The 11th Symposium on Accelerator Science and Technology, Harima Science Garden Ciiy,

1997

Beam Test of a Direct RF Feedba ck System for KEKB
Kazunor i AKAI, Eizi EZURA and ShiD:-ichi YOSHIM OTO
High Energy Accelerator Research Organiza tion (KEK)
1-1, Oho, Tsukuba , Ibaraki-ken, 305 JAPAN2 Experim ental Set Up

Abstrac t
This paper describes high beam current experimentsof a direct RF feedback (DRFB) system conducte d in
TRISTA N AR. The DRFB was operated with a prototype supercon ducting cavity for KEKB. It was observed that the DRFB greately improved stability of
the RF system under an extremely heavy beam loading.
For example, coherent synch~otron oscillation was suppressed and the phase margin for the stability limit wasincreased. Total stored current could be increased up
to 573mA and the high current beam was stably storedwith the DRFB on.
1 Introdu ction

The KEKB, an asymmetric electron-positron collider, will be operated with a beam current of several amperes. The ARES normal conducting cavities [1] and supercondu cting cavities (SCC) [2] will be used in KEKB.
Longitud inal coupled-bunch instabilities of modes J.t=1,-2, etc., (J.t is the coupled-bunch number) caused by detuning to compens ate for the reactive component of thebeam loading will be sufficiently suppressed, indebted tolarge stored energy in the ARES and SCC.
Even with the ARES and SCC, however, the beamloading is so heavy that it can degrade the stability ofthe operatin g RF (essentially J.t=O) mode. For example,
following problems are expected: (1} phase margin issmall for the static Robinson stability criterion, (2) theAutomat ic Level Control (ALC) and Phase Lock Loop(PLL) become unstable due to cross-talk between them,and (3) insufficient transient controllability on the occation of one station trip, beam dump, or others. In orderto solve these probletns, it is planned to equip·th e RFcontrol system with a direct RF feedback loop (DRFB),
in addition to the usual ALC and PLL loops.
The principle of the DRFB is to monitor the cavity
voltage seen by the beam and reinject it into the cavity. Then the impedance of a cavity seen by the beamand by driving RF signal is considerably reduced [3]. Inthe CERN SPS, during high intensity proton cycle theDRFB was used to reduce the impedance of a SCC toavoid beam instabilities. The cavity voltage was madenegligibly small even in the presence of the strong proton
beam current (0.2A) [4];In 1996, a series of high beam current experime nts
for KEKB was conducte d in TRISTA N Accumulation
Ring (AR) to test the ARES and SCC with a high current beam up to 0.5A [5]. In the experiment, the DRFB
was installed in the RF control system for the SCC. The
performance and the effect of DRFB on stabilizing theoperatin g RF mode were investigated. The results arepresented in this paper.

The AR had been operated as the injector of theTRISTA N Main Ring and as a SOR machine : at thattime 4 units of 11-cell APS type cavities were used. Prior
to the experiment, these APS cavities were removed temporarily and one SCC and two sets of ARES cavities. wereinstalled. During the experime nt of the DRFB, only theSCC was operated and the ARES's were detuned. The
sec used for the experiment is a single-cell dampedcavity. All monopole and dipole ROMs are extracted
through the beam pipes with large diameter s and absorbed by ferrite dampers. Table 1 shows main machineparamete rs of the AR for the experime nt in parallel withparamete rs of the accelerating mode of the sec. Detailsof the sec, together with beam test results of cavity
performances, are reported elsewhere l6J [7].
Table 1Main paramete rs of the AR and SCC(AR)
Particles
Beam Energy Et,
Beam Current Ib
RF frequency !R F
Harmonic number
Radiatio n loss/turn Uo
Radiatio n damping time Te
RF voltage by SCC Vc

