Tune Measurement in RHIC1
M. Brennan, P. Cameron, P. Cerniglia, R. Connolly, J. Cupolo, W. Dawson, C. Degen,
A. DellaPenna, J. DeLong, A. Drees, D. Gassner, M. Kesselman, R. Lee, A. Marusic,
J. Mead, R. Michnoff, C. Schultheiss, R. Sikora, and J.Van Zeijts
Brookhaven National Laboratory, Upton, NY 11973, USA
Abstract. Three basic tune measurement methods are employed in RHIC; kicked beam, Schottky, and
phase-locked loop. The kicked beam and 2GHz Schottky systems have been in operation since the first
commissioning of circulating beam in RHIC in 1999. Preliminary PLL measurements utilizing a
commercial off-the-shelf lockin amplifier were completed during that run, and the resonant BPM used
in that system also delivered 230MHz Schottky spectra. With encouraging preliminary results and the
thought of tune feedback in mind, a PLL tune system was implemented in the FPGA/DSP environment
of the RHIC BPM system for the RHIC 2001 run. During that run this system functioned at the level of
the present state-of-the-art in tune measurement accuracy and resolution, and was successfully
incorporated into a tune feedback system for use during acceleration. Each of the tune measurement
systems has particular strengths and weaknesses. We present specific and comparative details of
systems design and operation. In addition, we present detailed tune measurements and their utilization
in the measurement of chromaticity and the implementation of tune feedback. Finally, we discuss
planned upgrades for the RHIC 2003 run.
Introduction
RHIC is a superconducting two-ring synchrotron, with the capability to
accelerate and store particle species ranging from protons to Gold. All species heavier
than protons must cross transition during acceleration. The effect of intra-beam
scattering (IBS) on emittance grows with the square of charge, so that for heavier
species such as Gold the luminosity lifetime at store is limited by longitudinal beam
loss out of the bucket due to IBS. Ramp rate requirements and hysteresis effects in the
superconducting magnets limit the machine cycle time from injection to store and
back to injection to a minimum of about 30 minutes under optimum conditions.
Without beam cooling, fast and efficient machine cycles are essential to maximize the
integrated luminosity. The primary requirement for tune measurement in RHIC is
defined by this need for fast and efficient machine cycles.
A variety of problems are encountered in the development of an acceleration
ramp. The first and most fundamental is that the machine model does not permit to
accurately set the tunes to a predetermined value, but rather that the tunes during a
ramp attempt must be measured and corrected, either by feedforward during the next
ramp attempt, or by tune feedback during acceleration. The situation is complicated by
the fact that lattice optics change up the ramp; due to aperture limitations beam is
injected with (5*=10, and beta squeeze in the IRs is accomplished during ramping. As
a result, when running without tune feedback a good many unsuccessful attempts,
1
Work performed under the auspices of the U.S. Department of Energy
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
134
often over the span of many weeks, have been required in the development of a
successful ramp, and a ramp remained successful only so long as machine conditions
didn't change.
Beyond the problem with model accuracy, which does not appear to be
surmountable in the foreseeable future, there are many additional problems to
overcome in ramp development. Early in the ramp there are fast changes in tune and
chromaticity due to snapback [1]. Through the ramp good chromaticity control is
essential, but not always present during ramp development. The head-tail instability
requires negative chromaticity below transition and positive above. Even with the
correct sign, large chromaticities are harmful, first because the fast decoherence makes
tune measurement difficult or impossible, and second because the large linewidth
results in resonance overlap and beam loss. Beam loss drives currents in pickup
electrodes, which often obscure beam signals at the time when measurements are most
needed. Transition crossing presents its own special set of problems for tune
measurement. The need for precise tune measurement to confirm the chromaticity sign
change is made more difficult by transverse size oscillations and beam loss in
dispersive regions (where the tune pickups are located) as a result of longitudinal
quadrupole oscillations following the phase jump. The dynamic range problem always
present in tune measurement (observation of the small difference signal at the betatron
frequency in the presence of the much larger signal due to beam offset and sum mode
at the revolution frequency) is sometimes aggravated by orbit changes at transition.
Coupling often complicates the measurement and interpretation of tune data. And
finally, there remain all the usual problems of data acquisition and processing,
integration with the control system, and operator friendliness. Each of the tune
measurements systems has its' own specific strengths and weaknesses in dealing with
the problems outlined above.
tune
small
timing con/
accuracy
chrom
req'd? incoh?
chrom on ramp?
coupling?
comments
need big kick
from inj oscillations
req'd?
BPMs
10^3
yes
ARTUS
10^3
yes
yes
con
decoh (sign?)
close approach
emittance growth
HFSchottky
10^3
no
no
incoh
sideband width
from line shape
continuous, non-pert
LFSchottky
10M
no
no
incoh
sideband width
line presence
continuous, non-pert
PLL
10^5
yes
no
incoh? 1 Hz radial mod
line presence
cont, non-pert, sensitive
QMM
?
?
no
incoh
Head-Tail
10^3
yes
yes
coh
no?
coh?
AC Dipole
con
inj matching, sensitivity?
data analysis?
parasitic to ARTUS
DXBPM electronics?
TABLE 1. Characteristics of various tune measurement methods.
135
The table above outlines characteristics of various tune measurement methods.
