Coupled bunch mode zero correction within theOrbit feedback bandwidth

Pavana Sirisha Kallakuri
N. Sereno, A. Brill, J. Carwardine, L. Emery2023 International Beam Instrumentation Conference
11 Sept 2023
Work supported by the U.S. Department of Energy, Office of Science, under Contract No. DE-ACO2-O6CH11357.

Motivation§ The Advanced Photon Source Upgrade (APS-U) project at the Argonne National Laboratory will replace theexisting 7-GeV, double bend storage ring lattice with a new 6-GeV hybrid 7 bend achromat lattice.
§ Coupled bunch mode 0 (CBM0) oscillations where energy oscillations of all bunches are in-phase with eachother, induce horizontal orbit motion at synchrotron frequency.
§ The Fast orbit feedback (FOFB) bandwidth in APS-U will be DC-1000 Hz while the synchrotron frequency
will lie anywhere between 100 and 560 Hz.
– This frequency overlap places CBM0 induced horizontal position offsets within the orbit feedback
bandwidth range, potentially affecting our ability to achieve APS-U goals for beam stability.
§ Large storage-rings such as APS (1.1-km circumference) would need longitudinal feedback system with highkick voltage capability for CBM0 suppression.
– APS-U longitudinal feedback kicker is not strong enough to damp CBM0 oscillations.

2Introduction§ New orbit to RF phase feedback configuration to suppress CBM0 oscillations,– Beam position measurements at dispersive bpms are dynamic inputs– Low level RF (LLRF) phase is used as actuator– Orbit feedback controller generates RF phase setpoint using energy induced component extracted frommeasured orbit.

§ Proof of concept experiments using 7 GeV operations lattice1– Synchrotron frequency is outside the orbit feedback bandwidth– Demonstrated orbit feedback operation together with CBM0 correction in experiments and simulations§ Experimental study with 6 GeV low-alpha lattice configuration– Synchrotron frequency is inside the orbit feedback bandwidth resembling APS-U– Demonstrated CBM0 correction within the orbit feedback bandwidth

1. P. Kallakuri et al., PRAB 25, 082801

3Proposed orbit to rf phase feedback configuration§ Feedback model to suppress CBM0 oscillations is developed based on synchrotron oscillation theory.
§ Derivative of phase error is computed using dispersion and measured position at dispersive bpms,𝑑∅𝜼⋅𝐱= 𝜔!" 𝛼#… (1)𝑑𝑡𝜼⋅𝜼(!" )#*⋅'*⋅*-Phase error!∅

PIDController

Phase drive!#+& BPMs
Position vector!

'(#)

Dispersion

Disturbances!(#)
H(s)"($)
Θ($) Transfer function rf phase to beam

rf phase
setpoint𝐱- Horizontal position deviation

𝜼- Dispersion

Φ- Beam phase𝜔!" - RF frequency𝛼#- Momentum compaction factor

𝛼%- Damping rate𝛺- Synchrotron frequency

𝜃- RF phase noise

Closed loop schematic of proposed orbit to RF phase feedback method§ Transfer function from rf phase noise to beam position deviation represents the open loop dynamics.
– Under damped harmonic oscillator with resonant peak at synchrotron frequency.
Ω$𝑠
𝐻 s =… (2)𝜔!" 𝛼# 𝑠 $ + 2𝑠𝛼% + Ω$
4

Experimental setup – Orbit feedback controller with RF actuator
Orbit Feedback Controller
BPM
setpoints-Corrector Errors

BPM
errorsCorrector IRM
Phase IRM

BPMpositions

Phase Error

Phase Drive

PID_rfPhTransfer function
rf phase to beamDispersion

Corrector Drives

PID_OFB

Drive Gain Gd(Current to Phase)

Corrector RM

Accelerator

Corrector power supply+ Corrector magnet+ Vacuum chamber

To LLRFsystemphase input
To corrector
magnet powersupplies§ Orbit feedback algorithm used for corrector drives is used to generate RF phase setpoints.
§ Phase computations are incorporated as an additional row in Inverse Response Matrix (IRM) dot product.
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Proof of concept experiments with operations lattice
Synchrotron frequency outside orbit feedback bandwidth1§ Coupled bunch mode zero correction is demonstrated using,– APS-U prototype FOFB system with 22.6 kHz sampling rate, 4 fast correctors and 12 BPMs.
– Operations lattice where synchrotron frequency (2.2 kHz) is outside the FOFB bandwidth (920 Hz).
-10-20Open Loop
Closed Loop, K d = -5e-6

