of the beam current in LER is
not caused by the -1 mode instability. The beam current
is rather determined in view of optimizing the luminosity.
1600
1400
1200
1000
800
600
400200Feedback offFeedback on0
3:30 PM
03.6.30

3:45 PM

4:00 PMDate

Figure 6: LER beam injection with and without the feedback.

TOWARD SUPERKEKB

-80

-100

-120-60= 1.0 A= 2.09 kHz= -60 kHz= 1 kHz-100

LER Current [mA]

According to a calculation, the growth rate is about thesame as the radiation damping rate at 2 A in LER. It turnedout, however, that the -1 mode instability occurred at 1 A,
much lower current than the expectation. One reason is thatthe operating RF voltage is lower than the design value.
Another possible reason is that the feedback loop in the RFsystem for the zero-mode stabilization may affect the -1
mode impedance.
In order to increase the beam current, it was decided toimplement the -1 mode damping system that we had developed as a backup scheme for the ARES.

-60

Beam loss & abort
Beam Curentƒs
Detuning
Filter BW-40

Necessity of the -1 mode damper-40-20508.787508.788

508.789508.790508.791

Frequency [MHz]Figure 4: Measured spectrum of the -1 mode with and without the feedback in LER.

Operating Status
After this experiment, the -1 mode damper was incorporated into the RF system and has been operating stably.

SuperKEKB is planned as an upgrade of KEKB to increase the luminosity by several ten times. In SuperKEKB
the LER beam current will be increased from 2.6 A to 9.4
A. With the existing ARES cavities the detuning frequency
becomes close to the revolution frequency and the growthrate of the -1 mode is 5631 sec -1 , nearly two orders of magnitude larger than that of KEKB.
Although a highly improved -1 mode damper may beable to cure the instability, it is also desired to relax the requirement for the damper, if possible. Consequently, it isplanned to modify the ARES so that the ratio of stored energy in the accelerating (U a ) and storage cavity (U s ) will

Amplitude [dBm]

The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

ƒrf - ƒrev-40

ƒrf - ƒrev + ƒs(a)

-60
-80
-100
-120

Amplitude [dBm]-1

-0.99

-0.98

-0.97

-0.96

Frequency ∆ƒ/ƒrevƒrf - ƒrev

-40

-0.95

(b)

-60

ƒrf - ƒrev + ƒs

-80
-100-1

-0.99

-0.98

-0.97

-0.96

Frequency ∆ƒ/ƒrev-0.95

Table 1: RF parameters for SuperKEKB LER
U s /Ua
Beam current
Bunch length
Radiation loss
Unloaded Q
Cavity voltage# of cell
R /Q
Coupling factor
Detuning frequency
Power dissipation
Growthm = −1rate
m = −2m = −3

Figure 7: Measured spectrum of the -1 mode in LER (a) at
1.0 A without feedback, and (b) at 1.8 A with feedback.

91.11155.4
71.5
150
5631
240
56.4

15
9.4
3
1.23
1.27
0.5
28
9.4
4.1
44.8
210
659
52.2
9.6

1000

SUMMARY
We have developed the -1 mode damping system to curethe coupled-bunch instability due to the accelerating modeof cavities. Even with the high stored energy scheme(ARES and SCC) of KEKB, the instability occurred at 1
A in LER without the damper. We tested the damper inLER and proved its effectiveness in damping the instabil-Growth rate [1/s]

1.32

7.9
3.8
37.6
240365
31.3
4.5Amm
MeV/tern× 10 5MV/cav
W /cav
kHzkW/cav
sec −1
sec −1
sec −1µ = -1

4

be changed. It increases the total stored energy and thus
decreases the detuning frequency to some extent. Table 1shows RF parameters for various values of the stored energy ratio. The larger ratio gives the lower growth rate.
On the other hand, the power dissipation at the cavity wall
increases as the energy ratio. The ratio U s /Ua = 15 is considered to be the optimum value. Then the growth rate isreduced to 659 sec- 1 . Figure 8 shows the calculated growthrate as a function of the beam current for this case.
With the modification of the ARES, the required damping time for the -1 mode damper is 1.5 ms. The growth rateof the -2 mode also exceeds the radiation damping rate.
The existing -1 mode damper needs to be improved to decrease the damping time and to include the -2 mode. Inaddition, the damper will need to be implemented in every
RF station, instead of only one station in KEKB.
It is also expected that other modes of coupled-bunch instabilities can be excited due to a possible imbalance of theimpedance at the 0 and p modes of the ARES caused by thelarge detuning of the accelerating cavity [4]. Since the frequency of these modes is more than 4 MHz apart from theRF frequency, which is outside the bandwidth of klystrons,
it cannot be cured by the RF control system including the-1 mode damper. A longitudinal bunch-by-bunch feedback
system may be needed to cure it, while an effort to avoid
the instability by optimizing the cavity parameters is underway.

1821004µ = -2Radiation damping

210µ = -342102468

Beam current [A]Figure 8: Calculated growth rate of the coupled-bunch
instabilities due to the accelerating mode for the case ofU s /Ua = 15 in SuperKEKB.
ity. The damper was incorporated into LER and has beenstably operating. The instability is completely suppressedby the damper and the beam current has been successfullyincreased up to 1.86 A.
In SuperKEKB, the instability will be much severer. The
damping system needs to be improved to achieve the damping time of 1.5 ms and to implement the -2 mode damping,provided that the ARES is modified to increase the storedenergy.

ACKNOWLEDGEMENTS
We would like to thank the members of the KEKB commissioning group for their help in carrying out the beam
test.

REFERENCES[1] Y. Yamazaki and T. Kageyama, Part. Accel. 44 p. 107, 1994.
[2] T. Furuya, et al., APAC’98, Tsukuba, June, 1998.
[3] E. Ezura, et al., International Workshop on Collective Effects
and Impedance for B-factories, Tsukuba, Japan, June, 1995.
[4] T. Kageyama, et al., ”The Growth Potential of the ARES Cavity System toward Super KEKB”, in this conference.