There has been experience with all these methods (except measurement of the
quadrupole moment) in the first two RHIC beam runs. The first five methods will be
discussed in greater detail in the following sections
The ARTUS System
The acronym ARTUS [2] is derived from "A Rhic Tune measurement
System". Betatron oscillations are excited with a fast transverse kicker magnet and
beam positions are recorded from a BPM. The fractional tunes are extracted by
performing a FFT analysis. The BPM assigned to the tune meter resides at a location
with high horizontal betatron function and moderately high vertical betatron function
(at the Q3 magnets at 2 o'clock). The capability of multiple turn-by-turn kicks is
included to ensure the needed signal amplitude at all beam energy settings. The
readout electronics and controls are installed in a VME crate in the 1002 service
building.
control room
tunnel
power supply
BPM
FIGURE 1. ARTUS block diagram
Each ring has two kicker modules with four 2-m stainless steel striplines,
allowing both horizontal and vertical kicks. The two kickers are connected in series to
provide 4 m of stripline. Each stripline subtends an angle of 70 degrees with an
aperture of 7 cm. The assembly is designed to give 50Q impedance when opposing
lines are driven in the difference mode. Single pulses can power each of the four
136
planes independently. The kick pulses are generated by fast
fast FET switches, producing
pulses that are approximately 140 ns long. Single bunch excitation is possible with
even up to 120 bunches per ring. All switches for all
all striplines in both rings
rings are
are
charged by one 5kV/2A power supply. The kick angle after
after one pulse with 3 kV
received by an ion going through
through the
the kickers
kickers isis approximately
approximately 10 jirad
µrad at
at injection
injection
energy (y^lO).
(γ≅10).
Figure
shows BPM
signal processing
Figure 11 shows
BPM signal
processing and
and kicker
kicker triggering.
triggering. The
The FET
FET
switches
are
triggered
by
a
TTL
pulse
of
200
ns
width
from
a
numerically-controlled
switches are triggered by a TTL pulse of 200 ns width from a numerically-controlled
oscillator (NCO)
(NCO) board. The NCO outputs pulses with the required phase and a
remotely settable
settable frequency
of up
up to 20 MHz. The phase and frequency
frequency of
frequency resolutions are
0.09 degrees and 11.6 mHz respectively. By selecting a NCO
NCO frequency
frequency close
close to
to the
the
betatron
betatron frequency
frequency the
the beam
beam is
is kicked
kicked resonantly,
resonantly, enhancing
enhancing the
the effect
effect on
on the
the beam
beam
significantly compared
with aa single
single kick.
significantly
compared with
kick. A
A set
set point
point equal
equal or
or very
very close
close to
to the
the
betatron
was shown
shown to
betatron frequency
frequency was
to kick
kick the
the beam
beam out
out of
of the
the ring
ring if
if the
the number
number of
of turns
turns
was too high. In order to control the total number of kicks, the NCO is triggered
synchronously with
sync trigger
synchronously
with the
the beam
beam using
using an
an in-house
in-house beam
beam sync
trigger VI24
V124 board.
board. Other
Other
channels
of
the
same
VI24
board
trigger
the
data
acquisition
from
the
channels of the same V124 board trigger the data acquisition from the BPM.
BPM. This
This
board
board allows
allows the
the tune
tune measurement
measurement to
to be
be triggered
triggered by
by any
any event
event broadcasted
broadcasted on
on the
the
beam
synchronous link
link or
or on
Thus the
beam synchronous
on demand.
demand. Thus
the tunes
tunes can
can be
be easily
easily correlated
correlated any
any time
time
with
with any
any other
other instrumentation.
instrumentation.
16
0-1B 0-20 0-22 O 24- 0 ZS D-ZB
FIGURE
ARTUS tune
FIGURE 2.
2. ARTUS
tune measurement
measurement during
during an
an acceleration
acceleration ramp
ramp
137
oze O-ZB
Figure 2 above shows ARTUS tune measurement results during an
acceleration ramp in September of 2001. Horizontal tune is in the left panel, and
vertical in the right. The beginning of the ramp is at the bottom of the figure, transition
is about 1/4 of the way up, and flat-top is at the top. Several interesting observations
can be made about this data. For the first 20% of the ramp the horizontal signal is
obscured by broadband noise due to beam loss, and the vertical signal is absent,
perhaps due to large chromaticity. When tune information does appear the horizontal
tune is brushing the 1/5 resonance, and the horizontal signal is stronger than the
vertical in the vertical spectrum. Horizontal tune again brushes 1/5 about 30% into the
ramp, and then the spectrum becomes broad and somewhat confusing until midpoint.
Shortly after midpoint horizontal tune sits on 1/5 for about 30 seconds, while vertical
briefly walks onto the 1/4 resonance. For most of the last quarter of the ramp
horizontal and vertical signals are virtually identical. The effect of coupling is
somewhat confusing here. Finally, it appears that the tunes cross shortly before the end
of the ramp. This ramp illustrates some of the difficulties of interpreting ARTUS
spectra, as well as the fact that tunes and chromaticities were not under control in
September, despite the fact that the run had been in progress for several months.
Improvements planned for the RHIC 2003 run include moving the kicker to a region
of higher beta, utilizing separate PUEs for horizontal and vertical to maximize pickup
beta in both planes, and modifying the analog front end to simplify timing.
The High Frequency Schottky System
Two high-frequency cavities from Lawrence Berkeley National Laboratory [3]
are used to detect Schottky signals from both beams. The transverse modes are TM120
and TM210 at 2.069±0.002GHz. They have measured Q of 4700, and are separated by
4 MHz. A longitudinal mode is at 2.741 GHz. The signals are down-converted to
2MHz and amplified in the tunnel, then transported to an external 10MHz bandwidth
FFT analyzer. Data is provided to the control system through Lab VIEW
communicating with the FFT analyzer via TCP, as well as through a remote Xterm
scope application.