electrons
2.5 GeV
573 mA (max)508.58 MHz
640
0.146 MeV
21 msec
0.6,..... 2.5 MV

R/Q

93 0
8.9x104cscc) ·Loaded-Q QL

Fig. 1 shows a schematic view of the RF system. The
DRFB loop is formed by combining the pick-up signal
with the main driving RF signal. The phase and amplitude of the feedback signal with respect to the driving
RF are monitored and appropri ately adjusted . There isan additiona l phase lock loop in the DRFB line, which
compensates for a possible slow phase drift in the RFamplifier and. the modulato r. The bandwid th of thisloop is limited to very low frequency by the LPF in or-,der not to affect the response of the DRFB loop. Other
conventional feedback loops employed are: the ALC andPLL loops to control the cavity voltage, another PLL tocompens ate for a phase change around the klystron, anda tuning control loop to adjust the resonant frequencyof the cavity.

3 Stabilit y Limit with DRFB
Fig. 2 shows a block diagram of the DRFB loop.
We discuss here the effect of the DRFBro n the stabUityfor a very simplified case where delay around the loop
is neglected (r=O) and G is represen ted as K/ R (K is-179-The 11th Symposium on Accelerator Scienc;e and Technology, Harima Science Garden City, 1997

Vd//

I/

I/"I/

I/

II/

1-',/ lb

Fig. 3 Phasor diagram of the system.

8Fig. 1 Schematic view of the RF control system for

6sec.

Y_max
4

a real number and R is the shunt impedance). It isalso assumed that WscTf « 1, where Wsc and Tf are thecoherent synchrotron frequency and the filling time ofthe cavity, respectively. In this case we obtain a phasor diagram shown in Fig. 3. It is seen that the static
Robinson stability limit corresponds to ¢{ - ¢~ = ¢ 5 ,which leads to sin 4Ys + Y~ax sin 2¢~/2 = 0. (Y' andY are defined as Ib/I; cos¢~ and Ib/ IT cos ¢z, respectively.) Since G is a real number, Y' = Y/(1 + K) andtan¢~= tan¢z/(1+K). From theserelationsweobtain,= O.
Ymax tan ¢zsin¢ +s (1 + K) 2 + tan 2 ¢z(2)which is obtained from the vectors, Ymax can finally berepresented as a function of ¢L , 4Ys and K.
IbIf L - - - i0( -S't)

Fig. 2 Block diagram of the direct RF feedback loop.
As an example, Fig. 4 shows the Ymax as a function of ¢L for the cases K = 0 (no DRFB), K = 1 andK = 2 for ¢s = 75°. It also shows a curve of ¢z = 0,
which gives another limit concerning the dynamic stability condition. The area between the two lines is a stableregion. It is seen clearly that the DRFB increases thisarea. For an actual system, the delay, an exact formof G, and other loops such as ALC and PLL should betaken into account. Nevertheless, this simple model isuseful to help intuitively understand the system.

102030405060phi_L(deg)Fig. 4 Calculated stability limit for the simplified
model. Observed beam losses without theDRFB are marked by x.
4 Beam Test Results(1)(If we set K = 0, eq. 1 gives the well-known equationof sin¢ 5 + Ymax sin2¢z/2 = 0 without theDRFB.) By
combining eq. 1 with a relation oftan ¢z =tan ¢L + Y(tan ¢L cos 4Ys- sin 4Ys),

