Feedback Control of Particle Beam InstabiltiesUSPAS Control Theory and Applications Talk Outline...

eory and Applications

lties

J. F ut, A. Young, S. Uemura

C03-76SF0515

USPAS Control Th

Feedback Control of Particle Beam Instabi

ox, J. Cesaratto, T. Mastorides, C. Rivetta, D. Van Winkle, O. Turg

SLAC

A. Drago, M. Serio

LNF-INFN

J. Flanagan, M. Tobiyama

KEK

D. Teytelman

Dimtel, Inc.

W. Hoefle, R. De Maria

CERN

Work supported by U.S. Department of Energy contract DE-A


Backg

• Fee• Req

Possib

• Exa

• para es

• Kick

Accele

• Mod

• Imp

• Ion

Funda

Intere

Summ

USPAS Control Th

Talk Outline

round - Accelerator Instabilities, Feedback control

dback basicsuirements for beam instability control

le Solutions andTechnical Challenges - State of the Art Review

mple systems from around the world

llel processing DSP structures, flexible reconfigurable architectur

er antennas and power structures

rator Diagnosticsvia transient domain techniques

al Growth/damping rates

edances, noise driven motion

and Electron Cloud diagnostics

mental limits to performance and PromisingR&D Opportunities

sting new directions - ecloud instabilties in the SPS and LHC

ary


Applic

• Col

• Ligh

Couplperforthe lum

In thebelow

Howe e instability threshold. Forexamp mA instability threshold.

Feedb

USPAS Control Th

Motivation

ations of charged-particle circular accelerators

liders

t sources

ed-bunch instabilities cause beam loss or reducedmance affecting the intensity of light sources and

inosity of colliders.

past circular machines were designed to operate the instability threshold.

ver modern high-current accelerators are routinely run above thle the Advanced Light Source has 400 mA design current and 40

ack Control provides Stability - AND Accelerator Diagnostics

Active feedback isneeded for design

performance!


The oof a dya desior inp

Regulconsta

Servofollow

Feedb

The e stem performance. There aremany

• RM

• Ste t.

An ad ctuator effort. Peak actuatoreffort

Feedb t parameters or dynamicschang ?

Planty

xternal disturbances

USPAS Control Th

Feedback basics

bjective is to make the outputnamic system (plant) behave inred way by manipulating inpututs of the plant.

ator problem - keep small ornt

mechanism problem - make a reference signal

ack controller acts to reject the external disturbances.

rror between and the desired value is the measure of feedback syways to define the numerical performance metric

S or maximum errors in steady-state operation

p response performance such as rise time, settling time, overshoo

ditional measure of feedback performance is the average or peak ais almost always important due to the finite actuator range.

ack system robustness- how does the performance change if the plane? How do the changes in sensors and actuators affect the system

controller

sensors

actuatorsr u

ey

y

yr

y


Overview

Princi a system

Longit

Transin

Techn

Loop

Pickupo

ProceS

Noiseb

ExamfeN

all ana

sensornoise

z

yv

USPAS Control Th

Coupled-Bunch Feedback Principles - General

ple of Operation-Feedback can be used to change the dynamics of

udinal - measure - correct E

verse - measure( , ) - kick,

ical issues

Stability? Bandwidth?

, Kicker technologies? Requiredutput power?

ssing filter? DC removal?aturation effects?

? Diagnostics (system andeam)?

ple - the simplest transverseedback idea ( from Galayda,SLS)

log, cable delay for 1 turn

δφ

processnoise

w

u Controller

G

H

BeamδX δY

X' Y '


Equat

Damp ping

USPAS Control Th

Harmonic Oscillators, Revisited

ion of motion where

ing term proportional to - use feedback to ensure negative dam

ẋ̇ γ ẋ ω02

+ + f t( )= ω0km----=

γ ẋ

0 5 10 15 2010

−1

100

101

Frequency, kHz

Ma

gn

itu

de

0 5 10 15 20−200

−150

−100

−50

0

Frequency, kHz

Ph

ase

, d

eg

ree

s

0 0.2 0.4 0.6 0.8 1 1.2 1.4−6

−4

−2

0

2

4

6x 10

4

Time, ms

Am

plit

ud

e

Impulse response


Bunchstructusamplcoupli

Longitinto a- slopthe focoupli

Trans“kickstransv

For camplitsystem r damping times than shown)

e

n

bunch n+2

Time

USPAS Control Th

Coupled dynamics: multiple bunches

passing through a resonantre excites a wakefield which is

ed by the following bunches - ang mechanism

udinal bunch oscillation translatesphase modulation of the wakefielde of the wake voltage sampled byllowing bunches determines theng.

verse Oscillations excite transverse” - magnitude proportional toerse displacement*current

ertain combinations of wakefieldudes and frequencies the overall becomes unstable. (In practice the wakefields have much longe

Resonant structur

Vacuum chamber

n+1n+2

bunch n bunch n+1


N cou machines)

Drivin

Broad

Time D

• Pick

• Ban

An all uivalent to a bunch-by-bunch

USPAS Control Th

Normal Modes, Revisited

pled Oscillators,N Normal Modes ( so thousands of modes in large

g term provides coupling

band ( all-mode) vs. Narrowband Feedback

omain vs. Frequency Domain formalism

up, Kicker signals the same

dwidth Constraints identical

-mode frequency domain system ( with uniform gain) is formally eq time domain system - identical transfer functions

5-20008545A14

φi-2 φi-1 φi φi+1 φi+2


For an ven-fill eigenmode (EFEM)basis. l modes.

