JAERI-Conf 95-021

PB12Longitudinal Bunch Feedback Systemwith a Two-Tap FIR Filter Prototype
Makoto Tobiyama, Eiji Kikutani and Yasuyuki Minagawa*National Laboratory for High Energy Physics, 1-1 Oho, Tsukuba 305, Japan*The Graduate University for Advanced Studies, 1-1 Oho, Tsukuba 305, Japan
2 Tap FIR Prototype Board

Abstract
Feasibility of the prototype digital filter for the longitudinal bunch feedback system for KEKB rings. has been
examined in TRISTAN-AR. Detected longitudinal positions for individual bunches were digitized and recorded
on memories. The hardwired FIR filter with 2 tap wasused to shift the phase over goo and to suppress the unnecessary DC component. The feedback signal was supplied
to beam in the form of the phase modulation of accelerating cavities. The feedback system worked with the loop
gain up to 30 dB. Detuning the RF cavities to excite single bunch Robinson instability with the feedback working,the instability was completely suppressed even under thegrowth time of 0.3 rns.

I. Introduction
In a storage ring which accumulates many bunches withhigh beam current, such as KEKB rings, strong coupledbunch instabilities with many modes will occur both intransverse and longitudinal planes. To cure the instabilities, we are now developing bunch-by-bunch feedback systems for KEKB accelerators1 11. In the longitudinal plane,a digital filter of two-tap FIR scheme will be used to shift
the phase of the detected position signal over goo and to
suppress the unnecessary static (DC} component.
Prior to the fabrication of the filter complex with fullfunction, which will work for 5120 bunches with 508 MHzof system clock, we have examined the feasibility of thetwo-tap FIR scheme with a quick-prototype board. Using
the RF cavities as the kicker, the longitudinal feedback
loop was closed for single bunch beam in TRISTAN-AR
at 2.5 GeV. Feedback parameters such as the loop gainor the damping time was measured successfully. Relatedparameters for TRISTAN-AR at the feedback experiment
are listed in Table I.
EnergyCircumference
Beam current
RF frequency
RF voltage
Harmonic number
Synchrotron tune

EcIb/RFVnF

hv.

2.5377.26
1rv4
508.5808
1 rv 1.5
6400.025 rv 0.032

GeVmrnAMHzMVLongitudinal Fronte dBeamBPMarray

Figure. 1. Longitudinal bunch-by-bunch feedback systemprototype at TRISTAN-AR. The phase of the detectedlongitudinal signal is shifted by goo with the 2-tap FIR
filter made of pure hardware logic circuit. RF cavities
were used as the longitudinal kicker.

A. Longitudinal position detection system
The longitudinal position of a bunch is measured withthe wideband phase detection system which is capable
to distinguish individual signals from the bunches withthe bunch spacing of 2 ns. Signals from the longitudinal aligned series button electrodes are combined with theperiod corresponding to the 4-th harmonic of the RF frequency, that is 2.034 GHz in our case. Clearly this circuit
makes an FIR band pass filter with the first center frequency of 2.034 GHz. The output is, therefore, a burst
sine-like pulse train signal. Three pairs of electrodes installed in the south interaction region in AR were used 12 1.
Here, because of the narrow size of the vacuum chamber,
70 mm in inner diameter around the pickups, we can use
the beam signal up to 2.6 GHz without being bothered byheavy noise that propagate in the vacuum chamber justas the microwave in a circular wave guide.
The pulse train is expressed byh cos(nwnFt + <Psin(w.t))

Table I
Main parameters for TRISTAN-AR with the prototype
longitudinal feedback

where n = 4 and <P and w. are the amplitude of thesynchrotron oscillation and the angular synchrotr01i frequency, respectively. By multiplying the reference signal
with a double balanced mixer (DBM, R&K M-21}, a wideband homodyne phase detector is formed. The IF outputof the DBM becomesh cos(nwnFt + <P sin(w.t)) x sin(nwnFt)= h (sin(2nwnF-t + <Psin(w.t))- sin(<Psin(w.t))).
2II. Experimental Setup
A block diagram of the longitudinal feedback systemprototype at TRISTAN-AR is shown in Fig. 1. The system consists of the position detection part, phase shifter
filter part and kicker part.

By rejecting the higher frequency component with a low
pass filter (LPF, fc=1 GHz}, baseband component of thesynchrotron oscillation is detected as the form of-281-Ib sin( <P sin(w.t)} rv h<P sin(w.t}.

JAERI-Conf 95-021

The linear bunch current dependence of the output, thatmeans the current dependence of the loop gain, is not sosevere problem because the growth rates of the instabilities
will also depend on the bunch current and will be slower
than the linear dependence in many cases.

B. Two-tap FIR ftl,ter prototype board
In our feedback system, the signal process (phase shiftby 90° and elimination of static (DC) offset) is performed
with a 2-tap FIR filter realized by a simple hardware system. As the algorithm of the 2-tap FIR filter has been described elsewhere1 3 1, we will give only a short explanationon the filter. The response of the FIR filter has the formof the linear combination of the data which have been obtained as a time series, x(1), x(2), · · ·. The 2-tap filter has
only two terms the coefficients of which are 1 and -1 so
the output has the form ofFigure. 3.
filter.