The usefulness of the 2GHz Schottky system during acceleration of Gold
beams is limited by the large width and resulting overlap of the revolution and
betatron lines at and near injection energies, where the relativistic slip factor is large.
In addition, the 0.4% increase in RHIC revolution frequency during ramps results in
line movement of 8MHz at 2GHZ during the ramp, causing rapid sweeping of the
spectral lines across the 400KHz wide cavity resonance. The possibility of using a
beam-synchronous frequency for down conversion was investigated and discarded
because of bandwidth problems in the available frequency multiplier, and more
significantly because of the timing system interface required to implement the linehopping needed to track the cavity resonance as it would then sweep under the
stationary spectrum. A consequence was that averaging could not be used to decrease
noise during ramps. Solutions to the problems arising out of the non-stationary
spectrum were also hampered by limitations in the interface in the FFT analyzer,
138
which
rate of
of about
about 1Hz.
IHz. Within
Within the
the
which permitted
permitted transfer
transfer of
of spectra
spectra at
at aa maximum
maximum rate
limitations
of
available
memory,
some
of
these
deficiencies
could
be
overcome
by
limitations of available memory, some of these deficiencies could be overcome by
utilizing
the
FFT
analyzer
in
time
capture
mode.
In
this
mode
it
digitized
as
fast
as
utilizing the FFT analyzer in time capture mode. In this mode it digitized as fast as
possible
for
a
given
resolution
bandwidth,
then
replayed
the
capture
buffer
to
postpossible for a given resolution bandwidth, then replayed the capture buffer to postprocess
10 seconds
seconds of
of data
data could
could be
be
processthe
theFFT
FFToff-line.
off-line. In
In aa typical
typical ramping
ramping setup
setup about
about 10
saved
in
capture
mode.
Figure
3
shows
a
time
capture
of
the
first
successful
transition
saved in capture mode. Figure 3 shows a time capture of the first successful transition
crossing
crossingin
inRHIC.
RHIC.
FIGURE3.3. HF
HF Schottky
Schottky measurement
measurement of
of first
first successful
successful transition
FIGURE
transition crossing
crossing
Thehorizontal
horizontal axis
axis spans
spans aa spectrum width of 78.125KHz.
The
78.125KHz. The
The vertical
vertical axis
axis isis
time,the
thetop
topof
of the
the figure
figure is
is about Is
1s before transition, and
time,
and the
the bottom
bottom isis about
about 2s
2safter
after
transition.The
Therevolution
revolution line
line and betatron sidebands are
transition.
are sweeping
sweeping from
from upper
upper right
right toto
lowerleft.
left.The
The frequency
frequency sweeping
sweeping results
results from
from the
the fact,
lower
fact, as
as mentioned
mentioned above,
above, that
that the
the
local oscillator
oscillator used
used for
for down-conversion
down-conversion was
was not
not beam
beam synchronous.
synchronous. Two
local
Two sets
sets of
of
betatron sidebands
sidebands of
of unequal
unequal intensity
intensity appear,
appear, caused
betatron
caused by
by weak
weak coupling
coupling of
of the
the tunes.
tunes.
Attransition
transition the
the sidebands
sidebands cross
cross due
due to
to nonzero
nonzero chromaticity.
chromaticity. It
At
It isis clear
clear that
that the
the signs
signs
of
vertical
and
horizontal
chromaticity
were
opposite
at
transition.
The
broadband
of vertical and horizontal chromaticity were opposite at transition. The broadband
noise inin the
the Schottky
Schottky spectrum
spectrum after
after transition
transition has
has aa period
period of
noise
of 0.08
0.08 seconds,
seconds, which
which
corresponds
to
the
period
of
bunch
length
oscillations
observed
by
the
corresponds to the period of bunch length oscillations observed by the wall
wall current
current
monitor atat the
the same
same time.
time. These
These oscillations
oscillations were
just sufficient
monitor
were just
sufficient to
to drive
drive the
the tails
tails of
of
the
transverse
distribution
into
the
beampipe
walls
in
high
dispersion
regions
the transverse distribution into the beampipe walls in high dispersion regions
(including the
the location
location of
of the
the Schottky
Schottky cavities)
cavities) at
at times
times of
of maximum
(including
maximum intrabunch
intrabunch
momentum
spread,
causing
currents
that
excited
broadband
noise
momentum spread, causing currents that excited broadband noise in
in the
the cavity.
cavity. The
The
139
phenomenon
noise in
in the
the Schottky
Schottky spectrum
spectrum during
during beam
beam loss
loss isis
phenomenon of
of broadband
broadband noise
frequently
observed
at
RHIC,
for
instance
at
transition
in
Figure
4
below.
frequently observed at RHIC, for instance at transition in Figure 4 below.
FIGURE 4.
4. HF
HF Schottky
Schottky measurement
measurementof
oftune
tuneup
upthe
theramp
ramp
FIGURE
During
RHIC 2000
2000 aa Lab
LabVIEW
application that
that centered
centeredthe
therevolution
revolutionline
lineinin
During RHIC
VIEW application
each
and permitted
permitted visual
visual averaging
averaging of
of the
the resulting
resulting spectrogram
spectrogramwas
was
each raw
raw spectrum
spectrum and
created
partially circumvent
circumvent the
the FFT
FFT box
box difficulties
difficulties discussed
discussed above.
above.Figure
Figure44isisaa
created to
to partially
spectrogram
during aa complete
complete ramp
ramp from
from y^lO.3
γ=10.3 to
to y^70.
