Set-up of PEP-II Longitudinal Feedback Systems
for Even/Odd Bunch Spacings
D. Teytelman* and J. Fox*
* Stanford Linear Accelerator Center^
P.O. Box 4349, Stanford, CA 94309
Abstract. Feedback systems installed for control of coupled-bunch longitudinal instabilities in
PEP-II collider have been designed to process bunch data at one half of the ring RF frequency.
As a result these systems are ideally suited for controlling ring fills where only even or only odd RF
buckets are populated (even bunch spacings). However in the operation of PEP-II per bunch charge
considerations require fill patterns that alternately populate even and odd buckets. In this note we
present a technique that allows to use existing hardware to provide feedback control of all bunches
in such fills.
INTRODUCTION
PEP-II is a collider comprised of two circular accelerators of differing energies, Low
Energy Ring (LER) and High Energy Ring (HER) [1, 2], Both rings operate above
coupled-bunch instability thresholds at the design currents. Feedback systems are required to stabilize the beams in transverse and longitudinal planes [3, 4]. Both rings
have a 476 MHz RF frequency which corresponds to a bucket spacing of 2.1 ns. The operation was planned around filled bucket spacings of 4.2 ns or every other RF bucket. In
order to reduce the digital signal processing load and analog bandwidth the longitudinal
feedback systems were designed to operate at a 238 MHz sampling frequency (one half
oftheRF).
The operation of a collider is driven by luminosity considerations. Among many
factors affecting the luminosity is per bunch charge. During the operation of PEP-II the
combination of operating current and optimal per bunch charge made fill patterns with
6.3 ns (every third bucket) and 10.5 ns (every fifth) bunch spacings desirable. In their
initial configurations the longitudinal feedback systems could not control fill patterns
where both even and odd RF buckets were populated (mixed fills). A modification of the
design has been made to address that problem. Here we will describe the design changes
required, present corrected beam timing procedures and provide experimental results for
the new mode of operation.
There are three signal processing components involved in controlling unstable motion:
front-end detection and sampling, filtering by digital signal processors (DSPs), and kick
signal generation in the back-end. These components are illustrated in Fig. 1. In order to
1
Work supported by Department of Energy contract No. DE-AC03-76SF00515
CP648, Beam Instrumentation Workshop 2002: Tenth Workshop, edited by G. A. Smith and T. Russo
© 2002 American Institute of Physics 0-7354-0103-9/02/$19.00
474
From the BPMs
To the kicker
Analog front−end
processing
Analog back−end
processing
ADC
Digital signal
processing
DAC
FIGURE1.1. Block
Blockdiagram
diagramofofthe
thePEP-II
PEP-IIlongitudinal
longitudinal feedback
feedback system
system
FIGURE
supportmixed
mixedfills
fillssignals
signalsfrom
from both
both even
even and
and odd
odd buckets
buckets must
must go
go through
through the
support
the signal
signal
processing
chain
and
the
kicker
signal
has
to
be
correctly
aligned
with
the
passing
processing chain and the kicker signal has to be correctly aligned with the passing bunch.
bunch.
Let'sstart
startthe
thediscussion
discussionfrom
from the
thefront-end.
front-end.
Let’s
FRONT-ENDSIGNAL
SIGNAL PROCESSING
PROCESSING
FRONT-END
Analogfront-end
front-endprocessing
processingof
ofthe
thelongitudinal
longitudinalfeedback
feedback system
system is
is designed
designed to
Analog
to measure
measure
time
of
arrival
of
each
bunch
relative
to
the
RF
master
oscillator
clock.
This
time of arrival of each bunch relative to the RF master oscillator clock. This is
is done
done
using
a
phase
detector
operating
with
the
master
oscillator
derived
carrier
at
6
x /..
using a phase detector operating with the master oscillator derived carrier at 6 ×
fr f .
Thebunch-induced
bunch-inducedsignal
signalon
onthe
theBPM
BPMoutput
output isis aa very
very short
short differentiated
differentiated pulse.