Longig

Real p ndamped natural frequency

The g nt system is unstable.

Two w damping

Lower or Direct RF feedback

Active ative real impedance

USPAS Control Th

Eigenmodes and impedances

even fill pattern the bunch motion can be easily projected into the e For coupled harmonic oscillators (bunches) there are norma

tudinal Modal eigenvalues are given by

art of the eigenvalue - exponential growth rate, Imaginary part - u

rowth rate is proportional to beam current.Above some threshold curre

ays to fight the instabilities: lower the impedance or use feedback

ing the impedance is achieved with RF cavity design ( for HOM’s)

Feedback techniques require signal processing and act as a neg

N N

Λm dr– iωsαe f rf2E0νs---------------I0Z

effmωrev ωs+( )+ +=

Zeff ω( ) 1ωrf

------- pωrf ω+( )Z pωrf ω+( )p ∞–=

∞

∑=}

Accelerator parameters Beam current Aliasedimpedance


For in

• extr quency,

• amp et damping for a givenimp

• gen t arbitrary if the systemand

Some

• Ban re?)

• DC s phase position, or staticorbi

• Sat

• Noi er)

• Max

• Dia

USPAS Control Th

Processing Requirements

stability control, the processing channel must

act (filter) information at the appropriate synchrotron or betatron fre

lify it (a net loop gain must be generated, large enough to cause nedance)

erate an output signal at anappropriate phase(nominally 90 degrees, bu cable delays, pickup and kicker locations are considered)

technical issues

dwidth/sampling rate ( 500 MHz RF (the bunch separation), or mo

offset removalfrom the processing channel (e.g. from DC synchronout offset)

uration on large input errors ( injection, or driven motion)

se in the input channel (e.g. bandwidth reduction via processing filt

imum supportablegain - limits from noise as well as loop stability

gnostics (processing system and beam dynamics)


Short

• KEK

• requ cker filling times)

• sets

• Res

•

Many

• KEK

• Nee

Ratio

• Nyq

• Bet

• Syn

• low -bandwidth product)

USPAS Control Th

Technical Challenges

interbunch Interval

-B, ALS, BESSY, PLS, etc. 2 ns, DAFNE 2.7 ns, PEP-II 4.2 ns

ires wideband pickups, kickers ( from required bunch isolation, ki

required processing bandwidths

olution - Longitudinal damped oscillation rms 0.6 picosecond

- Transverse damped oscillation ~microns

Bunches (many unstable modes)

-B 5120, PEP-II 1746

d to compactly implement bunch by bunch filters

of Frev to Fosc

uist limit Fosc< 1/2 Frev

atron Oscillations grossly undersampled

chrotron oscillations typically oversampled

synchrotron frequency sets scale of required filter memory (Delay


system

Firstprograinstall

PEP-IPLS,demo

Deteccorrec(optio

Scalaarray,

Samp

May wto redloadrateoscilla

wer

lifier

Kicker oscillator

locked to 9/4×frf

1071 MHz

QPSK modulator

Low-pass filter

structure

To RF stations

Woofer link3.2 1⋅

USPAS Control Th

Block diagram of a longitudinal feedback

Generation DSP,mmable system

ed in:

I, ALS, BESSY-II,DAΦNE and

nstrated at SPEAR

tion at ,tion at 9/4 RFns 11/4, 13/4)

ble processingup to

MAC/sec.

ling at 500 MHz

ant Downsamplinguce computational(match processing

to synchrotrontion frequency)

Low-pass filter

AD

C,dow

nsam

ple

rDSP

Hold

buffer,

DAC

Po

amp

Beam

Phase servo

× ×

BPM

Comb generator

LNA

locked to 6×frf

Master oscillator

2856 MHz

Farm of digitalsignal processors

Kicker

Timing and control6 FRF×

09

USPAS Control Th
HER and LER Systems at PEP-II


Termin

• Tim

• freqSamp utput phase, limits noise,contro

Gener

Gener

wide b

narrow

Maxim

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Filter Implementation Options

ology

e domain - bandpass bunch by bunch filters

uency domain - modal selection, notch at Frevling process suggests discrete time filter (filter generates correct ols saturation)

al form of IIR filter (infinite impulse response)

al form ofFIR filter (finite impulse response)

andwidth filter - insensitive to variations in machine tune

bandwidth filter - helps reject detector noise

um gain - when noise in front-end saturates DSP processing

yn akyn k– bkxn k–k 0=

M

∑+k 1=

N

∑=

yn bkxn k–k 0=

M

∑=


Each

The ebroadbandw

Exam4 5 6

008;|H|var

= 1.0365; Gain ratio = 1

8 10 12

.1 at 6.595 kHz)

8 10 12

rees at 6.595 kHz)

−

−0.

