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COUPLED BUNCH MODE ZERO CORRECTION WITHINTHE ORBIT FEEDBACK BANDWIDTH ∗P. Kallakuri† , A. Brill, J. Carwardine, L. Emery and N. Sereno
Argonne National Lab, Lemont, USA
Abstract
The fast orbit feedback (FOFB) bandwidth for Advanced
photon source upgrade (APS-U) will be DC-1 kHz and thesynchrotron frequency will be between 100-560 Hz. Thisfrequency overlap places coupled bunch mode 0 (CBM0)
induced horizontal orbit motion inside the orbit feedback
bandwidth, potentially affecting our ability to achieve beamstability goals. Longitudinal feedback kicker is not strong
enough to damp CBM0 oscillations. We developed new
beam-based feedback method to suppress CBM0 oscillations with low level RF phase as actuator. It uses existent
FOFB framework with no changes to the feedback algorithm.
Effectiveness of this method is verified using present APS
operations lattice where synchrotron frequency is outside
orbit feedback bandwidth. In the present work, low alpha lattice is created to emulate APS-U setting where synchrotron
frequency is inside the orbit feedback bandwidth. Experiments with this lattice successfully demonstrated CBM0
correction within orbit feedback bandwidth. Combined operation of orbit feedback and CBM0 correction is stable, and
CBM0 oscillations are damped. We achieved better orbit
motion suppression and corrector drive efforts are reduced
as well.

This is a preprint — the final version is published with IOP

INTRODUCTION
The target bandwidth of the Advanced Photon Source Upgrade (APS-U) Fast Orbit Feedback (FOFB) is DC-1000 Hz
where the synchrotron tune will be between 100-560 Hz.
This overlap places Coupled Bunch Mode 0 (CBM0) induced horizontal position offsets within the FOFB bandwidth range, affecting APS-U goals for beam stability. Largestorage-rings such as APS would need longitudinal feedback
system with high kick voltage capability for CBM0 suppression. APS-U longitudinal feedback kicker is not strong
enough to damp CBM0 oscillations. We developed new
orbit to RF phase feedback method using existent orbit feedback framework with no additional processing hardware
requirements [1]. It operates at the Low Level RF (LLRF)
signal level of the main RF system and does not require highkick voltages. Based on synchrotron oscillation theory [2,3],
we derived relationship between beam position deviation
at dispersive BPMs and RF phase noise that represents theopen loop dynamics of our feedback configuration. An analytical model is devised for the coupling mechanism ofsynchrotron oscillations to transverse orbit through dispersion. It allows an energy-induced component to be extracted∗ Work supported by the U.S. Department of Energy, Office of Science,

under Contract No. DE-ACO2-O6CH11357.

† pkallakuri@anl.gov

from the measured orbit which is derivative of the RF phaseerror. Using this the orbit feedback controller generates a
RF phase control signal as another drive signal in the orbit
feedback algorithm. Experiments conducted at the present
APS storage ring using 7 GeV operations lattice and APS-U
prototype fast orbit feedback controller [4, 5] demonstrated
the effectiveness of this method at damping coupled bunchmode zero oscillations.
In the above experiments [1] the synchrotron frequency(2.2 kHz) and orbit feedback bandwidth (920 Hz) are well
separated. We continued our study using low-alpha latticeconfiguration developed to mimic APS-U setting where,
synchrotron frequency (60 Hz) is within the orbit feedback
bandwidth (90 Hz). We would be able to study the interaction of both feedbacks more clearly in this setup. The
storage-ring energy is set to 6 GeV and low momentum
compaction factor of 3.6 · 10−06 is used to get synchrotron
frequency to around 60 Hz. Orbit feedback with 1.5 kHz
sampling rate used for APS operations is termed as RealTime Feedback (RTFB) [6]. Experiments with low-alphalattice are conducted using RTFB system so that we would
be able to use 38 fast correctors and 154 BPMs around thering. With the prototype system we could only use 3 fast
correctors and 12 BPMs in 2 sectors that is not adequate todeal with larger noise seen in low-alpha lattice. Details of
our experimental setup with RTFB controller, closed loop
performance of orbit to RF phase feedback, and results fromthe simultaneous operation of RTFB and CBM0 correction
with low alpha lattice are presented in next sections.