The
pulse. If
If such
such
pulseisisused
usedasasananinput
inputtotothe
thephase
phasedetector,
detector, the
the output
output signal
signal will
will be
be also
also aa short
short
a apulse
baseband
pulse.
As
a
result
sampled
signal
will
be
very
sensitive
to
both
pulse
and
clock
baseband pulse. As a result sampled signal will be very sensitive to both pulse and clock
timing. In order to avoid this problem in PEP-II the longitudinal feedback systems use
timing. In order to avoid this problem in PEP-II the longitudinal feedback systems use
a comb generator filter. In response to a BPM output pulse this filter produces a burst
a comb generator filter. In response to a BPM output pulse this filter produces a burst
of pulses spaced at TrJ6. When such a burst is phase detected baseband signal has a
of pulses spaced at Tr f /6. When such a burst is phase detected baseband signal has a
rectangular envelope with duration equal to that of the input burst [5]. Figure 2 shows
rectangular envelope with duration equal to that of the input burst [5]. Figure 2 shows
the front-end block diagram.
the front-end block diagram.
Originally both PEP-II longitudinal systems were equipped with 4-tap comb generaOriginally
both PEP-II
longitudinal
equipped
with 4-tap
comb
generators
that resulted
in a baseband
pulse systems
of 1.4 nswere
duration.
A timing
diagram
using
such
tors
that
resulted
in
a
baseband
pulse
of
1.4
ns
duration.
A
timing
diagram
using
comb generators is given in Fig. 3. By comparing the baseband phase signal withsuch
the
comb
is given
Fig. 3. By
theonly
baseband
phase can
signal
the
ADCgenerators
sampling clock
we in
determine
thatcomparing
only even or
odd buckets
be with
sampled
ADC
sampling
clock
we
determine
that
only
even
or
only
odd
buckets
can
be
sampled
for a fixed clock.
for aThe
fixed
clock.
comb
generator design allows one to stretch the detected pulse. If we lengthen
The
comb
design
allows
one(2.1
to stretch
pulse.
If weclock
lengthen
the basebandgenerator
pulse to span
2 RF
buckets
ns < Tthelsedetected
< 4.2 ns),
the ADC
can
the baseband pulse to span 2 RF buckets (2.1 ns < Tpulse < 4.2 ns), the ADC clock can
be set up to sample both even and odd buckets. This arrangement is illustrated in Fig. 4
beforseta up
to sample
even and
oddcase
buckets.
This arrangement
is If
illustrated
Fig. 4
10-tap
comb both
generator.
In this
the pulse
is 3.5 ns long.
for eveninbuckets
for
a
10-tap
comb
generator.
In
this
case
the
pulse
is
3.5
ns
long.
If
for
even
buckets
we put the sampling clock within T0^set < 1.4 ns of either rising or falling edges of the
we
put the
clock
To within
or falling edges of the
f f set < T1.4lsens—of
pulse,
oddsampling
buckets will
be within
sampled
Treither
— T0ffrising
set = 1.4 ns — T0ffset of the
pulse, odd buckets will be sampled within T pulse − Tr f − To f f set = 1.4 ns − To f f set of the
475
From BPMs
LNA
Double-balanced
mixer
X
6xRF
FIGURE 2.
Low pass filter
\
ToADC
Prog
de
delay
line
Block diagram of longitudinal front-end analog processing
opposite edge. To minimize timing jitter sensitivity we set T0ttset = 700 ps.
We can arbitrarily select whether to sample filled even buckets near the front or the tail
of the pulse. However that choice, as we will see later, affects set up of the back-end. In
addition, examining Fig. 4 we see, that for the timing shown bucket 3 is sampled by clock
pulse 1. If even buckets are sampled near the front of the pulse, bucket 3 gets sampled
by clock pulse 2. This sample shift would not affect feedback processing in these bunchby-bunch feedback systems with independent digital signal processing for each bunch.
