experience with feedback systems in modern synchrotron light … 2019-04-03 · experience with...

Experience with feedbacksystems in modern

synchrotron light sources

Introduction

Similarities UnderFeedback Control

Feedback StoriesANKA Detective Story

NSLS-II Residual Motion Story

Future ChallengesMain Issues

Transverse Feedback and Noise

Longitudinal Instabilities and HarmonicCavities

Summary

Extra Slides

Experience with feedback systems in modernsynchrotron light sources

D. Teytelman

Dimtel, Inc., San Jose, CA, USA

Accelerator Performance and Concepts WorkshopFrankfurt, December 10-12, 2018

Introduction

Summary

Extra Slides

Outline

Introduction

Similarities Under Feedback Control

Feedback StoriesANKA Detective StoryNSLS-II Residual Motion Story

Future ChallengesMain IssuesTransverse Feedback and NoiseLongitudinal Instabilities and Harmonic Cavities

Extra Slides

Introduction

Summary

Extra Slides

Learning From Many FacilitiesMachines

Ring C, m E, GeVMLS 48 0.1–0.6HLS 66 0.8LNLS UVX 93 0.5–1.37MAX IV 1.5 GeV 96 1.5DAΦNE 98 0.51Duke SR-FEL 108 0.2–1.2ANKA 110 0.5–2.5DELTA 115 1.5TLS 120 1.5ELSA 164 1.2–3.2Indus-2 173 0.55–2.5Photon Factory 187 2.5ALS 197 1.9Australian Synchrotron 216 3SPEAR3 234 3BEPC-II 238 1.89BESSY II 240 1.7TPS 518 3MAX IV 3 GeV 528 3CESR-TA 768 1.5–6NSLS-II 792 3SuperKEKB 3016 4/7

I Over the last 12 years I had apleasure of directly or indirectlyparticipating in commissioningbunch-by-bunch feedback in 22machines;

I A definite learning opportunity!I Helped me gain some

understanding of feedback limitingfactors;

I Becoming more important in futureaccelerators.

Introduction

Summary

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Introduction

Summary

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Introduction

Summary

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Introduction

Summary

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Steady State Spectra Under Feedback Control

Feedback Beam∑

Transverse/longitudinal position

Detection noise

Disturbances

I In transverse planes there arevery few steady-statedisturbances;

I Instabilities are damped to thenoise floor;

I Spectrum is determined by thedetection noise and thefeedback loop response;

I Open loop transfer function L(ω)peaks at beam resonance;

I Transfer gain from detectionnoise to the feedback input is

11+L(ω) — a notch.

Introduction

Summary

Extra Slides

Feedback Beam∑

Detection noise

Disturbances

Introduction

Summary

Extra Slides

Feedback Beam∑

Detection noise

Disturbances

Introduction

Summary

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0.1 0.15 0.2 0.25 0.3−40

Fractional frequency

Magnitude (

Introduction

Summary

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0.1 0.15 0.2 0.25 0.3−12

Fractional frequency

Magnitude (

Introduction

Summary

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Examples of Steady State Spectra

0 100 200 300 400 500 600

10−1

Freq (kHz)

Counts

jan0513/213833: Signal spectrum averaged (quadratic) over all bunches

I Averaged spectra of allbunches under closed-loopfeedback control;

I BESSY II1 Y at 298 mA;I Zoomed in;I Aichi SR2 X at 300 mA;I Zoomed in;I TLS3 at 200 mA;I Two notches - dual plane (X

and Y) feedback;I Clean horizontal notch;I A line poking through the

vertical notch — evidence ofion-driven instabilities.

