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

A Longitudinal Feedback System used under Low-Energy 4-Bunch Operationof the Photon Factory Storage Ring
S. Sakanaka, A. Ueda, K. Haga and H. Kobayakawa
National Laboratory for High Energy Physics (KEK)
1-1 Oho, Tsukuba-shi, Ibaraki-ken, 305 Japan

Abstract
This paper describes a longitudinal feedback system used tocure longitudinal coupled-bunch instabilities under low-energy
operation of the Photon Factory storage ring (PF ring) atKEK. A bunch-by-bunch feedback system which operates onup to four equally spaced bunches was constructed using conventional analog circuits and a simple feedback cavity. Thesystem worked well, and the longitudinal coupled-bunch instabilities were largely suppressed under low-energy operation.

I. INTRODUCTION
Research on a free electron laser (FEL) for the shortwavelength region is under way [1] at the PF ring. For thispurpose, an optical klystron has been installed in the ring, anda measurement of the FEL gain is being prepared. The FEL
experiments require high-quality positron beams at a lowbeam-energy (0.75 GeV). Although the gain measurement
will be carried out with a single bunch, further experiments
concerning FEL oscillation call for four bunches in the ring.
At the low beam-energy, problems due to beam instabilities
are serious because the radiation damping time is long.
Therefore, cures for the instabilities are particularly important

to obtain stable beams. (Some of the ring parameters are
given in Table 1 for beam energies of 2.5 and 0.75 GeV.)
Studies on low-energy operation of the PF ring have been
carried out since November, 1989 [2]. Positron beams wereinjected at a beam energy of 2.5 GeV (the nominal energy of
the PF ring), and were then slowly deccelerated to 0.75 GeV.
Beam currents of up to 40 rnA in a single bunch have beensuccessfully stored at 0.75 GeV. However, the beam currents
and beam quality were largely limited by longitudinal coupledbunch instabilities under four-bunch operation. In order tosuppress these instabilities, a longitudinal feedback system
was developed. Among several feedback schemes that havebeen either constructed or proposed [3-7], we built a system
similar to that for UVSOR [6] and for the proposed PEP SR
project [7].
Table 1. Parameters of the PF ring at 2.5 and 0.75 GeV.
0.75
2.5E(GeV)
Beam energy
145
3. 9-rt;(msec)
Longitudinal damping time
0.85
1.7Vc(MV)
Cavity gap voltage*
35.6 46.6
fs (kHz)
Synchrotron frequency
500.1
frJ(MHz)rf frequency for acceleration
1.603
fr CMHz)
Revolution frequency* used under present operations.

BEAM

FEEDBACKCAVITYeg~~y r"-'-'--+
250W

TO
SCOPE

RING Rr
500MHzI

LOCAL RFI TO PHASE DETECTOR IITORFSWwI•4PO 'Power Divider
PS ' Phase Shiller
DBM 'Double Balanced Mixer
DC ' Direclional Coupler
LF PS ' Low Frequency Phase Shiller

TO ANALOG MPX' - - - - - J " " " " • 4A

Fig. 1. Longitudinal feedback system for the PF ring.

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II. FEEDBACK ELECTRONICS
A block diagram of the feedback system is shown in Fig.
I. Pulses induced by bunches in the upper and lower buttontype electrodes of a beam position monitor (BPM) are combined into one signal, which gives an amplitude that is nearly
independent of the beam position. The signal is distributed tofour separate channels which correspond to four bunches. Ineach channel, the signal from the corresponding bunch is gatedwith a GaAs rf switch; the phase of the bunch is then detectedby means of a phase detector. The output signal is filtered bya bandpass filter (BPF) which has a center frequency at aroundthe synchrotron frequency; it is amplified by 40-60 dB, resulting in a signal that represents the phase oscillation of thebunch. The phase of this signal is shifted by 90° in order toobtain a signal that represents the energy deviation. The output signals from four channels are gated again, summed up,
and used to modulate an rf of 500.1 MHz (which is locked tothe ring rf). The modulated rf signal is amplified with a power
amplifier (25 W max.), and is then fed into a feedback cavity,
which provides a correction voltage to each bunch.
The following is an additional description of some of thecomponents: a) The switching times of the rf switch and theanalog multiplexer are less than -10 nsec, which is much
shorter than the bunch spacing, 156 nsec. b) A block diagramof the phase detector is shown in Fig. 2. A direct phase comparison between the 312th harmonic of the beam and the ring
rf is made with a double-balanced mixer (DBM). The use of aBPF (center frequency is 500 MHz) and an rf amplifier before
the DBM improves the signal-to-noise ratio of the input
signal to the DBM.
RFAMPlldB