0.

Coe

ffici

ents

−2

−1

1

2

Mag

nitu

de [d

B.]

−20

−10

10

20

Pha

se [d

eg.]

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Example FIR filters

bunch gets an independent controller

xample 6 tap filter (longitudinal, PEP) hasbandwidth - longer filter would have narroweridth, but comcomitant longer group delay

ple 5-tap transverse filter for tune 0.190 1 2 3

−15

−10

−5

0

5

10

15

Ratio = 0.57946; ∆Θ = 178.5822; Θvar

= 44.1

0 2 4 6−40

−30

−20

−10

0

10

20

30

40Magnitude of Filter TF (35

0 2 4 6−200

−150

−100

−50

0

50

100

150

200Phase of Filter TF (90.2 deg

deg

Freq. (kHz)

1 1.5 2 2.5 3 3.5 4 4.5 51

5

0

5

1

Taps

Transfer function for a 5 TAP FIR Filter

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0

0

0

0

Normalized frequency

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0

0

0

0

Normalized frequency

Nominal Tune = 0.19

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Baseband transfer Function

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RF Transfer Function


ystems

NSLS

• 2 ta

ALS -

• 2 ns

• qua

UVSO

• 16 b

DESY

• 96 n

CESR

• 16 n

Elettra

• 2 ns ctronics

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Existing/Example Coupled-Bunch Feedback S

- Galayda, et al (transverse)

p analog FIR (“correlator filter”)

Barry, et al (transverse)

bunch spacing -2 tap analog FIR filter

drature pickups, sum for phase shift

R (Japan) - Kasuga et al. (longitudinal)

unches - 16 analog filters with multiplexing

- Kohaupt et al. (transverse and longitudinal)

s bunch spacing - 70 bunches - 3 tap digital FIR

- Billing, et al (transverse and longitudinal)

s bunch spacing, digital FIR filter

, SLS-Bulfone, et al ( transverse)

bunch spacing, mix of commercial ADC/DSP boards, custom ele


n

From

Quadr it suppression

USPAS Control Th

ALS Transverse Feedback Implementatio

W. Barry

ature processing via 2 pick-ups , Analog 2-tap FIR filter for DC orb


Exis cont.

PEP-I

• 2 - 4

• gen

• Algo

KEK-B

• 2 ns nts ( no multipliers)

• use ls

SPRIN PGA FIR implementation

iGp - T

• 2nd

• para umbers

• 2 ns

• flex

Libera with FPGA

USPAS Control Th

ting/Example Coupled-Bunch Feedback Systems,

I/ALS/DAFNE/BESSY/PLS - Fox, et al (longitudinal)

ns bunch spacing, 120 - 1746 bunches

eral purpose DSP processing

rithms for FIR and IIR filtering

- Tobiyama, et al (transverse, longitudinal)

spacing, 5120 bunches, 2 tap digital FIR with fixed +1/-1 coefficie

of custom GaAs multiplexing chip set, 16 way muliplexed channe

G-8(also TLS)Date,et al- 500 MHz,Transverse,4 way multiplexed, F

etytelman, et al ( general purpose, transverse, longitudinal)

/3rd Generation technology - reconfigurable gate arrays

llel processor - uneven stepping applicable to various harmonic n

spacing, 5120 bunches, 16 tap FIR,

ible transverse,longitudinal processor channel

Bunch-by-Bunch ( Instrumentation Technologies) - Multiplexed A/D


• 3c

• C(DKc

• T

• Lc

• H(5th

• Bind

• Spp

Applic

USPAS Control Th

Example -IGP processing channelrd generation instabilityontrol technology

ommerical productIMTEL) based on SLAC,

EK, LNF-INFN designollaboration -

ransverse instability control

ongitudinal instabilityontrol

igh-speed beam diagnostics00MHz sampling/roughput rate)

uilds on program instability control and beamiagnostics.

ignificant advance in therocessing speed and densityreviously achieved.

able to many installations


Inte r technologies

• How lling the speed of light?

• You ery 2 ns., without couplingone

• How iring independentcon

• How ron resolution every 2ns?

These

USPAS Control Th

ractions with the particle beam - pickup and kicke

do you measure thetime of arrivalof a mm long particle beam, trave

want sub-picosecond rms noise (600 fs), and you need to do it ev measurement to the other.

do you change the energyof the particle beam bykilovolts, again requtrol of the bunches every 2 ns?

do you measure thetransverse position of an electron beam with mic

are interesting transducer and actuator problems!