γ=70. The
Thevertical
verticalaxis
axis
spectrogram acquired
acquired during
frequency span of 78KHz, the
covers a frequency
the RHIC
RHIC revolution
revolution frequency,
frequency, so
so that
that only
only aa
single revolution line and set of betatron
single
betatron sidebands
sidebands are
are seen.
seen. The
The white
white horizontal
horizontal
lines are markers generated to indicate
indicate aa fractional
fractional tune
tune of
of 0.225.
0.225.The
Thebeginning
beginningofofthe
the
ramp is at the left
left of the figure.
figure. Betatron
Betatron sidebands
sidebands are
are not
not resolved
resolved until
until the
the
relativistic slip factor
factor becomes small about
about 30
30 seconds
seconds into
intothe
theramp.
ramp.All
Alllines
linesbecome
become
narrow as transition is approached, where
where by
by definition
definition the
therevolution
revolutionfrequency
frequencyisisthe
the
same for particles of differing
same
differing momentum.
momentum. Broadband
Broadband noise
noise isis observed
observedimmediately
immediately
following transition. Sidebands remain
remain clearly
clearly resolved
resolved until
until the
the end
end of
of the
the ramp,
ramp,
allowing easy measurement of tune. Note
the
asymmetry
between
sidebands
Note the asymmetry between sidebands ininthe
the
latter part of the ramp, indicating large
large chromaticity,
chromaticity, and
and the
the presence
presenceofoflines
linesfrom
from
both planes due to coupling. The betatron
width is
betatron line
linewidth
is quantitatively
quantitatively expressed
expressed [4]
[4] as:
as:
M = f00 ∆p/p
Ap/p[(n±v)T|
a
∆f
[(n + ν) η +
+ ξ]
where the
the revolution
where
revolution frequency
frequency fo~78KHz,
f0~78KHz, momentum
momentum spread
spread Ap/p~.001,
∆p/p~.001,harmonic
harmonic
number n~26500
n~26500 at
at 2.07GHz,
2.07GHz, tune
number
tune v~.23,
ν~.23, slip
slip factor
factor T|η varies
varies from
from -.008
-.008atatinjection
injection
to .002
.002 at
at store,
store, and
and chromaticity
chromaticity £ξ is
to
is typically
typically aa few
few units
units either
either positive
positive or
ornegative.
negative.
The chromatic
chromatic contribution
contribution to
The
to linewidth
linewidth adds
adds to
to the
the upper
upper sideband
sidebandand
andsubtracts
subtractsfrom
from
the lower.
lower.
the
140
In addition to the spectrogram displays of the previous figures, it has proven
useful [5] to construct stripchart displays of tune, chromaticity, momentum spread,
and transverse emittance as measured from the Schottky spectra.
Several improvements are planned for the RHIC 2003 beam run. Amplifier
saturation due to beam steering offsets and the effect of the 200MHz storage RF is
frequently encountered, and greatly diminishes the reliability of the data. Beam offsets
are present because of an aperture restriction that forces unconventional steering to get
good collisions at the adjacent IP. Efforts are underway to locate and remove the
obstruction. Sensitivity to beam loss might also be helped by this. An improved
VME/DSP based data acquisition system is planned to overcome the limitations of the
HP89410 DSAs. These instruments are good studies tools, but suffer from high cost,
poor data accessibility, and poor integration with the control and (perhaps more
significantly) timing systems. In addition, they seem to sometimes provoke networks
data storms. The improved controls and timing interface gained in the VME/DSP
based data acquisition system will permit tracking of the cavity resonance with a
beam-synchronous local oscillator, so that S/N can be straightforward improved with
signal averaging. Finally, improvements to chromaticity and emittance calculations are
planned.
The Low Frequency Schottky System
Initial motivation for the development of the LF Schottky came from
dissatisfaction with the comparatively poor frequency resolution of the HF Schottky
system. Implementing a resonant pickup at a frequency that is an order of magnitude
lower will result in momentum-dependent linewidths that are an order of magnitude
lower. The quarter-wave 50 ohm shorted striplines of a standard RHIC BPM were
resonated [6] in the lowest-order difference mode at ~240MHz by coupling them with
a half wavelength section of 3/8" heliax. Achieving optimal coupling (defined as
Qloaded = Qunloaded/2) to the quarter wave points was accomplished with a quarter
wave transmission line impedance transformation to 50 ohms. Fine tuning was
accomplished with capacitors at the end of additional quarter wave stubs. The
difference signal from a hybrid was filtered, amplified, and brought out of the tunnel.
Figure 5 shows data taken during a ramp when beam was lost shortly after
transition. The horizontal axis spans a spectrum width of 78.125KHz. The vertical axis
is time, with the top of the figure at the start of the ramp, and the bottom shortly after
transition. The revolution line is at the center. Unlike the HF Schottky, all lines are
clearly resolved at injection energy. Due to coupling, signals from both planes are
visible, and it appears that the tunes crossed a third of the way to transition. At
transition both tunes shift down, and chromaticities are the same sign and
approximately the same magnitude in horizontal and vertical. Sidebands around the
revolution line at transition are probably due to oscillation of the RF loops as beam
intensity drops below that required for stability. Sharp lines are also prominent at the
quarter and at .375. In general sharp resonance lines are most often observed at
frequencies that oddly enough correspond to the traditional British fractions, and the
amount of spectral power present correlates with beam loss. An accelerator physics
explanation of these lines is not yet available.
141
Improvements
Improvements to
to the
the LF
LF Schottky
Schottky for
for the
the RHIC
RHIC 2003
2003 beam
beam run
run are
are similar
similar to
to
those
those planned
planned for
for the
the HF
HF Schottky.