Sqrt Integrated PSD ( m)BPM position x (dB)

15

Closed Loop, K d = -2e-5
Closed Loop, K d = -4e-5-30
Synchrotron
Frequency-40-50
300

800

1300

1800

2150

2500

2900

Frequency (Hz)Chirp responses showing synchrotron frequency suppression

12Open LoopFOFB only
FOFB + CBM0 correction

S28A:P0X

Orbit motion at sychrotron
frequency suppressed during
simultaneous operation

96300.1

10360

2200 9000

Frequency (Hz)Comparison of measured AC rms orbit motion§ Achieved significant suppression around synchrotron frequency with orbit to RF phase feedback.
§ Stable FOFB + CBM0 correction• Retained 920 Hz orbit feedback bandwidth. Motion at 360 Hz is not affected.
1. P. Kallakuri et al., PRAB 25, 082801

6Simulation model for prototype FOFB + CBM0 correction1§ Developed a MATLAB/simulink model for prototype FOFB+CBM0
correction setup using theoretical knowledge and measurementbased system identification.
§ Open loop and closed loop simulation models are validated bycomparing model responses against measurements.

105Measured response
Model response

S27A:H30-5-10500

1000
2200
Frequency Hz

3500

10Phase drive gain (dB)Corrector Drive Gain (dB)

Simulation responses are in good agreement with measurements.

S28B:H450-5-10-15-20

Measured response
Model response

600

1000

Frequency (Hz)

2200

3500

Simulation vs Measurements - Horizontal
position responses to pulse input at Phase drive

Simulation vs Measurements – Input disturbance attenuation
at corrector and phase drives
1. P. Kallakuri et al., PRAB 25, 082801

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Coupled bunch mode zero correction within orbit feedback bandwidthExperimental study with low-alpha lattice§ 6 GeV low-alpha lattice: Synchrotron frequency (60 Hz) is within the orbit feedback bandwidth (90 Hz).
– Large RF system noise at 60 Hz harmonics.
§ Real time feedback system (RTFB) is used - orbit feedback system for APS operations– 38 fast correctors and 154 BPMs to deal with large noise.
– Limited functionality compared to prototype controller with 1.5 kHz sampling rate.

0.06

Open loop
CBM0 correction only
RTFB only
RTFB + CBM0 correction

0.05

S28A:P2X BPM error

Integrated PSD (mm2)0.07§ Stable combined operation of RTFB + CBM0 correction.
§ Partial suppression at synchrotron frequency when
feedbacks are operated individually.

0.04
0.03

§ More suppression at 60 Hz with both feedbacks running
together.

0.02
0.01
03060120240

360600Frequency (Hz)Cumulative mean square orbit motion with different
feedback configurations
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BPM responses measured at 154 BPMs around the storage-ring§ BPMs in the high dispersion area has larger
magnitudes compared to others.
§ Individual operation of RTFB or CBM0correction partially suppressed 60 Hz– Frequencies beyond 90 Hz are amplified.
§ Narrow resonant increase of RF noise at 60
Hz harmonics when high frequency motion isamplified.
§ RTFB + CBM0 correction– Significant suppression at 60 Hz– High frequency motion amplified byindividual feedback operation isattenuated up to 240 Hz.
PSDs of BPM errors at all 154 BPMs in open loop and different
closed loop configurations.
9Reduced feedback control efforts during combined operation§ Corrector and phase drive signals indicate feedback control efforts required to perform necessary correction.
§ During combined operation,– Energy and betatron components are corrected simultaneously, and feedback errors will be small.
– Drive magnitudes are less compared to respective individual operation of each feedback.

(A2)– More orbit motion suppression with less control effort from corrector and phase drives.

Comparison of drive efforts of each feedback individual operation with simultaneous operation.
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Conclusions§ Successfully demonstrated CBM0 correction within the orbit feedback bandwidth via experiments withlow-alpha lattice setup.
§ CBM0 oscillations are damped using orbit to RF phase feedback method.
– Energy-induced component is extracted from measured orbit and RF phase control signal isgenerated as if it were another corrector drive in the orbit feedback algorithm.
§ Individual operation of RTFB and CBM0 correction resulted in partial suppression at synchrotron
frequency.
§ The combination of CBM0 correction and RTFB was significantly more effective in suppressing
synchrotron frequency.
– Achieved better orbit motion suppression and reduction in feedback drive efforts.

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