5-20008545A11

B = 0 B < 1 B 1

1/γ

e – e – e –


Difficumakethe nuBPMburstsdetectfor A/D

Examshowsa resexpon

LongitRF ha

TransDelta-

7288A5

Terminated Lines

67.2400 ns6908A3

USPAS Control Th

Pickup and Frontend technology

lt to process picosecond bunch signals -a periodic coupler circuit which definesmber of couplers and the center frequency.impulses are converted to short “tone” for subseqent delta-sigma or phaseion processing, heterodyning to baseband input

ple 3 GHz comb, the measured signallittle coupling between the bunches. ( noteonant bandpass filter would decayentially)

udinal signal - Phase detectagainst 3 Ghzrmonic, baseband phase error

verse signal- needsAM detection andSigmaprocessing for X and Y coordinates

8 Cycle Tone Burstto Phase Detector

Impulse from BPM

10–92

57.2400 ns 62.2400 ns4-91


nal processing

ase detection againstsystem. sensitivity

nic

lta/sigma processingdifference signals.

at harmonic of RF, ort baseband

GEN

FROM

D

B

C

A

USPAS Control Th

Frontend sig

Longitudinal - phharmonic of RFscales with harmo

Transverse - Deprovides sum,Amplitude detectprocess directly a

PHASE

SHIFTER

6xRF

COMB

ERATOR

FAULTBEAM

DETECTOR

PHASE

SERVO

BPMs

AMP

MOTION

To DOWN SAMPLER

MOTION

ERROR MONITOR

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 (∆)

A

C

B

D

A + C

B + D

D − B

D + C − A − B

B + D − A − C

A + B + C + D

C − A A + D − B − C ∆X

∆Y

Σ


Basic

Like a

• Driv

• (com

• Dow

Longittube

(a trantubespropa

Over-D

a sortbe verbunch

Operaband.

5-20008545A13

vout

vout

USPAS Control Th

“Kicker” Technology Issues

ideas -Transverse Control viaStripline Electrodes

directional coupler

e signal goes “upstream”

bines E-field and B-field kicks)

nstream feed - E and B cancel

udinal kick via periodic drift-

smission line with shielding drift- excitation wave counter-

gates with beam)

amped resonant cavity -

of wideband RF cavity. Q musty low (4 or 5) to kick individuales nanoseconds apart

ting frequencies in the 1 - 2 GHz

Beam


icks

Longit

Baseb

320 p

QPSKm

Signacn

USPAS Control Th

Six Bunches and associated longitudinal k

udinal output amplifier control signal 2 ns bunch spacing

and risetime

s (2ns/div)

-AModulation

l phase invertsarrier foregative kick


A vi(AdvaLBL)kickerlongituanten

Theallowcorrectransvbeamenerg

USPAS Control Th

ALS Beamline

ew of the ALSnced Light Source,beamline showing Y, X kicker anddinal kicker

nas.

“kicker” structuresexternal wideband

tion fields toersely deflect thes or to add or subtracty from the beam.


Trans

Essen aseband ( except for KEK-B, usi

Corne ating beams. Also cleverduty-c

Ampli

Longit

Ceram

Loade SSY ( KEK-B?). Easy tocool. N ted to this design

Drift-tu sed by ALS, PLS, PEP-II.Usefu -II LER, above)

Opera WT power stages ( 200 W)

USPAS Control Th

Kicker Implementations

verse-

tially all striplines. Length limited by bunch spacing. Operation at bng two sets of kickers/amplifiers)

ll ( CESR) has clever short-circuited design to kick counter-propagycle modulated kicker driver, as opposed to linear amplifier drive

fiers - baseband ( 100kHz - 230 MHz)

udinal - Several designs

ic Gap ( UVSOR) - modest shunt impedance

d (damped) Cavity - Designed by LNF-INFN, used by DAFNE, BEeeds circulator. Reasonable shunt impedance. PEP-II LER upda

be structures - designed by LBL Beam Electrodynamics Group, ul in-band directivity. Cooling issues for ampere currents ( see PEP

ting in 1 - 1.5 GHz band. GaAs power amps ( 200 - 500 W), also T


Many

C

E

O

F

How t

P uency information

O stability threshold. Eachm .

C ted, depends strongly onth

T namics in a single 20 msm sient.

USPAS Control Th

Measuring beam & system dynamics

uses

ontroller algorithm design

stimation of operating margins

ptimization of operating conditions

eedback hardware testing

o characterize an unstable system? Possible approaches

ower Spectrum measurement - no phase information but shows freq

pen-loop transfer function -measurement is only possible below inode to be quantified requires a separate network analyzer sweep

losed-loop transfer function- extracting beam dynamics is complicae loop configuration.

ransient diagnostics- allow to characterize open and closed-loop dyeasurement. All unstable modes can be measured in a single tran


Feedb n extracted bunch

16

USPAS Control Th

Longitudinal Control at the ATF

ack reduces the driven noise spectrum, improves energy spread i

0 2 4 6 8 10 12 14

10−1

100

101

Frequency (kHz)

Cou

nts

Open loopClosed loop


E t Sources

Thank

USPAS Control Th

ffect of Longitudinal Stability on Synchrotron Ligh

s to Tony Warwick (ALS) for Undulator Spectrum

680 685 690 695 700 705 710 715 7200

1

2

3

4

5

6x 10

−9 Undulator Spectrum − Feedback on (−),off(− −)

