Orbit control at IP

Y. Funakoshi
for the IP orbit control working group
The 17th KEKB Accelerator Review
Feb. 20 2012

Contents• Algorism of orbit control• QCS vibraHon issues• Dithering method for luminosity FB

Orbit feedback at IP :Algorism• Beam‐beam deﬂecHon (SLC, KEKB verHcal)
BPM
Δy at BPM= ~1.3µm

Δy at IP=~5nm ~1/10σy*
IP

SupeKEKB case

BPM

Luminosity• Luminosity feedback (dithering)(PEP‐II)
yWhen we shake the beam at around the peak of
the luminosity, there appears twice of thefrequency of the dithering frequency.

• Beam size feedback (KEKB horizontal)
Luminosity
Beam sizeσy (LER)x

At KEKB before installaHon of crab caviHes,
the verHcal beam of LER was used for thehorizontal orbit feedback at IP.

QCS Vibration issues• The most serious source of orbit change at IP• Recent progress– Coherency of vibraHon of QC1{RL}E and QC1{RL}P– Further damping of vibraHons by using highdamping materials– Suppression of orbit diﬀerence by orbit feedbacksystem (H. Fukuma)

QCSL vertical position oscillation (measurement)
and orbit change (tracking) : KEKB LER
Vertical orbit at IP(simulation)
0.23µm offset ->0.14µm@IP(calc.)

QCSL vertical position(measurement)

0.23µmSimulation on vibrations of QCS
magnets (H. Yamaoka)• SimulaHon using ANSYS– Modal calculaHon• Resonant modes: ~26, 36, 39, 53 Hz– OscillaHon amplitude (PSD (power spectrumdensity)• Input of simulaHon: Measured data on ﬂoor vibraHon– Coherency of vibraHons of QC{12}RE andQC{12}RP or QC{12}LE and QC{12}LP• Coherency is very high– Further damping with high damping materials

FEM model

H. Yamaoka

Fixed

Fixed

7

Modal calculation
26Hz

39Hz

H. Yamaoka
36Hz

53Hz

8

P.S.D. (Power Spectrum Density) analysis

H. Yamaoka

In the vertical direction

Freq.(Hz) P.S.D.(m2/Hz)
0.1
5e-11
1.5
5e-16
3.0
5e-15
6.5
5e-17
8.0
1e-16
10.
3e-18
16.
3e-18
100.
5e-21
damping= 0.5%

Floor vibraHon: Input for the simulaHon

9

Results(Vertical direction)
H. Yamaoka

RE1-back
RP1-back RE1-top
RP1-topI(90)
R(180)(-180)

R(0)I(-90)QC1RP-top  QC1RE-top

QC1RP-back  QC1RE-back10

Results(Vertical direction)
H. Yamaoka

RE1-back
RP1-back RE1-top
RP1-top

I(90)
R(180)(-180)

R(0)I(-90)QC1RP-top  QC1RP-back

QC1RE-top  QC1RE-back11

Orbit change at IP with 1µm
offset of QCS magnets

QC1L
QC1R
QC2L
QC2R

COD

K1 (/m)Distance βQ [m]from IP[m]βIP[mm]Δψy/2πLER‐1.7170.912

2504.30.27

0.24995‐0.706HER‐1.142

1.390

5462.40.3

0.24997‐0.731

LER‐1.712

0.912

2567.70.27

HER‐1.070

1.430

5592.60.3

LER

0.84161

1.9099

962.2

0.27

HER

0.650232.67991923.30.3

LER

0.83924

1.9760

924.6

0.27

HER

0.55577

2.94491806.90.3!y =COD@IPfor 1µm
Q‐oﬀset[µm]>
0.24996 ‐0.713>
0.24997 ‐0.693
0.25004 0.2145>
0.25030 0.2470
0.25005 0.2097>
0.25004 0.2046

1
QCS magnets for LERとHER move
#Q # IP cos (!" " !$ )% Ifcoherently、orbit
diﬀerence of the two
2sin !"
beam becomes much smaller (1/10 ~1/20) than non‐coherent case.

Time domain vibration data toreproduce PSD from Yamaoka・ To make a mode to reproduce the ﬂoor
vibraHon (Ornstein‐Uhlenbeck process )・ 3 resonant modes (3, 36 and 53Hz) arecreated.