1h = 400, C = 240 m2h = 120,C = 72 m3h = 200,C = 120 m

Introduction

Summary

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310 315 320 325 330 335 340 345 350 35510

−1.8

10−1.7

10−1.6

Freq (kHz)

Counts

jan0513/213833: Signal spectrum averaged (quadratic) over all bunches

1h = 400, C = 240 m2h = 120,C = 72 m3h = 200,C = 120 m

Introduction

Summary

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0 500 1000 1500 200010

10−1

Freq (kHz)

Counts

oct2518/135004: Signal spectrum averaged (quadratic) over all bunches

1h = 400, C = 240 m2h = 120,C = 72 m3h = 200,C = 120 m

Introduction

Summary

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1020 1040 1060 1080 1100 1120 1140 1160

10−1.9

10−1.8

10−1.7

Freq (kHz)

Counts

oct2518/135004: Signal spectrum averaged (quadratic) over all bunches

1h = 400, C = 240 m2h = 120,C = 72 m3h = 200,C = 120 m

Introduction

Summary

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0 200 400 600 800 1000 1200

10−2

10−1

Freq (kHz)

Counts

apr0710/215244: Signal spectrum averaged (quadratic) over all bunches

1h = 400, C = 240 m2h = 120,C = 72 m3h = 200,C = 120 m

Introduction

Summary

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400 450 500 550 600 650 700 750 800 85010

10−2

10−1

Freq (kHz)

Counts

1h = 400, C = 240 m2h = 120,C = 72 m3h = 200,C = 120 m

Introduction

Summary

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730 740 750 760 770 780 790 800 810 82010

10−2

10−1

Freq (kHz)

Counts

1h = 400, C = 240 m2h = 120,C = 72 m3h = 200,C = 120 m

Introduction

Summary

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390 400 410 420 430 440 450 460 470 48010

10−2

10−1

Freq (kHz)

Counts

1h = 400, C = 240 m2h = 120,C = 72 m3h = 200,C = 120 m

Introduction

Summary

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Outline

Introduction

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Introduction

Summary

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Initial Assessment

19:40 20:09 20:38 21:07 21:36 19:40 20:09 20:38 21:070

ANKA, 2016−03−04

I A ramping machine, 500 MeVinjection, 2.5 GeV operation;

I Historically operated with onlytransverse feedback, withmoderate longitudinalinstabilities at injection energy;

I After a shutdown had problemsinjecting more than100–120 mA, limited bysudden partial beam loss.

Introduction

Summary

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Initial Assessment

19:40 20:09 20:38 21:07 21:36 19:40 20:09 20:38 21:070

ANKA, 2016−03−04

Introduction

Summary

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Initial Assessment

19:40 20:09 20:38 21:07 21:36 19:40 20:09 20:38 21:070

ANKA, 2016−03−04

Introduction

Summary

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Feedback in All Three Planes

I Turned on feedback in thelongitudinal plane;

I Still hitting a limit during injection,with partial beam losses;

I Feedback tuned near absolutelimit, growth time 2.3× Ts,damping time Ts;

Introduction

Summary

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I Turned on feedback in thelongitudinal plane;

Introduction

Summary

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0 0.2 0.4 0.6 0.8 1 1.2 1.40

Time (ms)

mar0516/143809 Data, Fit and Error for Mode #45

Error I Turned on feedback in thelongitudinal plane;

Introduction

Summary

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Capturing the Beam Loss Event

0 5 10 15 20 25 30−150

−100

Time (ms)

Longitudinal plane

0 5 10 15 20 25 30−100

Time (ms)

Vertical plane

I Noticed significant activity in thevertical plane during beam lossevents;

I Used baseband processor outputto trigger acquisition in all planes;

I Vertical correction signals arenormally small, only reachingfull-scale during beam loss;

I Longitudinal and vertical signalsfor bunch 140.

Introduction

Summary

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0 5 10 15 20 25 30−150

−100

Time (ms)

Longitudinal plane

0 5 10 15 20 25 30−100

Time (ms)

Vertical plane

Introduction

Summary

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0 5 10 15 20 25 30−150

−100

Time (ms)

Longitudinal plane

0 5 10 15 20 25 30−100

Time (ms)

Vertical plane

Introduction

Summary

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0 5 10 15 20 25 30−150

−100

Time (ms)

Longitudinal plane

0 5 10 15 20 25 30−100

Time (ms)

Vertical plane

Introduction

Summary

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Deciphering the Beam Loss Event

0 5 10 15 20 25 30−150

−100

Time (ms)

Longitudinal plane

0 5 10 15 20 25 30−100

Time (ms)

Vertical plane

I Which plane came first?I Zoom in, still too close;I Zoom more — looks like

longitudinal starts first, but couldbe trigger error;

I Longitudinal oscillation amplitudeexceeds 30◦;

I Modal analysis in Z shows mode46 rapidly running away under fullfeedback control.

