An FPGA-based bunch-to-bunch feedback system at the Advanced Photon Source

Abstract

The advanced photon source storage ring has several bunch fill patterns for user operation. The hybrids fill pattern consists of a single bunch with a charge of 16 mA and a bunch train of 56 bunches. Both horizontal and vertical instabilities are observed. Currently chromaticity correction is the only method available to overcome the instability. Beam lifetime and injection efficiency suffer because of high sextupole currents. A bunch-to-bunch feedback system is designed to overcome beam instability and reduce the required chromaticity correction. The feedback system is based on an FPGA DSP processor. The signal filtering algorithm is based on the time-domain-least-square (TDLF) method developed at SPring-8. We have just completed the integration of the system. We report the system design and some test results.

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AN FPGA-BASED BUNCH-TO-BUNCH FEEDBACK SYSTEM AT THE
ADVANCED PHOTON SOURCE*
C.-Y. Yao**, E. Norum, N. DiMonte, Argonne National Laboratory, Argonne, IL 60439, U.S.A.
Abstract
The Advanced Photon Source storage ring has several
bunch fill patterns for user operation. The hybrids fill
pattern consists of a single bunch with a charge of 16 mA
and a bunch train of 56 bunches. Both horizontal and
vertical instabilities are observed. Currently chromaticity
correction is the only method available to overcome the
instability. Beam lifetime and injection efficiency suffer
because of high sextupole currents. A bunch-to-bunch
feedback system is designed to overcome beam instability
and reduce the required chromaticity correction.
The feedback system is based on an FPGA DSP
processor. The signal filtering algorithm is based on the
time-domain-least-square (TDLF) method developed at
SPring-8. We have just completed the integration of the
system. We report the system design and some test
results.
INTRODUCTION
The Advanced Photon Source storage ring (SR) has
several bunch fill patterns for user operation. The hybrids
fill pattern consists of a single bunch with a charge of 16
mA and a bunch train of 56 bunches. Both horizontal and
vertical instabilities are observed. Currently we use high
sextupole strength and thus high chromaticities to control
instabilities. High sextupole strength causes reduction of
dynamic aperture and shortens beam lifetime. A single-
bunch feedback system is designed for the SR to
overcome horizontal and vertical beam instability of the
high charge leading bunch of the hybrids fill pattern.
Some relevant parameters of the SR are listed in Table 1.
Table 1: APS Parameters Related to Feedback System
Beam energy E0 (GeV)
Horizontal tune ?x
Vertical tune ?x
Horizontal beta function ?x (m)
at the PU and DRV
Vertical beta function ?y (m)
at the PU and DRV
Horizontal damping time ?x (ms)
Horizontal damping time ?x (ms)
Revolution time T0 (μs)
Harmonic number h
7
36.20
19.27
4.5
22.45
9.6
9.6
3.68
1296
SYSTEM DESCRIPTION
The system consists of a drive and a pick-up stripline
(PU), a drive stripline (DRV), four drive amplifiers, the
front-end signal conditioning circuits, and an FPGA-based
DSP processor. Figure 1 shows a diagram of the system.
Signals from a pickup stripline are sent to the front-end
electronics, which down-converts and stretches the beam
signal from ~1 ns to 100 ns. The signal is then sent to a
Stratix II DSP processor unit [1], which performs A/D
conversion, DC orbit suppression, FIR filtering, delay
adjustment, and D/A conversion.
The required bandwidth for a single bucket in the APS
storage ring is 135 kHz. With an 88-MHz sample and
processing rate, the system can be expanded to handle up
to 324 bunches with some modifications in the front-end
circuits. The initial design is aimed to handle 1 to 24
bunches.
Figure 1: Block diagram of the feedback system.
In order to achieve damping and not introduce tune
shift, the correction kick of the DRV needs to be
proportional to the slope of beam motion at the DRV
location [2, 3]. With digital signal processing the required
slope signal can be readily derived from multi-turn
readings of the PU. Therefore only a single PU is
necessary. The multi-turn processing introduces a delay of
a few turns in the system response time, which is much
shorter than the desired damping time and therefore not a
problem.
The front-end electronics for the system are adopted
from the newly upgraded monopulse receiver of the APS
storage ring beam position monitor (BPM) system [4].
The rf hybrids are used to convert the four blade signals to
sum and difference signals. The signals are filtered with
10-MHz bandwidth, 352-MHz center frequency bandpass
filters. The monopulse receiver converts the rf signal into
a pulse signal with a width of ~100 ns. Turn-by-turn beam
position reading is generated by averaging up to eight
samples per bunch.
An 88-MHz internal sample clock is generated from the
storage ring revolution
synchronization clock signal distributed by the APS main
___________________________________________
* Work supported by U.S. Department of Energy, Office of Science,
Office of Basic Energy Sciences, under Contract No. DEAC02-
06CH11357.
** Email: cyao@aps.anl.gov
pulse and a 44-MHz
MOPAN116Proceedings of PAC07, Albuquerque, New Mexico, USA
06 Instrumentation, Controls, Feedback & Operational Aspects
440
T05 Beam Feedback Systems
1-4244-0917-9/07/$25.00 c ?2007 IEEE