Schottky. Position
Position information
information from
from adjacent
adjacent BPMs
BPMs will
will be
be
used
used to
to center
center the
the moveable
moveable pickup
pickup on
on the
the beam,
beam, reducing
reducing dynamic range and
saturation
saturation problems.
problems. Sensitivity
Sensitivity will be improved by moving the pickup
pickup to a region
region of
of
higher
higher beta.
beta.
FIGURE 5.
5. LF
LF Schottky
Schottky measurement
measurement of
of tune
tune up
up the
the ramp
ramp
FIGURE
An improved
improved VME/DSP
VME/DSP based
based data
data acquisition
acquisition system
system is
is planned
planned to
to overcome
overcome
An
the constraints
constraints of
of the
the HP
HP FFT
FFT boxes.
boxes. Because
Because the
the signal
signal from
from the
the LF
LF Schottky
Schottky pickup
pickup
the
also used
used for
for tune
tune feedback
feedback and
and there
there was
was only
only aa single
single local
local oscillator,
oscillator, LF
LF Schottky
Schottky
isis also
spectra were
were not
not available
available simultaneously
simultaneously with
with PLL
PLL tune
tune measurements.
measurements. The
The signal
signal
spectra
will be
be split
split and
and separate
separate beam
beam synchronous
synchronous LOs
LOs will
will be
be available
available next
next run.
run. Finally,
Finally,
will
improvements to
to tune,
tune, chromaticity,
chromaticity, coupling,
coupling, and
and emittance
improvements
emittance calculations
calculations are
are planned.
planned.
The Phase
Phase Locked
Locked Loop
Loop Tune
Tune Measurement
Measurement System
System
The
The PLL
PLL utilizes
utilizes signals
signals from
from the
the LF
LF Schottky
Schottky pickup.
pickup. The
The primary
primary difficulty
difficulty
The
in constructing
constructing aa high
high sensitivity
sensitivity transverse
transverse pickup
pickup is
is the
the dynamic
dynamic range
range problem
problem that
that
in
results from
from trying
trying to
to see
see signals
signals at
at the
the Schottky
Schottky level
level in
in the
the presence
presence of
of the
the coherent
coherent
results
beam spectrum,
spectrum, which
which is
is typically
typically at
at least
least 100dB
the PLL
PLL tune
beam
lOOdB stronger.
stronger. In
In designing
designing the
tune
measurement
system
for
RHIC
2001
we
dealt
with
this
problem
in
several
ways.
We
measurement system for RHIC 2001 we dealt with this problem in several ways. We
placed
the
pickup
resonance
well
above
the
coherent
spectrum,
at
8.5
times
the
placed the pickup resonance well above the coherent spectrum, at 8.5 times the
28MHz acceleration
acceleration RF.
RF. We
We resonated
resonated only
only aa difference
difference mode
mode so
so that
that the
the sum
sum mode
mode
28MHz
142
coherent signal remaining at the pickup frequency would not enjoy enhancement of its
power by the Q of the difference mode. We utilized a moveable BPM so that the
remaining difference mode coherent signal at the revolution harmonic due to beam
offset could be minimized. We bandpass filtered the output of the BPM with a high-Q
cavity filter before the first stage of amplification to avoid saturation. And finally, we
employed a 1 KHz bandwidth high-Q filter at the baseband 78KHz input to the
digitizer to get rid of the revolution line ~15KHz away.
At the core of the PLL tune system is a custom numerically controlled
oscillator [7] sitting in VME and clocked from the 28MHz low level RF system. All
frequencies in the tune system are thus synchronous with the beam. To simplify the
discussion that follows, it is accurate only within the fractional portion of the betatron
tune at harmonic 3061. To this level of approximation, the output of the NCO is at
harmonic 96 of the 78 KHz revolution frequency. When the loop is locked and after
x32 frequency multiplication, the output of NCO C is at ~238MHz (i.e RFx8.5, or
harmonic 3060) plus the betatron frequency. These frequencies (harmonic 3060 and
harmonic 1) are mixed in a suppressed carrier single sideband modulator. The output
is at the betatron line above harmonic 3061, and is highpass filtered before entering a
10W class A amplifier. The output of the amplifier drives the 1m long 50 ohm kicker
striplines through a difference hybrid and about 100m of heliax into the tunnel. The
kicker excitation travels with the beam through the betatron-tune-dependent phase
shift between the kicker and the resonant pickup. Pickup output at 238MHz is
bandpass filtered, boosted by 30dB, and again transported via 100m of heliax to the
mixer, whose output is again at 78KHz. The signal is delivered to the high impedance
input of a Dynamic Signal Analyzer for FFT analysis and display, as well as to the 50
ohm input of the analog front end for amplification and filtering. By including the
betatron frequency in the local oscillator for up and down conversion, the tune signal
is always nominally at the same frequency (78KHz), and the need for a tracking filter
at the input to the digitizer is eliminated.
pickup
FIGURE 6. PLL/Tune Feedback Block Diagram
143
The
The digitizer
digitizer clock
clock isis generated
generated by
by aa divide-by-24
divide-by-24 in
in the
the gate
gate array
array of
of aa
modified RHIC
RHIC BPM
BPM module
module [8].