Introduction

Summary

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8 8.5 9 9.5 10 10.5 11 11.5 12−150

−100

Time (ms)

Longitudinal plane

8 8.5 9 9.5 10 10.5 11 11.5 12−100

Time (ms)

Vertical plane

Introduction

Summary

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9.6 9.7 9.8 9.9 10 10.1 10.2 10.3 10.4−150

−100

Time (ms)

Longitudinal plane

9.6 9.7 9.8 9.9 10 10.1 10.2 10.3 10.40

Time (ms)

Vertical plane

Introduction

Summary

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9.6 9.7 9.8 9.9 10 10.1 10.2 10.3 10.4−150

−100

Time (ms)

Longitudinal plane

9.6 9.7 9.8 9.9 10 10.1 10.2 10.3 10.40

Time (ms)

Vertical plane

Introduction

Summary

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Introduction

Summary

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Deciphering the Beam Loss Event, Continued

I Spectrogram of vertical bunchsignal settles it!

I Longitudinal motion starts first,seen mostly as second harmonicin the amplitude detector channel;

I At beam phase excursionsexceeding 90◦ at detectionfrequency, vertical feedback gainflips;

I Positive feedback excites verticalmotion, causes beam loss.

Introduction

Summary

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Introduction

Summary

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Introduction

Summary

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Introduction

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Fixing the Issue

I RF cavities in ANKA arecompression tuned;

I During injection, LLRF adjustscavity tuning to compensate forbeam loading;

I All cavity HOMs tune at the sametime;

I By adjusting cavity temperature weshifted the problematic HOMenough so that synchrotronsideband crossing happened atmuch lower beam current;

I Growth rates scale with current,feasible to control!

Introduction

Summary

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Fixing the Issue

Introduction

Summary

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Fixing the Issue

Introduction

Summary

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Fixing the Issue

Introduction

Summary

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Fixing the Issue

Introduction

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The Final Problem

18:43 19:12 19:40 20:09 20:38 18:43 19:12 19:40 20:090

ANKA, 2016−03−05

I After adjusting cavity temperaturewe were able to keep the beamstable in X, Y, and Z;

I New problem — with all planesstable, injection saturated around110 mA due to poor Touscheklifetime;

I Streak camera, stabilized beam;I Applied quadrupole excitation

through the LFB;I Bunch lengthening leads to

Touschek lifetime improvement;I With both feedback and

modulation injected 160 mA andramped to 2.5 GeV.

Introduction

Summary

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The Final Problem

18:43 19:12 19:40 20:09 20:38 18:43 19:12 19:40 20:090

ANKA, 2016−03−05

Introduction

Summary

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The Final ProblemI After adjusting cavity temperature

we were able to keep the beamstable in X, Y, and Z;

Introduction

Summary

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The Final ProblemI After adjusting cavity temperature

we were able to keep the beamstable in X, Y, and Z;

Introduction

Summary

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The Final Problem

00:28 00:57 01:26 01:55 02:24 00:28 00:57 01:26 01:550

ANKA, 2016−03−06

00:28 00:57 01:26 01:55 02:24 00:28 00:57 01:26 01:550

Introduction

Summary

Extra Slides

ANKA SummaryI Historically operated with only transverse feedback, relied on

moderate longitudinal instabilities at injection energy to providesufficient lifetime to accumulate beam;

I Changes during a shutdown prevented injection above100–120 mA

I Investigation showed:I Longitudinal HOM in RF cavity crossed synchrotron sideband

around 110 mA;I Vertical beam loss mechanism — large longitudinal oscillation

moved vertical bunch-by-bunch feedback into positive range;I Longitudinal growth rates unfeasible to control with feedback;I Adjusted cavity temperature to move sideband crossing to lower

current, could run with full feedback control in all three planes;I With fully stabilized beam, lifetime dropped, injection saturated at

110–115 mA;I Used swept quadrupole excitation to control bunch length and

lifetime, injected to 160 mA, successfully ramped.