However analysis of beam data acquired by the DSPs is dependent on which sampling
model (pulse front or tail) is chosen. In order to eliminate ambiguity we've chosen in
BPM signal
MAA/V
V
Comb generator oil tput
WAr
Baseband phase
Sampling clock
Time, RF periods
FIGURE 3. Timing with 4-tap comb generator. The top trace shows BPM signals for 3 bunches in the
every third bucket fill pattern. Dashed lines show ideal synchronous times, bunches 0 and 6 arrive early
while bunch 3 is late.
476
V
A/WW
Comb generator output
Baseband phase
Sampling clock
5
6
Time, RF periods
FIGURE 4. Timing with 10-tap comb generator.
PEP-II to sample even buckets at the tail of the pulse.
There are several trade-offs in mixed fill pattern sampling with a long comb generator.
First of all, the longer baseband pulse increases coupling between the neighboring
bunches. In an ideal system with fast pulse rise and fall times there would be no coupling
for pulse lengths below 4.2 ns. However due to ringing in RF components (such as the
low-pass filter) baseband pulse can last longer than the length of the comb generator
burst. The coupling is worst at the minimal bunch spacing of 4.2 ns. Since the pulse is
lengthened by a ringing tail, coupling is most significant for all odd bucket fill patterns.
Another negative effect comes from tap spacing errors in the comb generator. If tap
spacing is different from nominal Tr /6, frequency of the resulting burst is offset from
6 x fr,. Consequently detected phase pulse will ride on a slope. Since for mixed fill
patterns we sample the pulses at different points for even and odd buckets, the bunch
signals will have differing DC offsets. Even though overall DC offset is rejected by the
phase servo loop in the feedback front-end, these even to odd bucket offsets cannot be
easily compensated.
DSP FILTERS AND POST-PROCESSING
The feedback processing is done on a bunch-by-bunch basis. The harmonic number of
PEP-II is 3492 and so the feedback system acquires 3492/2 = 1746 bunch samples per
revolution. These bunch signals are downsampled and processed independently from
each other. Thus, as long as the bunch phase signal is properly sampled, it is processed
in the same manner within any of the 1746 processing channels.
However post-processing of the data acquired by the feedback system does depend on
the actual fill pattern. As shown in Fig. 4 the signal from filled bucket 0 or 1 appears in
processing channel 0. In order to accurately extract modal information from the bunchby-bunch time-domain record we need to know whether even or odd bucket is filled. This
477
Time, RF periods
FIGURE 5.
Back-end kick signals and timing to the bunch arrivals
information is not present in the data, therefore knowledge of the fill pattern is needed
for proper signal reconstruction. Once the fill pattern is known it is easy to determine
RF bucket to feedback processing channel correspondence. For front-end timing setup
described in section bucket and channel numbers are related as follows:
N.channel
(1)
BACK-END SIGNAL PROCESSING
The correction values computed by the DSPs are converted into a baseband analog signal
using a D/A clocked at frf/2. The D/A output is then a series of 4.2 ns long steps. In
the frequency domain most of the power is in the DC to /ry/4 band. The longitudinal
feedback kicker for PEP-II is designed with center frequency of 9frJ4. Therefore the
baseband output of the D/A is mixed with a carrier frequency to place the power within
kicker bandwidth. A carrier signal at 9/ry/4 undergoes a 90 degree phase shift over one
RF period. If bunch 0 is timed for maximum positive kick, bunches 1 and 3 will arrive at
zero crossings while bunch 2 will see negative kick. To avoid this in PEP-II longitudinal
feedbacks phase of the carrier is shifted by -90 degrees every RF period using quadrature
phase shift keying (QPSK).
In this discussion we will consider the bunch passage time through the longitudinal
kicker to be short relative to the carrier wavelength. PEP-II kickers have three field
gaps spaced at 1/4 carrier wavelength. However we can model these as a single short
(broadband) gap in combination with a bandpass kicker transfer function. When the
bunch passes through the gap it samples the kick voltage. In order to maximize the
effect, the kick has to be timed so that a bunch samples the peak of the waveform. As the
single-bunch kick is 4.2 ns long there are multiple peaks that can be synchronized with
the beam. However, the requirement to affect both even and odd RF buckets restricts the
timing. In Fig. 5 waveforms of the back-end signals are shown. Our goal is to chose a
kick timing relative to the beam so that both buckets 0 and 1 would sample peaks of
the channel 0 kick waveform. There are 5 possible timing settings. However, in order to
478
−60
-60
−65
-65
Response (dBV)
−70
-70
Even
Odd
L.