An example of the frequency response of they(n) = x(nl)- x(n2).
and has the favorite frequency of 1/2(nl - n2). By suitably selecting the tap positions, n1 and n2, that means byselecting the address-shift of the memory, we can tune thecenter frequency and the group delay of the filter.
The quick-prototype board we have made does not use
digital demultiplexing technique. Therefore it works only
below the bunch frequency of 6.4 MHz. This board consists of a 125 MHz ADC (AD9002) in the front-end anda 40 MHz DAC (SONY CXD1171) in the back-end circuit, full-adders (SN74HC283) and two sets of memories(HM62832UHP-15) in the digital filter. The size of thememory is 4 k bytes in total. The board is packaged in a
1-span CAMAC module. The tap positioning of the filter
is set through the CAMAC command very easily. Figure 2 shows the modulation input for the beam and theoutput of the filter. An example of the frequency responseis shown in Fig. 3.

Figure. 2. Synchrotron oscillation modulation signal forthe beam (upper trace) and the output of the filter (lowertrace). The clock of the filter was 8 X frev, though there
was only one bunch.

C. Feedback kicker
Because the longitudinal kicker is still on the designstage, we used the accelerating cavities as a longitudinal kicker. In AR, there are two RF stations, EAST andWEST, each of which has 4 APS cavities of 9 cell structure. Our kicker was 4 cavities of the WEST station. We
modulated the phase of the accelerating RF signal at thelow level circuit. The feedback filter and the phase shifter
at WEST station was connected with a coaxial cable oflength of about 140 m. As the passband of the cavity isfairly narrow, we can only use single-bunch beam for thefeedback experiment.

III. Result and discussion
At first, the longitudinal oscillation was excited artificially with the phase modulation of the EAST cavities,
Under the condition, we tuned the tap positions of the filter to maximize the loop gain of the feedback. The tap
position was chosen to be (n1 = 30, n2 = 182), where
the clock frequency of the filter was 8 X !rev· The difference of (182-30)/8=19 agreed with the synchrotron tuneof 1/2v. "' 20 clearly. With increasing the analog gain, itbegan to excite an oscillation with some other frequencies
than the synchrotron frequency which virtually limited thegain of the loop. The maximum gain of the feedback was
about 20 dB. Note that this gain does not show the maximum gain of the feedback loop for instabilities because theenergy of the excitation was supplied continuously under
the condition.
Next, the longitudinal oscillation was excited by intentionally shifting the resonant frequency of the cavities toarise the single-bunch Robinson instability. By tuning theresonant frequency shift, we controlled the growth rate of
the instability. With setting the tuning angle of the accelerating cavities to be +10°, we could excite constantlongitudinal oscillation without losing the beam. Figure 4
shows the beam spectrum before and after the closing feedback loop at the detunig angle of the RF cavities of +10°.
The synchrotron sidebands were suppressed below thenoise level. That clearly shows the loop gain is grater than
30 dB.
We have increased the detuning angle of the cavities
to excite the Robinson instability with the gain of thefeedback loop increasing to find the break point where
feedback are no longer works correctly. We found thatthe growth time of the instability was about 0.1 ms at thebreak point.

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Robinson Instability
250c

2000~

8. 150(ijc'0.-E 100c"'0_J

50

3000

2000

4000

Number of turns

Figure. 5. The observed oscillations just after the feedback was turned off. The abscissa is the turn number
and the ordinate is the longitudinal position in an arbitrary unit. The slow oscillation corresponds to the growthtime of about 1 ms and the fast one corresponds to about
0.3 ms.

Figure. 4. The beam spectrum before (upper) and after(lower) the closing of the longitudinal feedback loop.

system is powerful enough for the signal processing of thelongitudinal bunch feedback system.
We are now installing a longitudinal kicker with thebandwidth of 125 MHz with the expected shunt impedanceof about 1.1 kn at TRISTAN-AR. With the power amplifiers that can supply up to 0.5 kW to the kickers, we expect the maximum feedback voltage of about 900 V /turn.
This value corresponds to the damping time of about 7 msat the saturating amplitude of l::.E / E=0.1 %.
References[1]

We measured the oscillation also by a turn-by-turn position detection system. The front-end circuit of the measurement system was equivalent to that of the feedback
system but completely independent of the feedback loop.
By this system we observed the change in the oscillation
around at the very moment of the feedback on/off. Examples of the observed data are shown in Fig. 5. We havecaught the growth of the oscillation with the maximum
growth time of about 300 turns or 0.36 ms.
When we change the RF voltage, the shift in the synchrotron frequency occurs that loses the gain of the feedback system. Our filter worked well with the RF voltage
1 MV and 1.5 MV by selecting suitable tap positions foreach operation. This shows the good flexibility of the feedback system under various conditions.

[2]

[3]

IV. Summary
We have examined the feasibility of the bunch-bybunch feedback scheme with the two-tap FIR filter quickprototype in TRISTAN-AR. The frequency performance
was measured in a bench and expected characteristics wereobtained by the quick-prototype board.
The experiment of the longitudinal feedback has also
been performed. The kicker for the system was not an
actual one but the accelerating cavities. The oscillation
was safely damped by the feedback system and the damping time of, roughly, 0.1 ms was obtained. Based on theexperiment, we have confirmed that the 2-tap FIR filter-283-

E. Kikutani, et. al., in Proceedings of 1995 IEEE Particle Accelerator Conference, Dallas Texas. U.S.A./KEK Preprint 95-20.
E. Kikutani, et. al., AlP Conference Proceedings 333,(363) 1995.
E. Kikutani and Y. Minagawa, KEK Report 94-5,1994.