Introduction

Summary

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Outline

Introduction

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Introduction

Summary

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Averaged Bunch Spectra vs. Feedback Gain 4

80 85 90 95 100 105 110 11510

Frequency (kHz)

Vertical feedback channel, loop gain 1

80 85 90 95 100 105 110 115

10−0.5

10−0.3

10−0.1

Frequency (kHz)

Monitor channel, loop gain 1

I Two independent channelsmonitoring vertical motion, one inthe feedback loop, one out of theloop;

I Roughly similar sensitivities,250 mA in 1000 bunches;

I At low feedback gain a visibleresidual motion line due to ionexcitation;

I Double the feedback gain;I Again;I Again;I Once more;I A wider bandwidth comparison.

4Measurements courtesy of Weixing Cheng of NSLS-II.

Introduction

Summary

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80 85 90 95 100 105 110 11510

Frequency (kHz)

80 85 90 95 100 105 110 115

10−0.5

10−0.3

10−0.1

Frequency (kHz)

Introduction

Summary

Extra Slides

80 85 90 95 100 105 110 11510

Frequency (kHz)

80 85 90 95 100 105 110 115

10−0.5

10−0.3

10−0.1

Frequency (kHz)

Introduction

Summary

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80 85 90 95 100 105 110 11510

Frequency (kHz)

80 85 90 95 100 105 110 115

10−0.5

10−0.3

10−0.1

Frequency (kHz)

Introduction

Summary

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80 85 90 95 100 105 110 11510

Frequency (kHz)

80 85 90 95 100 105 110 115

10−0.5

10−0.3

10−0.1

Frequency (kHz)

Introduction

Summary

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80 85 90 95 100 105 110 11510

Frequency (kHz)

80 85 90 95 100 105 110 115

10−0.5

10−0.3

10−0.1

Frequency (kHz)

Introduction

Summary

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80 85 90 95 100 105 110 11510

Frequency (kHz)

80 85 90 95 100 105 110 115

10−0.5

10−0.3

10−0.1

Frequency (kHz)

Introduction

Summary

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20 40 60 80 100 120 140 160 180

10−0.7

10−0.5

10−0.3

10−0.1

Frequency (kHz)

Vertical feedback channel

20 40 60 80 100 120 140 160 180

10−0.4

10−0.3

10−0.2

10−0.1

Frequency (kHz)

Monitor channel

Gain 1

Gain 16

Introduction

Summary

Extra Slides

Beam Size vs. Feedback Gain 5

0 2 4 6 8 10 12 14 1614

Feedback gain (arb. units)

Vertical beam size measured by pinhole camera

I Vertical beam size measuredby a pinhole camera;

I A superposition of true beamsize and residual dipolemotion;

I Vertical emittance, calculatedfrom pinhole camera data;

I Beam lifetime is correlated withbeam size measurements,suggesting vertical sizeblow-up;

I Could get a better estimate oftrue beam size by subtractingknown dipole motion term.

Introduction

Summary

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0 2 4 6 8 10 12 14 1614

Vertical beam size measured by pinhole camera

Introduction

Summary

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0 2 4 6 8 10 12 14 168

NSLS−II vertical emittance

Introduction

Summary

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0 2 4 6 8 10 12 14 168

Introduction

Summary

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0 2 4 6 8 10 12 14 168

Introduction

Summary

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Outline

Introduction

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Introduction

Summary

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New Machines and Challenges

I Transversely, new light sources and colliders are going becomemore and more sensitive to residual dipole motion;

I Rule of thumb: residual dipole motion should be kept below 10% ofthe transverse beam size;

I Usually more critical in the vertical plane;I Low-noise techniques in RF front end and digitizer design are

required;I Most system designers do not care about spurs 100 dB below ADC

full scale;I Since bunch-by-bunch feedback settles to the front end/digitizer

noise floor, any spur can potentially ruin performance.I Longitudinally, harmonic cavities used for lifetime improvement

create major difficulties for bunch-by-bunch feedback:I HCs result in low synchrotron tune with large tune spread;I Conventional topology can handle tune spread of 2:1 at most.