−75
−80
-85
−85
-90
−90
-95
−95
0
1
22
3
3
Delay (ns)
(ns)
Delay
4
4
5
6
FIGURE6.
6. PEP-II
PEP-IILER
front-end timing
timing sweep.
sweep. Approximate
Approximate extent of the phase detector output pulse
FIGURE
LER front-end
indicatedby
bydashed
dashed vertical
vertical lines.
lines. The
The "even"
"even" arrow
arrow indicates
indicates where the pulse from an even filled bucket
isisindicated
sampled by
by the
the ADC,
ADC, while
while "odd"
"odd" pointer
pointer shows
shows the
the sampling
sampling for the odd bucket.
isis sampled
minimize interbunch
interbunch coupling
coupling we
we try to use the peaks closest to the burst center point.
minimize
For the
the carrier
carrier phasing
phasing shown
shown in
in Fig.
Fig. 55 there
there are
are two
two timing settings which place either
For
the
even
or
the
odd
bunch
closer
to
the
center
point.
The choice between the two settings
the even or the odd bunch closer to the center
arbitrary.
isis arbitrary.
interesting to
to note
note that
that both
both in
in the
the front-end
front-end and
and the back-end we are dealing
ItIt isis interesting
with sampling
sampling of
of aa finite-duration
finite-duration pulse.
pulse. In
In the
the front-end, the ADC clock samples the
with
baseband phase
phase while
while in
in the
the back-end the bunch samples an amplitude-modulated QPSK
baseband
carrier.However
However for
for the
the front-end
front-end setup
setup where
where ADC
ADC samples
samples the
carrier.
the tail
tail of
of the
the pulse
pulse we
we have
have
to configure
configure the
the back-end
back-end so
so that
that the
the bunch samples
samples the head of the kick pulse.
to
EXPERIMENTAL RESULTS
EXPERIMENTAL
In this
this section
section we
we will
will describe
describe the
the procedures for setting up the correct front-end
front-end and
In
back-end timings
timings and
and present
present experimental
experimental data
data for feedback control of even/odd filling
back-end
filling
patterns. The
The front-end
front-end timing
timing is
is controlled
controlled by by the setting of the programmable delay
patterns.
line. The
The delay
delay line
line allows
allows one
one to
to adjust
adjust the
the placement of the phase detector output pulse
line.
relative to
to the
the ADC
ADC clock.
clock. The clock signal
signal is locked to the ring master oscillator and
relative
for fixed
fixed RF
RF voltage
voltage phase remains in a constant relation to the beam phase.
for
In order
order to
to determine
determine optimal
optimal setting
setting for
for the
the front-end
front-end delay
delay line
line an
an automated
automated timing
In
timing
utility isis used.
used. First
First aa single
single bucket
bucket in
in the
the ring
ring is
is filled
filled to
to nominal
nominal per
per bunch
bunch charge.
charge. The
The
utility
feedback system
system is
is set
set up
up to
to deliver
deliver aa back-end
back-end correction
correction signal
signal for
for only
only one
one channel
channel
feedback
the channel
channel that
that must
must sample
sample the
the filled
filled bucket.
bucket. Then
Then under
under program
program control
control the
the delay
delay
-- the
479
−45
-45
Odd
Even
−50
-50
Response (dBV)
−55
-55
−60
>-60
CO
−65
-65
IT −70
-70
−75
-75
−80
-80
−85
-85
9
10
10
11
11
12
13
12
13
Delay
Delay (ns)
(ns)
14
14
15
15
16
16
FIGURE
LER back-end
FIGURE 7.
7. PEP-II
PEP-IILER
back-end timing
timing sweep.
sweep. The
The dashed
dashed lines
lines show
show the
the DAC
DAC pulse
pulse length
length of
of 4.2
4.2 ns.
ns.