2

Most of the DRFB experiment was conducted at a
total beam current of 400mA in 16 bunches and the cavity voltage of 1.0 ,. . ., 1.5MV. The loop gain was set as
K = 2 "'J 4. Without the DRFB, we observed a strong
coherent synchrotron oscillation of mode JL=O, in spite ofa relatively large loading angle (¢L = -15°) introduced
to increase the margin for the stability. The amplitudeof the cavity phase oscillation was fluctuating, as an envelope of the oscillation is shown in Fig. 5a. When theoscillation was blown up, the amplitude reached as highas 1.4° of the RF signal (Fig. 5b). With the DRFB
on, the oscillation was sufficiently suppressed down toless than 0.2° (Fig. 5c). Fig. 6 shows spectra of thepick-up signal observed by a spectrum analyzer. The
synchrotron side bands are reduced by 10 dB with theDRFB on.
Next we studied the effect of the DRFB on the phasemargin. A beam of 400mA was stored at Vc=l.5MV(Y=2.2) and ¢L = -15°. Then the ¢L was increasedslowly until the beam was lost due to the coherent oscillation. Without the DRFB, the beam was lost at¢L = +14°. With the DRFB on, the beam could bekept up to ¢L = +23.3°. This study was done also at
Vc=l.OMV (Y=3.3). The beam was lost at ¢L = +0.5°
without, and at ¢L = +8.4° with the DRFB on, respectively. Thus the phase margin was largely increased withthe DRF'B. If we compare the results with the calculated-180-

The llth Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997fs!
(a)(a):::Jll r~~lllllllllllllll
FxdXY 10HzlOOk~) :::Tl~llllllllllfiHI

(b)

(c)

FxdXY 10Fig. 5 Phase of the cavity voltage: (a) an envelopeand (b) the maximum amplitude without theDRFB, and (c) with the DRFB on.

(a)

Log

Log

HzlOOk

Fig. 7 Frequency response of the closed loop of thePLL: (a) without and (b) with the DRFB.
fully increased up to 573mA and stably stored. We had
no beam loss due to the instability with the DRFB on.
This current limitation (573mA) was not by the instability, nor by cavity performances, but by a saturation
due to a ballance between the beam life time and theinjection rate.

I-40dB5 Conclusion(b)

I-50dB

Fig. 6 Spectra of the pick-up signal: (a) without and(b) with the DRFB.

The DRFB was tested in the AR with a high current beam of 0.5A. It effectively suppressed the coherent synchrotron oscillation and increased the phase margin. The stability of the system was greatly improved
and thus the stored current could be increased. It wasdemonstrated that the DRFB plays an important roll in
the KEKB RF system.
Acknowled gement

limit shown in Fig. 4, there is a fairly good agreement
for the cases of no DRFB. With the DRFB, however,the beam loss occurred at smaller </h than the calculated values: this might be attributed to the loop delayor the cross talk between the ALC and PLL. Further
analysis including the delay is in progress.
Frequency response of the closed loops of the ALC
and PLL with a beam was measured using a FFT dynamic signal analyzer. Without the DRFB, a sharp peak
appeared at 21 kHz corresponding to the synchrotron
frequency (Fig. 7a), which leads to an excitation of theoscillation. With the DRFB on, the peak was eliminated(Fig. 7b). This means that the DRFB prevents the oscillation from being excited by the ALC and PLL loops.
Finally, the maximum stored current could be increased with the DRFB. On the last day of the experiment, we tried to increase the beam current as high aspossible. After several times of beam loss around 500mA
due to the coherent oscillation without the DRFB, weswitched the DRFB on. Then the current was success-The authors would like to thank the members ofKEKB superconducting cavity group for their support
in the experiment. We also thank Dr. Y. Funakoshi forthe helpful operation.
References[1] Y. Yamazaki and T. Kageyama, Part. Accel. 44, p.
107 (1994).
[2] S. Mitsunobu et al., Proc. Int. Workshop on B Factories (BFWS92), KEK, p. 140 (1992).
[3] D. Boussard, IEEE Trans. Nucl. Sci. NS-32, No. 5,p. 1852 (1985).
[4] D. Boussard et. al., Proc. 1st EPAC, p. 985 (1988).
[5] Y. Funakoshi and K. Akai, presented at the 1997
PAC; KEK Preprint 97-62 (1997).
[6] T. Furuya et al., presented at the 1997 PAC; KEK
Preprint 97-18 (1997).
[7] T. Tajima et al., presented at the 1997 PAC; KEK
Preprint 97-87 (1997).

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