DBM

LF AMP
l5dB

SIGNALINPUT

h~~fRF ( 0 ) . . . . - - - - - - - . . J
1500MHtl

Fig. 2. Block diagram of the phase detector.

Ill. FEEDBACK CAVITY
A choice for the energy feedback device must be madewhile considering required feedback voltage and bandwidth.
The maximum voltage required for the feedback cavity is given
by [4]
2E t1E

VFB = eifr.E 'where t1EIE is the relative energy error and r is the damping
time required for the feedback system. In our case, it is reasonable to set r to be 4 msec, which is of the same order as
the radiation damping time at 2.5 Ge V, since we can avoid theinstabilities at that energy, at least up to 100 rnA (the presenttarget current). Assuming the energy error to be - 3x 10- 3 ,which is a fraction of the rf bucket height, the required voltage
becomes -700 V. The filling time of the cavity should beless than about one third of the bunch spacing [4], which
imposes the filling time to be less than -50 nsec.
For our system, a feedback cavity with a ceramic gap wasFig. 3. Cross-sectional view of the feedback cavity.

Fig. 4. Photograph of the feedback cavity.

adopted, since it is easy to fabricate and is economical. Thisis because there is no need to develop an in-vacuum tuner oran input window. A cross-sectional view and a photograph ofthe feedback cavity are shown in Figs. 3 and 4. The cavity
body has a rectangular shape (inner dimensions of 24 7x24 7x
180 in mm), and is made of stainless-steel plates. A ceramicgap (120 mm in length) breaks the ring vacuum from the air.
The left and right side walls of the cavity are movable within±30 mm, thus providing a wide tuning range of more than
±20 MHz. This tuning range covers anticipated frequency
errors due to mechanical tolerances of the ceramic gap, whileallowing one to sufficiently detune the cavity when desired.
The basic dimensions of the cavity were determined using
the MAFIA 3D code. The resonant frequency is 500.1 MHz,
which is the same as the ring rf frequency. The measured
unloaded-Q (Qo) is 710, 44% of the calculated value. The
main contribution to this degradation is possibly due to imperfect electric contacts used at the cavity noses and the tuner
walls. With the measured Qo and a calculated RshfQ of 179
Q, the shunt impedance was estimated to be 127 kQ.
The cavity has a large input loop at the top wall, and adamping loop at the side wall. By adjusting these loops, aloaded-Q of 72 was obtained for the fundamental mode, whichcorresponds to a filling time of 46 nsec. The input power
required to produce the feedback voltage (VFB) is given by

O+fJJ+fJ2P VFi
Pg=4fJJ .Rsh'
where fJ1 and fJ2 are the coupling factors of the input anddamping loops, respectively. A feedback voltage of 630 Vis-396-

available with an input power of 16 W, using the measured
factors of /3}=4.8 and /h=4.1. Both loops also damp some
harmful HOMs (higher-order-m odes). For example, for
TMIIO-Iike modes (two quasi-degenerated modes), which havean Rr!Q of 1820 (Q/m), the loaded-Q's were lowered to -300.
The parasitic mode loss for the fundamental mode of thecavity was estimated to be -240 W at a stored current of 100
rnA in 4 bunches. Since only 10% of the loss is dissipated in
the cavity, the cavity can be easily cooled down by forced airflow. On the other hand, under routine operations of up to360 rnA in 312 bunches, and under single-bunch operations athigh currents, the cavity body is removed from the ring inorder to avoid any problems due to the parasitic mode loss or
beam instabilities. For this purpose, the cavity body can besplit into two parts, thus allowing quick removal and re-installation. After the cavity body is removed, the ceramic gap iselectrically shielded by a cover made of aluminum alloy.