[8]. The
The 78KHz
78KHz signal
signal which
which isis up-converted,
up-converted, phase
phase
modified
shifted by
by the
the beam
beam tune
tune and
and down-converted,
down-converted, isis generated
generated by
by an
an additional
additional divide-bydivide-byshifted
to permit
permit aa simple
simple I/Q
I/Q demodulation
demodulation [9]
[9] of
of the
the signal.
signal. The
The data
data isis processed
processed in
in the
the
44 to
DSP of
of the
the BPM
BPM module.
module. The
The functions
functions performed
performed by
by the
the DSP
DSP include
include I/Q
I/Q
DSP
demodulation, phase
phase compensation
compensation during
during the
the frequency
frequency swing
swing of
of acceleration,
acceleration, loop
loop
demodulation,
gain/linewidth compensation
compensation during
during the
the relativistic
relativistic slip
slip factor
factor swing
swing of
of acceleration,
acceleration,
gain/linewidth
signal averaging/lowpass
averaging/lowpass filtering,
filtering, and
and NCO
NCO control.
control. The
The processing
processing is
is performed on
on
signal
blocks of
of data,
data, whose
whose length
length isis typically
typically 8KB.
8KB. Update
Update of
of the
the NCO
NCO is
is at
at around
around 30Hz.
30Hz.
blocks
The DSP
DSP communicates
communicates with
with VME
VME via
via IEEE1394.
IEEE1394. High-level
High-level control
control of
of the
the PLL
The
system isis accomplished
accomplished with
with aa MacIntosh
Macintosh running
running LabVIEW,
Lab VIEW, communicating
communicating with
with
system
VME via
via ethernet.
ethernet. The
The functions
functions performed
performed by
by the
the LabVIEW
Lab VIEW program
program include
include writing
writing
VME
setup parameters,
parameters, calculating
calculating and
and writing
writing the
the loop
loop lock
lock indicator,
indicator, and
and beam
beam transfer
transfer
setup
function (BTF)
(BTF)measurement.
measurement. BTF
BTF measurements
measurements were
were used
used to determine
determine the amount
function
of phase
phase shift
shift compensation
compensation required
required during
during ramping.
ramping. AA typical
typical BTF
BTF isis shown
shown in
in
of
figure 7.
7.
figure
FIGURE 7.
7. BTF
BTF atat Injection
Injection Energy
Energy
FIGURE
The revolution
revolution line
line isis the
the slight
slight disturbance
disturbance at
at the
the center
center of
of the
the image,
image, and
and its
The
smallness indicates
indicates that
that beam
beam was
was well
well centered
centered in
in the
the pickup.
pickup. The
The difference
difference in
in
smallness
linewidth between
between the
the upper
upper and
and lower
lower sidebands
sidebands indicates
indicates chromaticity
chromaticity was
was small
small and
and
linewidth
negative. What
What appears
appears to
to be
be fuzz
fuzz or
or noise
noise in
in the
the signal
signal is
is the
the structure
structure of the
negative.
synchrotron satellites.
satellites.
synchrotron
Figure 88 shows
shows horizontal
horizontal and
and vertical
vertical tune
tune as
as measured
measured by
by both
both the
the PLL
PLL and
and
Figure
Artus
during
a
ramp.
The
lower
black
continuous
trace
is
the
horizontal
PLL,
and
the
Artus during a ramp. The lower black continuous trace is the horizontal PLL, and the
blue
dots
that
overlay
it
are
Artus
measurements.
The
PLL
appears
unperturbed
while
blue dots that overlay it are Artus measurements. The PLL appears unperturbed while
Artus isis delivering
delivering instantaneous
instantaneous kicker
kicker power
power ~80dB
~80dB above
above the
the PLL
PLL excitation
excitation at
at
Artus
random phase
phase every
every two
two seconds.
seconds. The
The upper
upper red
red trace
trace isis vertical
vertical PLL,
PLL, and
and the
the green
green
random
dots are
are vertical
vertical Artus.
Artus. Agreement
Agreement between
between PLL
PLL and
and Artus
Artus isis generally
generally quite
quite good.
good.
dots
The left
left vertical
vertical scale
scale isis fractional
fractional tune.
tune. The
The right
right vertical
vertical scale
scale isis beam
beam intensity,
intensity, and
and
The
144
refers
It shows
shows significant
significant
refers to
to the
the blue
blue line
line that
that starts
starts at
at the
the upper
upper left
left of
of the
the image.
image. It
beam
loss
early
in
the
ramp,
which
is
probably
a
result
of
the
tail
of
the
horizontal
tune
beam loss early in the ramp, which is probably a result of the tail of the horizontal tune
distribution
crossing
the
1/5
resonance.
In
an
effort
to
measure
chromaticity,
during
distribution crossing the 1/5 resonance. In an effort to measure chromaticity, during
this
at 1Hz.
IHz. The
The modulation
modulation
this ramp
ramp the
the radial
radial beam
beam position
position was
was modulated
modulated by
by 200|i
200µ at
pattern
was
on
for
3
seconds,
then
off
for
3
seconds.
The
resulting
tune
modulation
pattern was on for 3 seconds, then off for 3 seconds. The resulting tune modulation is
is
clearly
this
clearly visible
visible near
near the
the end
end of
of the
the ramp
ramp in
in the
the horizontal.
horizontal. If
If one
one looks
looks closely
closely this
pattern
and vertical
vertical at
at other
other times
times in
in the
the ramp.
ramp.
pattern can
can also
also be
be discerned
discerned in
in both
both horizontal
horizontal and
A
A detailed
detailed analysis
analysis is
is presented
presented elsewhere [11]. The large variance in the PLL data in
the
the second
second half
half of
of the
the ramp
ramp is
is probably
probably due to a combination of high loop gain and
beam-beam
beam-beam tune
tune shift.
shift.