Energy ( eV)

No

rma

lise

d O

ptic

al I

nte

nsi

ty (

arb

. u

nits

)

ALS 5th Harmonic Undulator Spectrum 108 mA 84 bunch pattern


Syn

USPAS Control Th

chrotron Light Images


t

stic technique that

the motion of all

l information

Trancharaof an

Lineawhengrow

trigger: or har

Normalfeedback

filter 0

USPAS Control Th

Grow/damp transient measuremen

A transient diagnogenerates

• 1.2MB record ofbunches

• Complete moda

sient measurement tocterize open-loop dynamics unstable system.

r time control is difficultmaking an exponentially

ing measurement.

softwaredware

Start ofrecording

Filter coefficientset switch

End ofrecording

Adjustablefilter switchbreakpoint

Adjustablehold-offdelay time

filter 1 filter 0 Normalfeedback


PLS

A 30 m

All fillTranssimpliin thismodaeigenvtransie

A singinstabopera

A veryas a fuetc. R

Difficuimpedexciteat a hswam

USPAS Control Th

Grow/damp measurement example from

s long data set with 15 ms open-loop section.

ed bunches participate in the modal motion.formation to the even-fill eigenmode basisfies the picture - there are three strong eigenmodes

transient. Fitting complex exponentials to thel motion we extract estimates of the modalalues for both open and closed-loop parts of thent.

le measurement like this only characterizes theilities and the feedback at a single acceleratorting point.

powerful technique- measure modal eigenvaluesnction of beam current, RF system configuration,

eveals the impedances directly driving the beam

lty - the “free” motion is dominated by the largestance(s). To study slowly-growing modes, you canthe mode of interest before the study - it then startsigher ( detectable) amplitude. In a while it is

ped by the fast modes.


ent

ased measurement of in-

grow-damp transients,cies, as the watere is varied ( this sweepsmpling frequency of the−400

−20

0

20

40

60

80

100

ℜ(Z

|| ) (

kΩ)

−400−60

−40

−20

0

20

40

60

ℑ(Z

|| ) (

kΩ)

USPAS Control Th

ALS HOM Complex Impedance Measurem

These techniques allow beam-bsitu HOM impedances

The measurement is made viameasuring complex frequentemperature of the cavity structurthe HOM frequency across the sabeam)

−300 −200 −100 0 100 200 300 400Frequency offset from resonance (kHz)

Fr=2.8532 GHz, R

s = 97±3kΩ; Q = 24000±2000; R

s/Q =4±0.3 Ω

−300 −200 −100 0 100 200 300 400Frequency offset from resonance (kHz)


DAFN

• i

• qinind

Flexibnovel

• sth

• twd

• qsin

80 100 120

DualNotch

80 100 120

USPAS Control Th

Quadrupole instability control

E e+/e-collider at LNF

ncreased operating currents

uadrupole mode longitudinalstabilities have appeared (thestalled system suppresses theipole modes).

le DSP code implemented aquadrupole control filter

oftware programmability ofe DSP farm

o parallel control paths foripole and quadrupole modes.

uadrupole control has beenuccessful, allowing a 20%crease in luminosity.

0 20 40 60

−40

−20

0

20

40

Frequency (kHz)

Gai

n (d

B)

0 20 40 60−200

−100

0

100

200

Frequency (kHz)

Pha

se (

deg)


lysis

Advan

Comp aches allow measurementsof gro

In a tra mode-by-mode narrowbandmeasu

From rowth rates, but alsooscilla

Large

Difficu

Expon

Large

USPAS Control Th

Advantages and difficulties of transient ana

tages

lementary to narrowband frequency domain detection. Both approwth/damping rates.

nsient all unstable modes are measured at once - much faster thanrement when there are hundreds of unstable modes

a transient measurement we get complex eigenvalues - not only gtion frequencies.

datasets - information about the motion of every bunch

lties

ential growth rates - easy to lose control of the beam.

datasets


Ultim

What ance)?

Sever

I). Noi several stages -

Front namic range, steady-stateoffsets ceivers typically 10 - 20 dBabove A/D noise or DSP

Proce oise (broadband) is onesystem ater in contribution.Narrow lp with reduced sensitivityto ma t

Power expensive way to increasegain (m

Outpu scillation amplitude fromwhich mplicated

Driven mit on achievable gain

Intere 802,2010

USPAS Control Th

ate/Practical Limits to Instability Control

Limits theMaximum Gain(e.g. fastest growth rate, or allowed imped

al Mechanisms

se in feedback filter bandwidth, limits on noise saturation. Gain is from

End (BPM to baseband signal) gain limited by required oscillation dy(synchronous phase transients, orbit offsets). Noise floors in the re

A/D quantizing noise.Damped equilibrium noise floor is not set by

ssing Block - gain limited by noise in filter bandwidth. Quantizing n limit - noise from RF system or front-end circuitry is typically greband filters help with broadband noise. Broad filter bandwidths he

chine tunes, operating point - or variations of dynamics with curren

stages - gain scales with kicker impedance, sqrt(output power). Anore kickers, more output power).