QCS‐sResults(Ver$cal direc$on)
Cryo‐Mid

Supp‐Top

Coil‐sSupp‐Back

Cryo‐top(Backward)

SuperKEKB

QCS‐t

H. Yamaoka

Coil‐tInput

KEKB14

Reproduced PSD

Resonance at ~53Hz
PSD from H. Yamaoka

2Δω = 2π * 0.7Hz
Q = ω0/2Δω ~75Reproduced by Funakoshi

COD simulation due to QC1R vibration in case that 
QC1RE and QC1RP
moveinthesameway± 1σyLERHER

LER ‐ HERMagnify

We need to suppress 3 Hz oscillaHon.

H. Yamaoka

300

High Damping Material: D2052

t1mm
500

A/δstMn‐base damping alloy

ω/ωn18

H. Yamaoka

Spring :k

F=a・cos(ωt)

F=1x104N
k=2x105N/mm
Materials（w/o damping material）
Cryostat: SUS
Coil:Cu
Supp.‐rod: Ti‐alloy
QCS table: SS400

13Hz

damping= 0.5%
 Response displacement： 12.4mmeigen‐frequency： 13Hz

19

H. Yamaoka
Materials
Cryostat: SUS
Coil:
Cu
Supp.‐rod: Ti‐alloy
QCS tables: damping material
damping= 5%bolts： damping material Response displacement： 3.2mm(damping: 74%）
eigen‐frequency： ９Hz
Materials
Cryostat: SUS
Coil:
Cu
Supp.‐rod: Ti‐alloy
QCS table: damping materialbolts： damping material

SS400

SS400

 Response displacement： 6.0mm(damping: 51%）
eigen‐frequency： 11.6Hz

20

H. Yamaoka
Materials
Cryostat: SUS
Coil:
Cu
Supp.‐rod: Ti‐alloy
QCS table: damping material
welding (t45mm）
bolts： damping material

SS400

SS400
SS400

 Response displacement： 6.9mm(damping: 44%）eigen‐frequency： 13.7Hz

This case seems realisHc.
Materials
Cryostat: SUS
Coil:Cu
Supp.‐rod: Ti‐alloy
QCS table: steel instead of damping
material welding(t45mm）
bolts： damping material

SS400

SS400
SS400

 Response displacement： 10.8mm(damping: 13%）eigen‐frequency： 13.7Hz
21

Orbit Feedback System
disturbancereference+-PID

Gp++

plant
power supply
eddy current

Mpmonitor outmonitor
FIR

first order lag

H. FukumaAnalysis of FB system by H. Fukuma
group delay = 5 samples (1.1ms)
dB
tau = 8.5ms

tau = 4.0ms

with delay compensation

without delay compensation

Hz
tau = 1.0ms

Disturbance suppression is weakerwith delay compensation.
If group delay is reduced to 1ms, rejection gain
at 10/100Hz is -22/-5 dB, and gain is almost
not dependent on time constant of the plant.
Tau is the time constant of the plant coming fromeddy current and delay in power supply etc.

Horizontal orbit feedback• Diﬃculty to develop FB based on the beam‐beam defecHon likethe verHcal case
– Small ξx• ξx ~ 0.0028(e+), 0.0017(e‐)– Two sources of horizontal beam‐beam kick
• Horizontal oﬀset and shim of collision Hming• Maybe we need a diﬀerent method for the Hor. feedback.
– Luminosity feedback (dithering) (like PEP‐II)– Beam size feedback (like KEKB Hor. feedback before crab)• Eﬀect of horizontal oﬀset with crab waist scheme– Due to Hor. oﬀset, the two beams collide at the posiHon which is shimed
from the waist point.
– The crab waist seems to compensate this shim of waist.
– However, the situaHon becomes worse with the crab waist, since wehave to keep the both beams at the design collision point with crab waistscheme.

• Feedback speed– Orbit change at IP due to fast vibraHon of IR quads is small. We do notneed very fast feedback.