17:58:30
1?:!
———— qLoopTune.bh:tuneBuffM[.]2095 (YD
........... uertical,tune,,lst.peak.2095 <Y1>
—*—— bluDCCTtota!2095 (Y2>
FIGURE 8.
8. Artus
Artus and
and PLL
PLL tunes
FIGURE
tunes up
up the
the ramp
ramp
In addition
addition to
to beam-beam
beam-beam tune
tune shift,
In
shift, several
several other
other interesting
interesting features
features are
are
illustrated
in
the
ramp
of
figure
9.
At
the
time
of
this
ramp
a
hardware
problem
illustrated in the ramp of figure 9. At the time of this ramp a hardware problem (since
(since
corrected) existed
existed which
which caused
caused loop
loop phase
phase on
on aa given
given ramp
ramp to
corrected)
to be
be arbitrary
arbitrary modulo
modulo
π/2.
Autolock
was
initiated
by
setting
a
window
around
the
injection
tune
as
measured
Ti/2. Autolock was initiated by setting a window around the injection tune as measured
by Artus,
Artus, then
then sampling
sampling the
the phase
phase within
within that
that window
by
window with
with loop
loop gain
gain very
very high.
high. The
The
average sampled
sampled phase
phase was
was then
then taken
taken to
to be
be the
the beam
beam phase,
phase, the
average
the loop
loop gain
gain was
was turned
turned
down, the
the window
window was
was opened,
opened, and
and the
the loop
loop would
would lock.
down,
lock. On
On this
this particular
particular ramp
ramp the
the
initial vertical
vertical tune
tune from
from Artus
Artus was
was incorrect,
incorrect, and
and the
initial
the loop
loop locked
locked lower
lower when
when the
the
window was
was opened.
opened. Early
Early in
in the
the ramp,
ramp, as
as the
the lower
lower horizontal
horizontal tune
window
tune rose
rose and
and
approached the
the vertical,
vertical, the
the vertical
vertical lock
lock jumped
jumped to
to the
the opposite
opposite side
approached
side of
of the
the horizontal
horizontal
line, then
then jumped
jumped back
back as
as the
the horizontal
horizontal tune
tune moved
moved away.
line,
away. This
This is
is typical
typical of
of behavior
behavior
often seen
seen in
in the
the PLL,
PLL, namely
namely that
that itit is
is not
not stable
stable as
as the
the tunes
tunes approach
approach each
each other.
often
other.
Around 16:07
16:07 the
the effect
effect of
of beam-beam
beam-beam tune
tune shift
Around
shift appears
appears dramatically
dramatically in
in the
the vertical
vertical
as the
the collision
collision point
point of
of the
the unclogged
unclogged beams
beams sweeps
sweeps alternately
alternately into
as
into and
and out
out of
of the
the
145
intersection region.
region. At
At the
the same
same time
time the
the horizontal
horizontal signal appears to be smoothed.
intersection
This probably
probably is
is the
the result
result of very
very large chromaticity, which causes the beam transfer
This
function portion
portion of the loop gain to be small and lowers the loop bandwidth, giving
function
giving the
the
effect of
of low-pass
low-pass filtering.
filtering. The
The ramp
ramp ends
ends at
at about
about 16:07:30.
effect
16:07:30. The
The vertical
vertical tune
tune is
is then
then
chirped as
as the
the rings
rings are
are first
first cogged,
cogged, then
then un-cogged
un-cogged and
and slipped
slipped to
to properly
properly align
chirped
align the
the
abort gaps,
gaps, then
then re-cogged.
re-cogged. Beam-beam
Beam-beam tune
tune shifts
shifts throughout
throughout are
abort
are about
about .002.
.002.
• desiredTune.bht*]
• qLoopTune.bv:tuneBuffM:valueflndTime[*]
• qLoopTune.bh:lockBuffM[*]
• desiredTune.bvM
• qLoopStren9th.bf:deltaStren9thBuffM:walueflndTiine[*]
• qLoopTune.bvllockBuffML*]
———— qLoopTune.bh:tuneBuffM:valueflndTiine[*]
qLoopStrength.bd^eltaStrengthBuffMrualueflndTimei:*]
FIGURE 9.
9. A
A ramp
ramp illustrating
illustrating several
several features
features of
of PLL
PLL measurement
FIGURE
measurement
Tune Feedback
Feedback
Tune
The tune
tune feedback
feedback control
control loop
loop [11,12]
[11,12] is
is implemented
implemented as
The
as aa digital
digital control
control loop
loop
running in
in aa power
power PC
PC Front
Front End
End Computer
Computer in
in VME.
VME. The
The horizontal
horizontal and
running
and vertical
vertical tunes
tunes
are converted
converted to
to horizontal
horizontal and
and vertical
vertical strengths
strengths through
through aa matrix
matrix that
that relates
relates the
are
the
desired tune
tune change
change to
to strengths.
strengths. The
The horizontal
horizontal and
and vertical
vertical strengths
not
desired
strengths are
are not
independent since
since this
this matrix
matrix contains
contains cross
cross terms.
terms. These
independent
These strengths
strengths are
are then
then used
used to
to
calculate
the
required
magnet
currents.
As
shown
in
the
block
diagram
of
figure
calculate the required magnet currents. As shown in the block diagram of figure 4,
4,
magnet coefficients
coefficients are
are calculated
calculated in
in the
the Front
Front End
End Computer
Computer local
local to
to the
the PLL
PLL tune
tune
magnet
measurement, then
then transported
transported via
via reflected
reflected memory
memory and
and aa dedicated
dedicated fiber
measurement,
fiber optic
optic line
line to
to
the
power
supply
building
600m
away,
where
quadrupole
currents
are
written
the power supply building 600m away, where quadrupole currents are written to
to the
the
power supplies
supplies via
via the
the Real
Real Time
Time Data
Data Link.