Introduction

Summary

Extra Slides

New Machines and Challenges

I Transversely, new light sources and colliders are going becomemore and more sensitive to residual dipole motion;

I Rule of thumb: residual dipole motion should be kept below 10% ofthe transverse beam size;

I Usually more critical in the vertical plane;I Low-noise techniques in RF front end and digitizer design are

required;I Most system designers do not care about spurs 100 dB below ADC

full scale;I Since bunch-by-bunch feedback settles to the front end/digitizer

noise floor, any spur can potentially ruin performance.I Longitudinally, harmonic cavities used for lifetime improvement

create major difficulties for bunch-by-bunch feedback:I HCs result in low synchrotron tune with large tune spread;I Conventional topology can handle tune spread of 2:1 at most.

Introduction

Summary

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Outline

Introduction

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Introduction

Summary

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Bunch-by-bunch Feedback

Controller

BeamKicker structure

Back−endFront−end

SensorBPM Actuator

I Sensor (pickup);I Analog front-end;I Controller;I Analog back-end;I Actuator (kicker).

Introduction

Summary

Extra Slides

Bunch-by-bunch Feedback

Controller

BeamKicker structure

Back−endFront−end

SensorBPM Actuator

I Sensor (pickup);I Analog front-end;I Controller;I Analog back-end;I Actuator (kicker).

Introduction

Summary

Extra Slides

BPM Hybrid Network

A (180◦)

B (0◦) C (Σ)

D (∆)

A (180◦)

B (0◦) C (Σ)

D (∆)

A (180◦)

B (0◦) C (Σ)

D (∆)

A (180◦)

B (0◦) C (Σ)

D (∆)

B + C − A−D

B +D − A− C

A+B + C +D

A+B −D − C ∆Y

B −D

C −AA

I First stage of BPM signal processing — separating X/Y/Z signalsI Since we are digitizing in the end, why not digitize raw signals?I For X and Y we are dealing with small differences of large signals;I If we can reject the common-mode at 20–30 dB level, that is also

the gain of low-noise amplifier we can use to improve sensitivity.

Introduction

Summary

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BPM Hybrid Network

A (180◦)

B (0◦) C (Σ)

D (∆)

A (180◦)

B (0◦) C (Σ)

D (∆)

A (180◦)

B (0◦) C (Σ)

D (∆)

A (180◦)

B (0◦) C (Σ)

D (∆)

B + C − A−D

B +D − A− C

A+B + C +D

A+B −D − C ∆Y

B −D

C −AA

Introduction

Summary

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BPM Hybrid Network

A (180◦)

B (0◦) C (Σ)

D (∆)

A (180◦)

B (0◦) C (Σ)

D (∆)

A (180◦)

B (0◦) C (Σ)

D (∆)

A (180◦)

B (0◦) C (Σ)

D (∆)

B + C − A−D

B +D − A− C

A+B + C +D

A+B −D − C ∆Y

B −D

C −AA

Introduction

Summary

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BPM Hybrid Network

A (180◦)

B (0◦) C (Σ)

D (∆)

A (180◦)

B (0◦) C (Σ)

D (∆)

A (180◦)

B (0◦) C (Σ)

D (∆)

A (180◦)

B (0◦) C (Σ)

D (∆)

B + C − A−D

B +D − A− C

A+B + C +D

A+B −D − C ∆Y

B −D

C −AA

Introduction

Summary

Extra Slides

Analog Front-end Design

BPM hybrid

Variableattenuator

Phase shifter

Frequency multiplierfrf

Bandpass filter

M × frf

Lowpass filter

To the ADC

MixerLNA

I Front-end requirements:I Low amplitude and phase noise;I Wideband to ensure high isolation between neighboring bunches.

I Input bandpass filter is an analog FIR filter that replicates BPMpulse with spacing, matched to detection frequency period;

I Detection frequency choice:I High frequencies for sensitivity;I Must stay below the propagation cut-off frequency of the vacuum

chamber.I Local oscillator adjusted for amplitude (transverse) or phase

(longitudinal) detection.