t power (actually maximum kicker voltage) determines maximum o linear (non-saturated) control is possible. Saturated behavior is co

noise ( e.g. from RF system, or from other excitations) may set li

sting Movie - loss of Control in PEP-II from RF noise PRST 13:052


art II

II) Sta s. control frequency)

Relate

For cir n pickup)

limit s ver control band

Appro

L

R

U

Negat for causal systems you paythe pr

USPAS Control Th

Ultimate/Practical Limits to Instability Control, p

bility of the feedback loop itself, (e.g. limits on phase shift and gain v

d to time delay between pickup, processing, and actuator

cular machines (systems with kick signal applied on later turn tha

et by revolution time, fastest growth rates, and filter phase slope o

priate for optimal control theory applications

QR

obust Control

ncertain Systems

ive group delay over a portion of the frequency band is possible, butice in increased phase slope away from the negative region


1 - 4 G

Gener le FPGA architectures.Softwa AC/KEK/CERNcollab filters. Allows I&Qproce

Low G

• pote dback in ILC

• Very ks, using electronic orelec

Kicker

existin with heating at high beamcurren

RF Fe xisting analog and hybridanalog and also LHC) are nearingtechno ital RF processing channellook v

USPAS Control Th

Promising Areas for R&D Efforts

S/sec. processing channels

al-purpose reconfigurable building blocks - based on reconfigurabre configured for multiple longitudinal/transverse applications. SL

oration has prototypes in evaluation, development of novel controlssing streams (2X sampling)

roup Delay processing channels

ntial applications in Energy Recovery Linacs, IP collision point fee

low group delay (e.g. 10s of nanosecond scale) FIR/IIR filter bloctro-optic technologies

structures

g drift tube, stripline and damped cavity kickers all have issuests, residual HOM content

edback techniquesto reduce impedances seen by the Beam - the e/digital RF feedback techniques in the LLRF systems at PEP-II (logy and operational limits. Efforts to develop a low group delay dig

ery attractive


rts

Ongoi

Proton PS injector)

• Pho

• Cou

• Sing

Resea

• Sim

• Mac ulations

• Wh

• Dev

Kicker

• Res icker

• Use ? overdamped cavity?

USPAS Control Th

LHC/SPS Ecloud driven instability R&D Effo

ng project SLAC/LBL/CERN via US LARP

machines,Ecloud driven instability - impacts upgraded LHC ( and S

toelectrons from synchrotron radiation - attacted to positive beam

pled-dynamics, electrons act as lens to kick transversely

le-bunch effect - head-tail (two-stream) instability

rch directions

ulations

hine measurements - understand required bandwidth, validate sim

at sort of feedback control is feasible?

elopment of 4 GS/sec. processing channel demonstrator

structures

earch effort to investigate useful 1 - 2 Ghz bandwdith transverse k

periodic slotline ( stochastic cooling)? Array of 1/4 wave striplines


Eclou2010.injectiTimetransv(Junebetwe

TMCIbunchinstab

data tpickupsampl

We nsimulabeam

Studie

pickupquant

bunch 47

50 100slice

bunch 119

50 100slice

USPAS Control Th

SPS MD Studies

d studies June 2009, April 2010 JulyVertical Instability develops after

on of second batch, within 100 turns.domain shows bunch charge, anderse displacement 1E11 p/bunch2009). Roughly 25 slices (250 ps)en displacement maxima and minima

Studies July/August 2010. Singleinjection at 1.3E11 (3E11). Vertical

ility develops - time scales of 1000 turns

aken via exponentially-tapered striplines, delta/sigma processing at baseband.ed 20 or 40 GS/sec.

eed MD data to compare beamtions and dynamics models, - extractdynamics necessary to design feedback.

s of bandwidth of motion, tune shifts

s -Noise, transverse resolution well-ified

0 50 100−400

−300

−200

−100

0

100

200

300

400

500 Vertical displacement of

slice

SU

M /

DIF

F s

igna

ls (

a.u)

0−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Ver

tical

dis

plac

emen

t (a.

u)

SUMDIFF

0 50 100−400

−300

−200

−100

0

100

200

300

400

500 Vertical displacement of

slice

SU

M /

DIF

F s

igna

ls (

a.u)

0−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Ver

tical

dis

plac

emen

t (a.

u)

SUMDIFF


MD da 2 RF voltages

Pre-pr ongitudinal motion

9 and

ug_09/)

1E11 a)

Injecti e)

Movie able)

Movie 19 e-clouds)