EXPERIMENTAL SETUP
Closed loop schematic of RTFB together with orbit to
RF phase feedback is shown in Figure 1. RTFB controller
hardware only allows use of total 160 BPMs (4 per sector)
for orbit feedback computations. We used 154 BPMs forbeam position measurements. Orbit feedback uses 38 horizontal fast correctors, and orbit to RF phase feedback is
integrated into RTFB framework by repurposing fast corrector (S40A:H3) analog drive signal as phase drive. DAC
output channel of S40A:H3 is connected to LLRF system [7]phase input. The cavity phase loop bandwidth is adequately
greater than the synchrotron oscillation frequency. So the
RF system is considered as simple gain term in the feedback model. PID_rtfb controller is used orbit correction and
PID_rfPh controller is used for CBM0 correction. Samefeedback algorithm that generates corrector power supply
set-points is used for phase drive. Phase computations areincorporated as additional row in Inverse Response Matrix(IRM) dot product. Horizontal BPM position vector x is

MO2C0308 Feedback Systems and Beam Stability

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BPM
setpoints-

BPM
errorsBPM
positions

Corrector IRM(38x154)
Phase IRM
(1x154)S2A:H3
to
S39A:H3
Corrector Errors

S40A:H3
Phase Drive

PID_rfPh

To LLRFsystemphase input

Drive Gain Gd(Current to Phase)Transfer function
rf phase to beam
Dispersion(154x1)S2A:H3
to
S39A:H3
Corrector Drives

PID_rtfb

S40A:H3
Phase Error

Corrector RM(154x38)
To corrector
magnet power
supplies

Corrector power supply+ Corrector magnet+ Vacuum chamber

180 1 𝜔𝑟 𝑓 𝛼𝑐𝜂𝜋 𝐺𝑑 𝜂 · 𝜂(1)

1
Drive gain 𝐺 𝑑 = 13
is to convert phase drive in amperes
to RF phase set-point in degrees. Phase IRM (1x154) computed from Eq. (1) and Corrector IRM (38x154) obtained
from orbit response matrix are concatenated as 39x154 IRM
used in the experiments. For beam-based studies we used
6 GeV low alpha lattice with storage-ring current of 14 mA
in 24 bunch operation and 24 mA in 48 bunch operation.
Relatively low currents are used since it was very difficult
to inject into this lattice. So, beam loading is negligible.

CBM0 Correction in Closed Loop Operation
After testing the open loop drive setup, studies are conducted with closed loop orbit to RF phase feedback configuration using 1x154 phase IRM. The storage ring configuration for this test is 24 bunches, 14 mA, 6 GeV low alphalattice with synchrotron frequency at 60 Hz. Closed loop

20 A Phase Drive Step Input
20
10
0

0.4

0.5

0.6

0.7

156

154

1.6 deg
RF Phase Step Change

152

0.4

0.5

0.6

0.7

Time (s)Figure 2: Open loop phase step response measured for 20 A
input step amplitude.
is stable with negative proportional gain and we achieved
suppression around synchrotron frequency. We tested 𝐾 𝑝
gains in the range -0.01 to -0.06, the beam was unstablebeyond -0.06. Motion at 360 Hz.

ORBIT TO RF PHASE FEEDBACK
FOR CBM0 CORRECTIONFirst step in our experiments is to establish LLRF phase
set-point control from RTFB controller in open loop, andthen verify the stability of orbit to RF phase feedback andsuppression of synchrotron frequency magnitude in closed
loop. For open loop measurements S40A:H3 drive signal is
the input, and beam phase response is the output. Figure 2
shows the step input to phase drive, and measured beamphase response. Input step of 20 A resulted in 1.6◦ change
1in RF phase response confirming drive gain 𝐺 𝑑 = 13
. Large360 Hz noise from klystron power supply is seen in the steadystate RF phase.

30

0.25
Orbit to RF phase FB loop

Open Loop
Closed loop, Kp = -0.02
Closed loop, Kp = -0.04
Closed loop, Kp = -0.06

0.2
0.15
0.1

Cumulative AC rms
S28A:P2X bpm error

0.05
0

0.02

0.1

1

10

60 120 360 1000

Frequency (Hz)Figure 3: Orbit motion measured in open loop, and closed
loop with different proportional gain values.
Figure 3 shows square root integrated Power Spectral
Density (PSD) of BPM error for open loop and closed loopwith different 𝐾 𝑝 gain values. Orbit motion suppression atsynchrotron frequency (60 Hz) is observed when the feedback is ON. Increase in proportional gain resulted in more
suppression at synchrotron frequency.