IV. OPERATION RESULTS
The feedback system was initially tested under singlebunch operation at 2.5 Ge V. A strong coherent oscillation ofa bunch was deliberately excited by tuning one of the main
accelerating cavities (which was not powered) to a frequency of
about lfrf + fs). By adjusting the electronics, this oscillation
was successfully damped by the feedback. Figures 5(a) and5(b) show the spectra of a BPM signal without and with thefeedback, respectively.
As the next step, a single-bunch beam was deccelerated to0.75 GeV. Due to the change of the synchrotron frequency
during the decceleration, additional phase shifts of the synchrotron oscillation signal arose in the filter amp and the lowfrequency phase shifter (LFPS). Thus, the LFPS was readjusted so as to retain the total phase shift of 90° withcanceling these additional phase shifts. Then, a longitudinaloscillation, which was observed at 0.75 GeV, was successfullydamped.
Finally, thesystem was tested under four-bunch operation.
The gate timings of the analog multiplexer were adjusted sothat each bunch felt the corresponding feedback voltage whenit crossed the cavity. The stored beam was then deccelerated to0.75 GeV. The longitudinal coupled-bunch instabilities werelargely suppressed by the feedback during decceleration. As aresult, a maximum beam current of 40 rnA in 4 bunches wasachieved at 0.75 GeV. The spectrum of a BPM signal underthat condition showed small synchrotron sidebands about 37
dB below from the main peak at the rf frequency. A future
subject is to reduce this residual oscillation.
During other studies under single-bunch operation at highcurrents, heating-up was observed in the ceramics shielded by
the cover. The temperature of the ceramics was raised up to100°C at -70 rnA/bunch. This was attributed to a large loss
parameter of the structure, which was found to be -0.20 V/pC
from a calculation using the T2 code in MAFIA. At present,
the maximum beam current under single-bunch operation islimited to 70 rnA due to this problem. No problems wereobserved during routine multibunch runs of up to 360 rnA.

(a) Feedback off.

(b) Feedback on.
Fig. 5. Spectra of a BPM signal without and with the feedback.
10 dB/division. Center frequency: 500.1 MHz, span: 200 kHz.
Beam energy: 2.5 GeV, beam current: 8.6 rnA (in single bunch).

V. CONCLUSION
The constructed feedback system is capable of controlling
longitudinal coupled-bunch instabilities on up to 4 bunches.
The system is now routinely used under low-energy operations
for FEL experiments. The heating-up problem in the ceramic
duct under single-bunch operation still calls for future
improvements.
Acknowledgments

The authors wish to thank M. Izawa and S. Tokumoto for
useful discussions in designing the system as well as M.
Katoh for low-energy operation during the studies.

VI. REFERENCES[1] See, for example, PHOTON FACfORY ACITVITY REPORT#10, 1992, to be published.
[2] PHOTON FACfORY ACTIVITY REPORT #8, 1990, p. R-6.
[3] J.-L Pellegrin, Nucl. Instr. and Meth. 108 (1973) p. 365.
[4] M.A. Allen, M; Cornacchia and A. Millich, IEEE Trans. on
Nucl. Sci. NS-26 (1979) pp. 3287-3290.
[5] M.A. Allen, L.G. Karvonen, R.A. McConnell, H. Schwarz,IEEE Trans. on Nucl. Sci. NS-28 (1981) pp. 2317-2319.
[6] T. Kasuga, M. Hasumoto, T. Kinoshita and H. Yonehara, Jpn.
J. Appl. Phys. 27 (1988) pp. 100-103.
[7] H.-D Nuhn et al., Conference record of the 1991 IEEE Particle Accelerator Conference, Vol. 3, pp. 1410-1412.

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