Movie signal by slice

Movie

Movie troid

These he system

We ne edback control

USPAS Control Th

Movies of June 16, 2009 SPS MD

ta at 1E11 P/bunch, with three chromaticity values (.1,.2 and -.1),

ocessing includes equalization (cable response), suppression of l

(www.slac.stanford.edu/~rivetta/e-clouds/movies_Aug0

also inhttp://www.slac.stanford.edu/~dandvan/e-clouds/a

P/bunch, 25 ns separation, 72 bunches/batch ( June 2009 MD dat

on of batch 1 ( stable) followed by 2nd batch ( which goes unstabl

1-Vdspl_bunch_47.avi Vdisplacement for bunch 47 1st batch (st

2 -Vdspl_bunch_119.avi Vdisplacement for bunch 47 2nd batch (#1

3 - tune_s.avi Sliding Window spectrogram of Bunch 117 vertical

4 -centroid.avi Centroid tune shift along 620 turns

5 -rms.avi RMS of slice motion with respect to the bunch cen

animations help show the complexity and non-linear behavior of t

ed to extract simpler model dynamics to use to design/estimate fe


Feed of ecloud/beam

Goal - lisms

• Equ

• Mod

• grow

• tune cess)

sliding

• slice

• vs.

RMS t e evolution, charge loss)

Estim s/noise in receivers, powerstages

Recen dels to data

Critica ne shifts, internal modes

USPAS Control Th

back Estimation- requires quantitative knowledgedynamics

develop quantitative analysis methods, normal-mode, other forma

alization, suppression of longitudinal motion effects

es within the bunch (e.g. bandwidth of feedback required)

th rates of modes (e.g. gain of feedback channel)

shifts, nonlinear effects (e.g. Stability, robustness of feedback pro

windowFFT techniques - check tunes, tune shifts

FFTs (tune per slice)

time (modes within a bunch)

echniques- on SUM and Delta (estimation of motion of the beam, tim

ate impacts - injection transients, external excitations, imperfection.

t Emphasis - System Identification methods to fit coupled-oscillator mo

l to estimate - required sampling rate (bandwidth), growth rates, tu


cale?

Frequ

sampl table modes)

Scale

• mea

SPS -

• 16 s evolution frequency

• 16 t

KEKB

• 1 sa on frequency.

Thesc ntroller model isnot verydiffere

What kicker structures, plusthe ne ates may be comparable

Impor eam. Controller complexity

USPAS Control Th

E-cloud Feedback Channel - Complexity? S

ency spectrograms suggest:

ing rate of 2 - 4 GS/sec. (Nyquist limited sampling of the most uns

of the numeric complexity in the DSP processing filter

sured in Multiply/Accumulate operations (MACs)/sec.

5 GigaMacs/sec. (6*72*16*16*43kHz)

amples/bunch per turn, 72 bunches/stack, 6 stacks/turn, 43 kHz r

ap filter (each slice)

(existing iGp system) -8 GigaMacs/sec.

mple/bunch per turn, 5120 bunches, 16 tap filters, 99 kHz revoluti

aleof an FIR based control filter using the single-slice diagonal cont than that achieved to date with the coupled-bunch systems.

isdifferent is therequired sampling rateandbandwidthsof the pickup,ed to havevery high instantaneous data rates, though the average data r

tant dynamics difference - Ecloud tune shifts, even for stabilized b


Develexpon

Can b

Estimchaoti

Idea -seque

Time dfunctio

Frequ

Can b

Valuabcontro

Progre

400W

Tunne /sec. D/A

USPAS Control Th

Driven Beam Experiments

op excitation technique using existingential striplines

e frequency domain or time domain study

ate dynamics below instability threshold (pre-c motion, see tune shifts below threshold)

use 4 GS/sec. DAC hardware todrive noisences onto selected bunch(es)

omain sequences - transform, average (transfern estimator)

ency response of internal structure and modes

e done as excitation in simulation, too.

le step in development of any possible feedbackller (Back End)

ss - Synchronized excitation code

(4 100W) 20 - 1000 MHZ amplifiers ordered

l “cart” in progress for 2011 SPS MD Doublet Response 4 GS


DAFN Diamond et al. all havesignifi ll routinely operate wellabove l and custom hardware.

Thein o the driving impedances.Runni rstand the practical limits ofthese argin limit for control of lowmode issioned.

The te performance of thesesystem n gain and phase fromloop s nore. Recent commercialactivit ck systems more feasible.Signifi beams.

The d re very useful in validatingdynam hey also provide many veryunique edances). Theflexibilityof the eds as the accelerators weremodifi novel IIR control filters, orthe qu

The n ew ideas in control

USPAS Control Th

The State of the Art

E, KEK-B, CESR, PEP-II, ALS, BESSY-II, PLS, Elettra, ESRF,cant experience running multi-bunch instability control systems. A instability thresholds. Other facilities developing mix of commercia

stabilitiesthemselves are proportional to current, and proportional tng these facilities at higher currents requires some analysis to undeinstability control systems. PEP-II pushed the fundamental phase ms, and a special low group delay channel ( the “woofer”) was comm

chnology of these systems may evolve, but thefundamental limitsto thes, e.g. thesaturation effects from noiselimiting the gain, and the limits o

tabilityof the feedback loop, are the central limits we must never igy in high speed FPGA platforms make 1-4 GS wideband feedbacant challenges exist in the transducers which sense and control

iagnostics possible with the programmable DSP based systems aics and understanding the performance of the instability control. Taccelerator diagnostics(such as measurement of complex HOM imp

se systems has been an opportunity to address several control need (such as the addition of harmonic cavities to the ALS, requiringadrupole mode control at DAFNE)

ew directions in Ecloud control for the SPS and LHC may require n


Multi-b

Proble eratemodulation offilling

• Des

• diffe des) and narrowband HOMstru

• Tec

• Issu

• Sen

Likely

Gener 8 Gs/sec. sampling rates.Softwa loud control.