Introduction

Summary

Extra Slides

BPM hybrid

Variableattenuator

Phase shifter

Bandpass filter

M × frf

Lowpass filter

To the ADC

MixerLNA

Introduction

Summary

Extra Slides

BPM hybrid

Variableattenuator

Phase shifter

Bandpass filter

M × frf

Lowpass filter

To the ADC

MixerLNA

Introduction

Summary

Extra Slides

Examples of Front-End Sensitivities Achieved

Vertical Plane

Machine Atten. Calibration At nominal currentSPEAR3 0 dB 0.54 counts/mA/µm 0.96 counts/µmMAX IV 3 GeV 0 dB 0.98 counts/mA/µm 2.8 counts/µmASLS 2 dB 1.24 counts/mA/µm 0.83 counts/µmNSLS-II6 0 dB 1.5 counts/mA/µm 0.75 counts/µm

I LSB of the 12-bit ADC in Dimtel iGp12 is only 5 times larger thanthermal noise in the ADC bandwidth (wide for good isolation downto 2 ns bunch spacing);

I Not a lot of room for improved sensitivity, need to be smart withpickup selection, feedback algorithms.

6Older front-end design with lower sensitivity

Introduction

Summary

Extra Slides

Sensitivity and Noise

∑ Error

Transverse position (y)

Disturbances

Feedback Beam

Detection noise (vn)

I Complementary sensitivity function T (ω) = L(ω)/(1 + L(ω)) is thetransfer function between noise vn and beam motion y ;

I Assuming flat spectral density for vn can calculate amplification orattenuation of sensing noise;

I Qualitatively, faster damping corresponds to wider bandwidth→higher noise sensitivity;

I Rule of thumb: closed loop damping rate should be of the samemagnitude as open-loop growth rate.

Introduction

Summary

Extra Slides

Sensitivity Functions Compared

0 500 1000 1500−80

Frequency (Hz)

Complementary sensitivity function, noise gain −18.7 dB

I Growth and damping times inturns;

I τol = τcl = 300: −18.7 dBI τol = τcl = 30: −8.1 dBI τol = 30, τcl = 3.2: −6.0 dBI τol = 5.4, τcl = 5.4: 3.8 dBI Fast growth rates result in

higher noise sensitivity.

Introduction

Summary

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0 500 1000 1500−80

Frequency (Hz)

Introduction

Summary

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0 500 1000 1500−80

Frequency (Hz)

Introduction

Summary

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0 500 1000 1500−80

Frequency (Hz)

Complementary sensitivity function, noise gain 3.8 dB

Introduction

Summary

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0 500 1000 1500−80

Frequency (Hz)

Complementary sensitivity function, noise gain 3.8 dB

Introduction

Summary

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Sensitivity vs. Feedback Gain

0 20 40 60 80 100−20

Gain (arb. units)

0 20 40 60 80 10010

Gain (arb. units)

I 300 turns growth time, fractionaltune of 0.2, 5-turn feedback filter;

I No excitation, purely flat noisefloor;

I Minimum integrated sensitivity atτol = τcl;

I Highly peaked T (ω) at low gains,very wide at high gains.

Introduction

Summary

Extra Slides

2 3 4 5 6 7 8 9 10−19

−18.5

−17.5

−16.5

Gain (arb. units)

2 3 4 5 6 7 8 9 1010

Gain (arb. units)

Introduction

Summary

Extra Slides

0.15 0.2 0.25−40

Fractional tune

Complementary sensitivity functions

1422 turns

846 turns

602 turns

467 turns

381 turns

322 turns

279 turns

245 turns

219 turns

78 turns

33 turns

14 turns

5 turns

Introduction

Summary

Extra Slides

Feedback Filter Design

0.1 0.15 0.2 0.25 0.3 0.35−70

Fractional tune

Magnitude response

5 taps

32 taps

64 taps

0.1 0.15 0.2 0.25 0.3 0.35−400

−300

−200

−100

Fractional tune

Phase response

5 taps

32 taps

64 taps

I Transverse feedback FIR filters,tune of 0.2, adjusted for thesame closed-loop damping time(τcl = τol = 300 turns);

I Conventional wisdom — shorterfilter can generate fasterdamping, longer filter is quieterdue to narrower bandwidth;

I Let’s see what complementarysensitivity function tells us.