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timing system. The clock is synchronized with the
circulating bunches in the storage ring.
The DSP processor reads and separates the signal from
each bunch into individual channels. Although the system
is intended to perform feedback on the leading bunch, the
actual design allows it to be expanded to 24 equally
spaced buckets with only minor changes in the front-end
signal conditioning circuits. At the core of the DSP
processor is a filter that derives the slope of the bunch at
the drive stripline from the multi-turn signal of the pick-
up.
A program delay unit provides a 10-ps resolution delay
adjustment. The output signal is then fed to four
amplifiers with a bandwidth of 220 MHz and power rating
of 150 W.
FILTER DESIGN
There are many ways to realize the FIR filter for a
transverse feedback system. We adopted an algorithm
based on the TDLF method developed by Nakamura [5].
The algorithm is briefly described here.
Beam position in a circular accelerator can be described
in matrix form as
(1)
,
0
?
0
??
?
?
??
?
?
?
??
?
?
??
?
?
?
n
x
x
M
x
x
n
n
where (x0, x'0) is the beam position and slope on the 0th
turn, (xn, x'n) is the beam position and slope on the nth
turns, M is the one-turn beam transfer matrix. The matrix
Mn can be expressed into Twiss functions of the lattice as
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
nsn
nns
n
scs
ssc
1
M
?
?
??
2
, (2)
where cs and sn are defined as
)2cos(
ncs
???
, (3)
)2sin(
nsn
???
?
. (4)
From the n-turn beam position readings of the PU we
can derive the present beam position x0 and slope x'0 by
minimizing the least square sum
, (5)
?
?
?
i
??
?
0
????
1
0
2
00
2
)(
Ni
nns
sxsxcxiy
???
where y(i) is the beam position reading on the ith turn.
Solving for x0 and x'0 and transforming them to the kicker
location would produce the position and slope there. The
resultant slope can be expressed as
, (6)
?
?
k
??
?
?
0
1
A
0
)(
Nk
k
kyx
where the Aks are the FIR filter coefficients.
A program was developed that directly extracts Twiss
parameters from the output data of an elegant [6]
simulation and generates the FIR filter coefficients. The
program also takes the order of the FIR, additional delay
turns, gain, and optional tune spread as input parameters.
Figure 2 shows the amplitude and phase response of a
filter generated with the TDLF method. A tune spread of
±0.03 is applied to improve the flatness at the tune
frequency. DC offset or the orbit component of the signal
is automatically removed by the algorithm.
Compared with the conventional frequency domain
approach, this method has the advantage of being able to
customize phase response for best feedback performance
and remove the slow orbit part of the beam motion signal.
Figure 2: Amplitude (top) and phase (bottom) response of
a 9-tap FIR filter generated with the TDLF method. The
red vertical line indicates machine tune.
SIMULATION WITH elegant
Several elegant simulations were performed to verify
the above algorithm. Figure 3 shows a plot of the output
drive signal versus trajectory slope at the kicker location.
One can see that the error is reasonably small for a 9th-
order filter. A linear lattice is used for this simulation.
The drive curve deviates more from straight line if
nonlinear terms are included in the simulation. At large
drive amplitude the curve also deviates more. We think
this is due to the break-down of the long damping time
assumption. Figure 4 shows the tracking results of
horizontal closed-loop beam centroid motion for a case
with pickup at sector 3 and kicker at sector 2 of the APS
storage ring. The maximum oscillation amplitude is 1 mm
and the maximum drive is 4.3 μrad. The fitted damping
time is 2.3 ms. In reality the amplifiers and stripline
cannot provide the same kick angle. So the damping time
will be longer.
Proceedings of PAC07, Albuquerque, New Mexico, USA MOPAN116
06 Instrumentation, Controls, Feedback & Operational Aspects
1-4244-0917-9/07/$25.00 c ?2007 IEEE
T05 Beam Feedback Systems
441

