USPAS Control Theory and Applications Feedback Control of Particle Beam Instabilties J. Fox, J. Cesaratto, T. Mastorides, C. Rivetta, D. Van Winkle, O. Turgut, A. Young, S. Uemura 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-AC03-76SF0515
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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
eory and Applications
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
uilds on program instability control and beamiagnostics.
ignificant advance in therocessing speed and densityreviously achieved.
able to many installations
eory and Applications
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!
5-2000 8545A11
B = 0 B < 1 B 1
1/γ
e – e – e –
eory and Applications
Difficumakethe nuBPMburstsdetectfor A/D
Examshowsa resexpon
LongitRF ha
TransDelta-
7288A5
Terminated Lines
67.2400 ns6908A3
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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 Burst to Phase Detector
Impulse from BPM
10–92
57.2400 ns 62.2400 ns4-91
eory and Applications
nal processing
ase detection againstsystem. sensitivity
nic
lta/sigma processingdifference signals.
at harmonic of RF, ort baseband
GEN
FROM
D
B
C
A
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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
eory and Applications
Basic
Like a
• Driv
• (com
• Dow
Longittube
(a trantubespropa
Over-D
a sortbe verbunch
Operaband.
5-2000 8545A13
vout
vout
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“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
eory and Applications
icks
Longit
Baseb
320 p
QPSKm
Signacn
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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
eory and Applications
A vi(AdvaLBL)kickerlongituanten
Theallowcorrectransvbeamenerg
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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.
eory and Applications
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)
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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
eory and Applications
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.
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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
eory and Applications
Feedb n extracted bunch
16
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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
eory and Applications
E t Sources
Thank
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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
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
eory and Applications
PLS
A 30 m
All fillTranssimpliin thismodaeigenvtransie
A singinstabopera
A veryas a fuetc. R
Difficuimpedexciteat a hswam
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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.
eory and Applications
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
|| ) (k
Ω)
−400−60
−40
−20
0
20
40
60
ℑ(Z
|| ) (k
Ω)
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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)
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)
eory and Applications
lysis
Advan
Comp aches allow measurementsof gro
In a tra mode-by-mode narrowbandmeasu
From rowth rates, but alsooscilla
Large
Difficu
Expon
Large
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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
eory and Applications
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
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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
eory and Applications
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
eory and Applications
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
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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
eory and Applications
rts
Ongoi
Proton PS injector)
• Pho
• Cou
• Sing
Resea
• Sim
• Mac ulations
• Wh
• Dev
Kicker
• Res icker
• Use ? overdamped cavity?
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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
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
eory and Applications
Eclou2010.injectiTimetransv(Junebetwe
TMCIbunchinstab
data tpickupsampl
We nsimulabeam
Studie
pickupquant
bunch 47
50 100slice
bunch 119
50 100slice
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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
eory and Applications
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
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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
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
eory and Applications
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
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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
eory and Applications
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
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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
eory and Applications
Develexpon
Can b
Estimchaoti
Idea -seque
Time dfunctio
Frequ
Can b
Valuabcontro
Progre
400W
Tunne /sec. D/A
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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
eory and Applications
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
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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