Introduction

Summary

Extra Slides

0.185 0.19 0.195 0.2 0.205 0.21 0.215−20

Fractional tune

Magnitude response

5 taps

32 taps

64 taps

0.185 0.19 0.195 0.2 0.205 0.21 0.2150

Fractional tune

Phase response

5 taps

32 taps

64 taps

Introduction

Summary

Extra Slides

0.185 0.19 0.195 0.2 0.205 0.21 0.215−20

Fractional tune

Magnitude response

5 taps

32 taps

64 taps

0.185 0.19 0.195 0.2 0.205 0.21 0.2150

Fractional tune

Phase response

5 taps

32 taps

64 taps

Introduction

Summary

Extra Slides

Residual Noise vs. Filter Length

0 10 20 30 40 50 60 70

−18.6

−18.5

−18.4

−18.3

−18.2

−18.1

Number of taps

0 10 20 30 40 50 60 70−302

−301.5

−301

−300.5

−300

−299.5

−299

−298.5

−298

Number of taps

I Moderate increase of theintegrated noise gain with filterlength;

I Effect of the group delay;I T (ω) shapes very similar near

the tune — reflect identicalclosed-loop damping pole;

I As an added bonus, shorterfilters are less sensitive to tunevariation.

Introduction

Summary

Extra Slides

0 10 20 30 40 50 60 70

−18.6

−18.5

−18.4

−18.3

−18.2

−18.1

Number of taps

0 10 20 30 40 50 60 70−302

−301.5

−301

−300.5

−300

−299.5

−299

−298.5

−298

Number of taps

Introduction

Summary

Extra Slides

0.195 0.2−15

Fractional tune

5 taps

6 taps

7 taps

8 taps

9 taps

10 taps

12 taps

15 taps

18 taps

21 taps

24 taps

32 taps

64 taps

Introduction

Summary

Extra Slides

0.17 0.18 0.19 0.2 0.21 0.22 0.23−80

Fractional tune

5 taps

6 taps

7 taps

8 taps

9 taps

10 taps

12 taps

15 taps

18 taps

21 taps

24 taps

32 taps

64 taps

Introduction

Summary

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Outline

Introduction

Extra Slides

Introduction

Summary

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Direct Energy Sensing

I Basic method: use horizontal signal from a pickup in a highdispersion location to sense energy oscillation directly;

I Eliminates the need to generate a 90◦ phase shift betweenlongitudinal position measurement and energy kick;

I Feedback filter is just a gain plus two constraints:I High-pass transition below the synchrotron frequency band to filter

out DC orbit offsets;I Low-pass transition above the synchrotron frequency band to

remove horizontal signals.I Can’t handle full lengthening (synchrotron frequency band extends

to DC);I Use two pickups with 0◦ or 180◦ relative phase advance to

eliminate horizontal signals?

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APS-U Example

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−150

−100

Frequency (Hz)

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I Possible filterresponse for APS-Uenergy sensing;

I fs = 620 Hz withoutharmonic cavities;

I Drops to100± 100 Hz underoptimal bunchlengthening;

I 2 dB gain and 12.5◦

phase ripple in20–800 Hz range.

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APS-U Example

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Summary

I Bunch-by-bunch feedback can make different machines look alike,but it takes good system design and thorough understanding ofdriving terms;

I Never trust a “mild” instability — you never know when it will turninto a showstopper;

I Characterization of instabilities is a definite must for robustfeedback operation;

I New low-emittance machines demand noise-figure optimized RFfront-ends and digitizers;

I Simplified models are very helpful in understanding feedbackalgorithm trade-offs;

I Longitudinal feedback in presence of harmonic cavities ischallenging, new (so far untested) energy sensing technique mighthelp.

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Acknowledgments

I Thank you for your attention!I I would also like to thank physicists, engineers, and operators at

many machines around the world who directly or indirectlycontributed to measurements presented here.

I Special thanks to Weixing Cheng for fruitful discussions andNSLS-II measurements.

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Root Locii in Complex Plane: Close Zoom

I Root locus on the complexplane:

I Starts at the open-loop pole(×), ends at the highest gainsetting (o);

I Real part corresponds togrowth (positive, right halfplane) or damping (negative,left half plane) rate;

I Imaginary part is thefrequency.

I Zoomed in around the dominantpole, all filters look the same.

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Root Locii in Complex Plane: Wider View

I Zooming out we see additionalpoles;

I These are due to the additionaldelay of the feedback controller;

I Added poles account forincreasing noise sensitivity.

experience with feedback systems in modern synchrotron light … 2019-04-03 · experience with...

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