This
This pulse
pulse isis stretched
stretched due
due to
to the
the bandlimiting in the kicker. The "even"
"even" arrow indicates the point where
the
the even
even bucket
bucket samples
samples the
the kick
kick waveform.
waveform.
line
line isis swept
swept through
through aa range
range of
of values
values and
and at
at each
each setting
setting the baseband spectrum of
the
the DAC
DAC output
output isis measured.
measured. Due
Due to the RF noise excitation the beam oscillates at the
synchrotron
synchrotron frequency.
frequency. That
That motion
motion is
is amplified
amplified by the feedback filter and allows the
determination
determination of
of the
the amplitude
amplitude sampled
sampled by
by the ADC. By selecting a spectral component
at
at the
the synchrotron
synchrotron resonance peak we obtain sampled signal amplitude versus delay as
shown
shown in
in Fig.
Fig. 6.
6. Note
Note that
that the
the delay
delay axis
axis goes
goes in the opposite direction from the time
axis,
axis, that
that isis larger
larger delay
delay setting
setting corresponds
corresponds to sampling
sampling the earlier part of the pulse.
Since
Since we
we decided
decided to sample
sample the even buckets towards the tail of the pulse the "even"
timing
timing arrow
arrow is
is placed
placed closer
closer to
to the
the left edge of the delay sweep.
A
A similar
similar automated
automated procedure
procedure is
is used
used to set
set the
the back-end delay line. In this case with
aa single
single bunch
bunch in
in the
the ring
ring we
we program
program the
the DSPs
DSPs to produce sinusoidal
sinusoidal excitation at the
synchrotron
synchrotron frequency
frequency in
in aa single
single channel.
channel. As the delay line is swept through the region
of
of interest
interest at
at each
each setting
setting we
we record
record the
the spectrum
spectrum of the beam via the phase-detector
output.
output. When
When the
the kicker burst is
is correctly
correctly aligned
aligned with the beam the driven motion
is
is maximal.
maximal. By
By plotting the signal
signal amplitude at the synchrotron frequency
frequency against the
delay
delay setting
setting we
we get
get the
the magnitude response of the kicker as illustrated in Fig. 7. Here
two response
response lobes
lobes 2.1
2.1 ns apart are selected for even and odd bucket timing. As expected
two
the positions of
of even
even and
and odd
odd buckets
buckets are
are reversed relative to the front-end sweep.
the
After the
the optimal
optimal timing
timing settings
settings are
are determined we are able to fill the rings in
After
the even/odd
even/odd fill
fill patterns,
patterns, for
for example every third bucket. After filling the LER to
the
800 mA
mA we
we recorded
recorded beam
beam data
data in
in the closed-loop feedback configuration to verify
800
verify
the system
system stability.
stability. In
In Fig.
Fig. 88 the
the RMS amplitudes
amplitudes of the recorded data are show
show for the
the
first 12
12 DSP
DSP channels.
channels. Empty
Empty channels
channels show
show RMS motion of 11 ADC count while the
first
480
RMS
RMSmotion
motion(ADC
(ADCcounts)
counts)
2.5
2.5
c
!*
0
2
2
Q
1.5
1.5
-1.5
o
'
0
0
-
1 1
o
0.5
0.50
io.5
0)
2
22
1
1
0
o
o
0
6
66
DSP channel
DSP
DSPchannel
channel
8
88
0
.
CO
4
44
10
10
10
12
12
1
FIGURE
8. RMS of
of the beam
beam data recorded
recorded by the
the DSPs. Bucket
Bucket 0 is sampled by
by channel 00 while
while
FIGURE
FIGURE8.8. RMS
RMS ofthe
the beamdata
data recordedby
by the DSPs.
DSPs. Bucket 00 isis sampled
sampled by channel
channel 0 while
bucket
3
signal
is
in
channel
1.
bucket
bucket33signal
signalisisininchannel
channel1.1.
channels
filled
buckets
show
counts.