Wideb

Very lo using electronic or electro-optic t

USPAS Control Th

Summary

unch instability control-

m can be addressed withimpedance control, carefulcavity tuning, delibpatterns, and/or active feedback

ign choices - all-mode vs. selected modes

rence between damped HOM structures (e.g. bands of unstable moctures

hnology choices - processing approaches

es of injected noise, required output power

sitivity to variations in operating configurations

Areas for future work

al-purpose reconfigurable building blocks - based on 1 GS/sec. tore configured for multiple longitudinal/transverse applications, Ec

and kicker and pickup technologies ( GHz bandwith systems)

w group delay (e.g. 10s of nanosecond scale) FIR/IIR filter blocks,echnologies


Pickup

( histo

Cable

Hybrid

• Cab

• Issu Bessel Filters

Data A , 10 or 40 PS/sample)

Offline

Equal udinal motion

RMS

• on S volution, charge loss)

FFT b

• slice

• with

USPAS Control Th

SPS Instrumentation - setup

s- wideband ( exponential taper) striplines ( T. Linnecar)

ry of directivity, past use in P-Pbar program)

plant from SPS Tunnel to Faraday cage ( instrument room)

receiver ( Anzac H9 Hybrids )

le delays trimmed, matched, hybrids selected for matching

es with 1700 MHz propagating modes - use of800 MHz ( 1 GHz etc.)

cquisition ( vertical plane) in Tektronix fast scope (2.5 GHz bandwidth

data analysis in Matlab ( and Python)

isation of stripline signal ( thanks WH and RDM), removal of longit

techniques ( with subtraction of DC transient)

UM and Delta ( estimation of motion of the beam, head-tail time e

ased sliding window techniques

by slice ( tune shifts within a bunch)

in bunch ( bandwidth or internal modes)


Const

• Con hift)

• DC

• Fre

FIR Fi

Desig

• Letwav

• Pha

• Set(DC

• Rescha

What avities).

What

10 20 30 40Frequency (kHz)

USPAS Control Th

A possible controller design approach

raints

trol of phase & gain at the oscillation frequency Fs (90 degree phase s

rejection

quency selectivity

lter implementation:

n approach

filter impulse response sample a sinee at the oscillation frequency.

se and gain adjustments are simple

sum of the impulse response to 0 rejection)

ulting filter has bandpassracteristic around the Fs

if the oscillation frequency changes with current?(ALS, Harmonic C

if quadrupole as well as dipole oscillations are present? (DAFNE)

yn bkxn k–k 0=

M

∑=

0 10 20 30 40−30

−20

−10

0

10

20

30

Frequency (kHz)

Gai

n (d

B)

0−300

−200

−100

0

100

200

Pha

se (

degr

ees)

Feedback Control of Particle Beam InstabiltiesTalk OutlineMotivationFeedback basicsCoupled-Bunch Feedback Principles - General OverviewHarmonic Oscillators, RevisitedCoupled dynamics: multiple bunchesNormal Modes, RevisitedEigenmodes and impedancesProcessing RequirementsTechnical ChallengesBlock diagram of a longitudinal feedback systemHER and LER Systems at PEP-IIFilter Implementation OptionsExample FIR filtersBaseband transfer FunctionRF Transfer FunctionExisting/Example Coupled-Bunch Feedback SystemsALS Transverse Feedback ImplementationExample -IGP processing channelInteractions with the particle beam - pickup and kicker technologiesPickup and Frontend technologyFrontend signal processing“Kicker” Technology IssuesSix Bunches and associated longitudinal kicksALS BeamlineKicker ImplementationsMeasuring beam & system dynamicsLongitudinal Control at the ATF

Effect of Longitudinal Stability on Synchrotron Light SourcesSynchrotron Light ImagesGrow/damp transient measurementGrow/damp measurement example from PLSALS HOM Complex Impedance MeasurementQuadrupole instability controlAdvantages and difficulties of transient analysis

Ultimate/Practical Limits to Instability Control, part IIPromising Areas for R&D EffortsLHC/SPS Ecloud driven instability R&D Efforts

SPS MD StudiesMovies of June 16, 2009 SPS MDFeedback Estimation- requires quantitative knowledge of ecloud/beam dynamicsE-cloud Feedback Channel - Complexity? Scale?Driven Beam ExperimentsThe State of the ArtSummarySPS Instrumentation - setupA possible controller design approach

Feedback Control of Particle Beam InstabiltiesUSPAS Control Theory and Applications Talk Outline...

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Transcript of Feedback Control of Particle Beam InstabiltiesUSPAS Control Theory and Applications Talk Outline...