MO2C038

08 Feedback Systems and Beam Stability

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𝑃ℎ𝑎𝑠𝑒_𝐼 𝑅𝑀 =RF Phase (deg)obtained from 154 BPMs. Phase error is calculated as dot
product of measured orbit and weighted dispersion vector
Phase_IRM as defined in Eq. (1). 𝛼𝑐 is the momentum compaction factor, 𝜔𝑟 𝑓 is RF angular frequency, and 𝜂 is thedispersion vector.

S40A:H3 Drive (A)Figure 1: Experimental setup for simultaneous operation of RTFB and orbit to RF phase feedback using APS RTFB system.

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REAL TIME FEEDBACK WITH COUPLEDBUNCH MODE ZERO CORRECTION
Next step in our experiments is to study interaction between CBM0 correction and RTFB during the simultaneous
operation of both feedbacks.The test configuration is 6 GeV
low alpha lattice with 48 bunches and 24 mA storage-ringcurrent. Synchrotron frequency 60 Hz is within the orbit
feedback bandwidth of 90 Hz emulating APS-U settings.
0.07

Integrated PSD (mm2)0.06Open loop
CBM0 correction only
RTFB only
RTFB + CBM0 correction

0.05
0.04
0.03
0.02
0.01
0

30

60

120

240

360

600

Frequency (Hz)Figure 4: Comparison of cumulative mean square orbit motion at S28A:P2X BPM for different feedback configurations.

This is a preprint — the final version is published with IOP

Closed loop with unified 39x154 IRM is stable with proportional controllers. For RTFB we used 𝐾 𝑝 gains in therange 0.01 to 0.03, and for orbit to RF phase feedback weused 𝐾 𝑝 gains in the range -0.01 to -0.05. For individual
operation optimum performance is achieved with maximum
permissible 𝐾 𝑝 gains in each case. For simultaneous operation we tuned the gains together for optimum performance.
For RTFB 𝐾 𝑝 = 0.02, and for CBM0 correction 𝐾 𝑝 = −0.03
are the optimal gains. The angle between dispersion and betatron closed orbits with 154 BPMs are in the range 83 − 97◦
which is comparable to 440 BPMs case shown in Ref. [1].

We are working on a simulation study to further understandwhether this near orthogonality is inferring complete decoupling when both corrections has a frequency overlap. BPM
noise response data is measured for different feedback configurations: open loop, CBM0 correction only 𝐾 𝑝 = −0.05,
RTFB only 𝐾 𝑝 = 0.03, RTFB 𝐾 𝑝 = 0.02 + CBM0 correction 𝐾 𝑝 = −0.03. Integrated PSD of BPM error in different
feedback configurations is shown in Figure 4. Open loop
orbit motion shows significant spike at 60 Hz, which is suppressed in all three closed loop configurations: RTFB only,
CBM0 correction only, and RTFB + CBM0 correction. During individual operation, orbit to RF phase feedback and
RTFB are correcting respective energy and betatron components at synchrotron frequency which resulted in partial
suppression at 60 Hz. High frequency motion beyond 90 Hz
is amplified during RTFB only operation. Motion at 120 Hz
is amplified when only CBM0 correction is used. With both
feedbacks running together we got significant suppression
at 60 Hz due to the combined effect. Also, high frequency
motion amplified by individual feedback operation is attenuated up to ≈220 Hz. Motion at 360 Hz is not suppressedby orbit to RF phase feedback. Perturbation at 360 Hz is inphase with RF phase modulation whereas perturbation atsynchrotron tune is 90° out of phase. So, we would needlarge controller gains to affect 360 Hz which could be beyond
the stability limit of synchrotron frequency damping.
BPM responses are measured at all 154 BPMs around thestorage-ring to analyze envelope of the orbit motion. Figure 5 shows power spectral density plots of measured BPM
errors in open loop and different closed loop configurations.
All BPM responses showed similar frequency response pattern, while BPMs in the high dispersion area has larger
magnitudes compared to others. Individual operation of
RTFB or CBM0 correction partially suppressed 60 Hz andfrequencies beyond 90 Hz are amplified. During combined

Figure 5: PSD of BPM errors at all 154 BPMs around the storage ring. Comparison of responses in open loop and different
closed loop configurations.

MO2C0308 Feedback Systems and Beam Stability

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operation significant suppression at 60 Hz and better orbit
motion suppression up to 240 Hz is achieved. APS RF system has noise at 360 Hz and other 60 Hz harmonics. Thesefrequencies have larger amplitudes in low alpha lattice configuration. Hence narrow resonant increase of noise at 60 Hz
harmonics is seen when high frequency motion is amplified
during individual and combined feedback operation.