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Figure 3: Kicker drive signal versus beam angle at the
kicker with pickup at S3 and kicker at S2 with low kicker
gain.
Figure 4: Beam trajectory tracking result with feedback
on for a configuration with S3 pickup at S3 and kicker at
S2.
CURRENT STATUS
Initial installation of hardware and DSP software were
completed last year. We have performed initial
commissioning of the FPGA module, the front-end
electronics, and the drive circuits of the amplifiers. Beam
position acquisitions were performed with 7-GeV beam.
We have identified two problems:
1. There is significant noise in the PU readbacks of
the FPGA, which was attributed to the impedance
mismatch between the FPGA input and the
monopulse receiver.
2. There is insufficient kick strength in the horizontal
plane due to the combination of the short stripline
length of 16.7 cm and low ?x at the locations of the
striplines.
A new monopulse receiver unit is being built and will
be ready for testing this month. We plan also to develop a
special lattice with higher ?x at the drive stripline location
to test the horizontal feedback loop. If successful, we will
install a separate stripline for the horizontal drive at a new
location. We plan to complete the improvement and
resume system commissioning next month.
SUMMARY
We developed an FPGA-based transverse bunch-to-
bunch feedback system based on the TDLF method.
Computer simulation results showed that the method is
effective and can provide the desired damping. System
installation is complete, and we performed preliminary
commissioning. We have found deficiencies in some
system components and are making improvements to
correct them. Further system commissioning and close-
loop tests are expected soon.
ACKNOWLEDGEMENTS
The authors thank Dr. T. Nakamura for his help and
many e-mail communications. We acknowledge Bob Lill,
Michael Borland, Nick Sereno, Louis Emery, Glenn
Decker, Frank Lenkszus, and Om Singh for many
suggestions and discussions. We thank Chuck Gold and
the APS Diagnostics Group, RF Group, and ME Group
for their support and assistance during the installation and
commissioning.
REFERENCES
[1] “Stratix II EP2S60 DSP Development Board Data
Sheet,” http://www.altera.com/literature/ds/ds_stratix
II_dsp_dev_board.pdf
[2] J. Fox et al., “Feedback Control of Coupled-Bunch
Instabilities,” Proc. of PAC 1993, Portland, May
2003, http://www.jacow.org.
[3] D. Bulfone et al., “Bunch-by-bunch control of
instabilities with the Elettra/SLS Digital feedback
systems,” Proc. of ICALEPCS 2003, Gyeongju,
Korea, http://www.jacow.org.
[4] “Design of Beam Position Monitor Electronics for the
APS Diagnostics,” APS internal report.
[5] T. Nakamura et al., “Transverse bunch-by-bunch
feedback system for the SPring-8 Storage Ring,”
Proc. of EPAC 2004, Lucerne, Switzerland, June
2004, http://www.jacow.org.
[6] M. Borland, “elegant: A Flexible SDDS-Compliant
Code for Accelerator Simulation,” Advanced Photon
Source LS-287, September 2000.
MOPAN116 Proceedings of PAC07, Albuquerque, New Mexico, USA
06 Instrumentation, Controls, Feedback & Operational Aspects
442
T05 Beam Feedback Systems
1-4244-0917-9/07/$25.00 c ?2007 IEEE