Since
the
front-end
is timed
timed to
to sample
sample
channels
sampling
channelssampling
samplingfilled
filled buckets
buckets show
show 222 counts.
counts. Since
Since the
the front-end
front-end isis
timed
to
sample
even
buckets
near
the
tail
of
the
pulse
we
can
reconstruct
the
underlying
fill
pattern
even
buckets
near
the
tail
of
the
pulse
we
can
reconstruct
the
underlying
fill
pattern
even buckets near the tail of the pulse we can reconstruct the
unambiguously.
unambiguously.
unambiguously.
In
amplitudes
of
the
coupled-bunch
eigenmodes
are
shown.
These
In
Fig.
average
In Fig.
Fig.999 average
average amplitudes
amplitudes of
of the
the coupled-bunch
coupled-bunch eigenmodes
eigenmodes are
are shown.
shown. These
These
values
are
obtained
by
transforming
the
abovementioned
data
set
to
the
eigenmodal
values
values are
are obtained
obtained by
by transforming
transforming the
the abovementioned
abovementioned data
data set
set to
to the
the eigenmodal
eigenmodal
basis.
measurement
was
made
in
the
closed-loop
configuration
we obtain
obtain the
the
basis.
Since
the
basis.Since
Sincethe
the measurement
measurement was
was made
made in
in the
the closed-loop
closed-loop configuration
configuration we
we
obtain
the
steady-state
modal
amplitudes.
Most
of
the
eigenmodes
are
damped
by
the
feedback
to
steady-state
steady-statemodal
modalamplitudes.
amplitudes.Most
Most of
of the
the eigenmodes
eigenmodes are
are damped
damped by
by the
the feedback
feedback to
the
noise
floor
with
the
notable
exception
of
eigenmode
0
oscillating
at
0.09
degrees.
the
the noise
noise floor
floor with
with the
the notable
notable exception
exception of
of eigenmode
eigenmode 00 oscillating
oscillating at
at 0.09
0.09degrees.
degrees.
This
mode
isis excited
excited
by
the
RF
noise
from
the klystron
klystron high-voltage
high-voltage
This
lowest-frequency
Thislowest-frequency
lowest-frequency mode
mode is
excited by
by the
the RF
RF noise
noise from
from the
the
klystron
power
The
fill
pattern
has
periodic
minigaps
which
act
to
alias
mode
every
power
supplies.
powersupplies.
supplies.The
Thefill
fill pattern
pattern has
has periodic
periodic minigaps
minigaps which
which act
act to
to alias
alias mode
mode 000 every
every
72
revolution
harmonics.
72
revolution
harmonics.
72 revolution harmonics.
SUMMARY
SUMMARY
SUMMARY
Amplitude
Amplitude (deg@RF)
(deg@RF)
Modification
in
combination
with proper
proper front-end
front-end
Modification of
of the
the comb
comb generator
generator length
length in
in combination
combination with
front-end and
and
back-end
have enabled
enabled PEP-II
PEP-II to
the mixed
mixed
back-end timing
timing procedures
procedures described
described here
here have
to use
use the
the
even/odd
optimize
luminosity. Under
Under these
even/odd ring
ring filling
filling patterns
patterns required
required to
to optimize
optimize luminosity.
these conditions
conditions
we
of
longitudinal
coupled-bunch instabilities
wehave
havedemonstrated
demonstratedfeedback
feedback stabilization
stabilization of
of longitudinal
longitudinalcoupled-bunch
instabilities
atatthe
thedesign
designbeam
beamcurrents.
currents.
0.1
0.1
0.08
O.06
0.06
0.04
0.02
-0.02
0
0
200
200
400
400
400
600
600
600
Mode
number
Modenumber
number
Mode
800
800
1000
1000
1000
1200
1200
FIGURE
modal
amplitudes
in
the LER
LER at
at 800
800 mA
mA
FIGURE9.
9. Average
Averagemodal
modalamplitudes
amplitudesin
inthe
481
REFERENCES
1. PEP-II: An asymmetric B factory, conceptual design report (1993).
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3. Barry, W., et al., "Design of the PEP-II transverse coupled bunch feedback system," in Proceedings of
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