Link.
power
Data
from
the
first
successful
ramp
with tune
tune feedback
feedback is
Data from the first successful ramp with
is shown
shown in
in figure
figure 10.
10.
As in
in figure
figure 7,
7, the
the vertical
vertical scale
scale at
at the
the right
right and
and the
the blue
blue trace
trace correspond
correspond to
to beam
beam
As
current. Losses
Losses early
early in
in the
the ramp
ramp do
do not
not differ
differ much
much from
current.
from those
those in
in figure
figure 8,
8, and
and are
are
probably due
due again
again to
to large
large horizontal
horizontal tune
tune spread
spread overlapping
overlapping the
the 1/5
1/5 resonance.
resonance. The
probably
The
146
large excursion in vertical about one third the way up the ramp was due to a power
large
large excursion
excursion in
in vertical
vertical about
about one
one third
third the
the way
way up
up the
the ramp
ramp was
was due
due to
to aa power
power
supply problem, and resulted in about 15% beam loss. Without tune feedback the ramp
supply
supplyproblem,
problem, and
andresulted
resulted in
in about
about 15% beam
beam loss. Without
Without tune feedback the ramp
would
would
would
11:52:55 11:53:05 11:53:15 11:53:25 11:53:35 11:53:45 11:53:55 11:54:05 11:54:15 11:54:25 11:54:35 11:54:45 11:54:55 11:55:05 11:55:15
FIGURE
tune feedback
feedback
FIGURE10.
10. First
Firstsuccessful
successful ramp
ramp with
with tune
FIGURE
10.
First
successful
ramp
with
FIGURE11.
11. Down-ramp
Down-ramptune
tune and
and chromaticity
chromaticity from
from HF
HF Schottky
Schottky
FIGURE
11.
Down-ramp
tune
and
FIGURE
from
Schottky
147
have aborted at this point. Tune feedback was attempted on four additional up-ramps
before the end of the run, with one failure in the final second of the ramp due to
excessively large horizontal chromaticity.
Near the end of the polarized proton run the greater portion of a shift was
devoted to down-ramps. The motivation was to decelerate polarized beam and remeasure polarization at injection energy, where the analyzing power of the p-Carbon
polarimeter is known, to get a lower limit on polarization at lOOGeV, where the
analyzing power is not known. Figure 11 shows data from the horizontal HF Schottky
during an attempted down-ramp. The ramp begins at the discontinuity near the top of
the image. Tune regulation is good for the first half of the ramp. As chromaticity gets
large and coupling appears the combination of reduced BTF/ loop gain and phase
information from the opposite plane causes tune control to suffer. The huge
chromaticity becomes evident from the striking difference in upper and lower
sideband widths. Perhaps the most interesting aspect of the down-ramp effort was that
it revealed a divergence in the view of just what kind of tool one possesses in the
PLL/tune feedback, and how this tool might best be used. The controversy arose over
whether tune feedback is a ramp development tool, or a control that is engaged after
the ramp development effort is complete. The bulk of the effort was done without tune
feedback, and down-ramps were not successful. The benefits of this failure were that
the importance of chromaticity in tune feedback became evident to all, and clear
thought was stimulated on the nature of tune feedback as a ramp development tool.
Several improvements in PLL/tune feedback are planned for RHIC 2003. The
system will benefit from the pickup improvements mentioned in the LF Schottky
section. In ramp development emittance growth is a secondary concern, so rather than
kicker excitations of less than IW that were typical of RHIC 2001, the full 10W of
amplifier power can be applied. Kickers are also being moved to a region of larger
beta to better utilize the available kicker power. To coherently kick all bunches in a
multi-bunch fill, the excitation frequency must be Q+v (sum of integer and fractional
tunes) plus an integer multiple of the bunching frequency [13]. This condition was not
observed during the last run, will be observed during the next, and will result in more
efficient excitation (and may remove some ambiguities in phase). Moving beyond
pickup and kicker improvements, the BPM module-based data acquisition system will
be replaced with a VME-based FPGA/DSP system. Baseband frequency will be
shifted from 78KHz to 455KHz, permitting the use of easily available very sharp
ceramic filters to remove the adjacent revolution line, as well as resulting in an
additional 6dB of processing gain. Improved digital filtering will be implemented. The
VME-based system will permit operation from the control room rather that the
diagnostics building, improving communications and accelerating the development of
operator familiarity. Finally, a considerable effort is underway to model system
behavior, including PLL behavior in Matlab and beam behavior via UAL [14].
Summary
A variety of sophisticated tune measurement systems exist in RHIC. This is the
result of significant effort by a great many individuals over the span of several years,
and that effort continues in the form significant improvements for the coming beam
148
run. The plan for RHIC 2003 is to commission the machine from day one with tune
feedback. This will require the best possible operation of all tune, chromaticity, and
coupling measurement systems.
Acknowledgements
The authors would like to express their gratitude to the many individuals who
supported the design, development, and operation of the systems described in this
paper. We are particularly grateful to Mike Harrison for his initiative in the
collaboration with Berkeley to create the HF Schottky system, and to Tom Shea for his
excellent accomplishment in building the foundation for RHIC Beam Instrumentation.
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1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
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EPAC2002, Paris.
P. Cameron et al, "Tune Feedback at RHIC", PAC2001, NY.
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149