Analysis of Feedback Control Efforts
Feedback control effort is the input to the actuator fromthe dynamic controller to perform necessary correction. Reduction in control efforts is beneficial to the feedback operation.The corrector and phase drive signals in our caseindicate the control efforts. In order to analyze the drive
efforts of both feedbacks we used cumulative mean squareof phase and 38 corrector drive signals. Integrated PSDsof drive signals during individual operation of each feedback and combined operation of both feedbacks are shownin Figure 6. Drive magnitudes during individual operation

CONCLUSIONS
We successfully demonstrated CBM0 correction within
the orbit feedback bandwidth. We used 6 GeV low-alpha lattice that provides a test setup where synchrotron frequency(60 Hz) is within the RTFB bandwidth (90 Hz) similar to
APS-U configuration. First, we established LLRF phase
set-point control from RTFB controller open loop and thenverified the stability in closed loop. Orbit to RF phase feedback loop is stable and we achieved suppression aroundsynchrotron frequency. Closed loop operation with both
feedbacks using unified corrector and phase IRM is stablewith proportional controllers. During individual operation,
orbit to RF phase feedback and RTFB are correcting respective energy and betatron components at synchrotron frequency which resulted in partial suppression at 60 Hz. Orbit
feedback was effective at reducing motion at synchrotron
frequency, but did so at the expense of increasing broadband
rms motion beyond the open-loop level. This was consistent
with previous RTFB operating experience. Running CBM0
correction on its own also reduced motion at synchrotron
frequency and without increasing the broadband rms motion.
The combination of CBM0 correction and RTFB was significantly more effective than RTFB alone over all frequency
bands from DC to 360 Hz. Feedback drive efforts are also
reduced during combined operation of RTFB and CBM0
correction.

ACKNOWLEDGEMENTS
We are grateful to U.Wienands for the valuable insights.
We wish to thank T. Berenc, S. Xu, S. Shoaf, R. Blake, H.
Bui, and T. Madden for helping with experiments; V. Sajaev
for the help with low alpha lattice setup.

REFERENCES[1] P. Kallakuri, A. Brill, J. Carwardine, and N. Sereno, “Coupled
bunch mode zero correction using orbit measurements and RF
system phase feedback”, in Phys. Rev. Accel. Beams, vol. 25,
pp. 082801, 2022.
doi:10.1103/PhysRevAccelBeams.25.082801

Figure 6: Comparison of drive efforts of each feedback individual operation with drive efforts in simultaneous operation.
are larger compared to simultaneous operation. During individual operation the feedbacks see large error at synchrotron
frequency which results in more drive effort as the feedback
keeps trying to correct the error. When CBM0 correction
and orbit feedback are operated together both energy andbetatron components are corrected simultaneously, and theerror will be small. As a result phase and corrector drive
magnitudes for frequencies below 120 Hz are significantly
reduced in combined operation, and drive magnitudes up
to Nyquist frequency are also less compared to respective
individual operations. From these results we can say thatthe combined operation is aiding in control effort reductionof both feedbacks.

[2] W. Ormond and T. Rogers, “Synchrotron Oscillation Driven
by RF Phase Noise”, in Proc. PAC’97, Vancouver, Canada,
May 1997, paper 4V038, pp. 1822–1824.
https://jacow.org/pac97/papers/pdf/4V038.PDF[3] H. Wiedemann, Particle Accelerator Physics, 4th ed., Springer,
2015, ISBN: 978-3-319-30759-6.
[4] N. Sereno et al., “Beam Stability R&D for the APS MBA Upgrade”, in Proc. IPAC’15, Richmond, VA, USA, May 2015, pp.
1167–1169. doi:10.18429/JACoW-IPAC2015-MOPWI011[5] P. S. Kallakuri, A. R. Brill, J. Carwardine, and N. Sereno,“Closed Loop Modeling of the APS-U Orbit Feedback System”,
in Proc. NAPAC’19, Lansing, MI, USA, Sep. 2019, pp. 683–
686. doi:10.18429/JACoW-NAPAC2019-WEPLM11[6] J. Carwardine and F. Lenkszus, “Real-time orbit feedback at
the APS”, in Proc. BIW’98, Palo Alto, CA, USA, May 1998.
[7] J. J. Song et al., “Review of the APS SR RF Systems”, in Proc.
APAC’98, Tsukuba, Japan, Mar. 1998, paper 6D036, p. 767.

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08 Feedback Systems and Beam Stability

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