Dithering for Horizontal FB• We have started to consider the dithering system based on
experience at PEP‐II.
• Conceptual design– Monitoring• Fast luminosity monitor (ZDLM)– Detect gamma‐ray or lost parHcles from radiaHve Bhabha scaoering– Magnets for dithering• Dithering frequency: 60 < Freq. < 100Hz• Amplitude of dithering: ~<0.5σx ‐> steering kick angle: ~< 5µrad• Steering magnets: magnets with air core coils– Electronics• Lock‐in amp (PEP‐II) ‐> spectrum analyzer– Steering magnets for orbit correcHon• Use usual DC steering magnets for FB

S. Uehara

Where are the signals?
R‐sideL‐sideRecoil electron
γ from positron

LERHERγ from electron

OutsideRecoil positron

Possible locations
R‐sideS. UeharaL‐sideDeﬂected e‐γ, e+‐side
γ, e‐‐side

Deﬂected e+

OutsidePossible problems:Material quanHty of the beam chamber in r.l.
Undesirable sensiHvity to angle and posiHon/size of the beams at IP

Beam loss simulation from raditive
Bhabha: LER Loss Position & Rate

Loss rate: RLoss [mA/s] = 1000N [partices/s] e f0
e = 1.602 !10 "19 [C]
f0 # 100 [kHz]0.1mA/s ‐> 6.2GHz

# of survived particles (LER)e+Azimuthal angle distribution of lostparticles (LER)

Zero degree: horizontal (outside of ring)Lost posiHon: 4m < s < 16m from IP

Expected ZDLM rate (Uehara)
0.1mA/s ‐> 6.2GHz• Funakoshi‐san’s coeﬃcient• The rate should be proporHonal to luminosity
1035 luminosity ‐‐‐ ~ 1GHz

‐ EﬀecHve detector length ‐‐‐ ~ 0.1m
‐ Eﬃciency ‐‐‐ 10%(angular coverage and shower loss)
Expected Rate ‐‐‐ 0.1mA/s  10 MHz
LER 4 m point (upstream BLC1LP)~ 2MHz @1035
9 m point (downstream BLC1LP) ~ 2MHz @1035Luminosity DitheringMonte Carlo simulation

S.Uehara(KEK)ParametersS. Uehara

・A set of measurement: measure the change of ZDLM rate for one
second・Sampling rate 1024Hz
measure every 0.977ms
・Dithering ‐‐ frequency f = 77Hzr ~ sin 2π.
Assume that the luminosity depends on r with a Gaussian
distribu$on.
L(t) ~ Exp[‐(q+p sin 2π. )2/2]
q：oﬀsetp：dithering amplitude
f：dithering frequency （here we assume f=77Hz)

S. Uehara

Dithering|q|>p – move along slope

Current
Luminosity posiHon|q|<p ‐‐ move around peak

dithering±pσqσ

Parameter r for dithering
As for actual luminosity dependence on the orbit
oﬀset , we have to rely on the beam‐beam simulaHon.
Such simulaHon predicts that the luminosity loss with 1
σx oﬀset is about 15%.

K. Ohmi

βy*~300µm
Swaist:1/10 βy* (~30µm)‐> Lum. Loss ~ 3.5%

S. Uehara

Result with Mathematica8
p =0.5, q=1.0, event rate=10kHz
Luminosity↓（model curve）

Sqrt of Power Spectrum
77Hz (dithering frequency)

39% Loss（MC data）→

S. Uehara

p =0.5, q=0.6, event rate=10kHz
Luminosity

Sqrt of Power Spectrum77Hz

２×77Hz

20% LossS. Uehara

p =0.5, q=0.2, event rate=10kHz
Luminosity

Sqrt of Power Spectrum
77Hz
２×77Hz

8% Loss

S. Uehara

p =0.5, q=0.2, event rate=50kHz
Luminosity

Sqrt of Power Spectrum
77Hz
２×77Hz

8% Loss

S. Uehara

p =0.5, q=0, event rate=50kHz
Luminosity

Sqrt of Power Spectrum

２×77Hz

6% Loss

S. Uehara

p =0.2, q=0
Luminosity

Sqrt of Power Spectrum
２×77Hz50kHz

1.0% Loss
300kHz300kHzConclusion of dithering
simulation• Dithering with 0.5σ amplitude– 50k event/s : OK– 10k event/s: not suﬃcient– Luminosity loss: ~6% at peak of luminosity• Dithering with 0.2σ amplitude– We need > 300k event /s.
– Luminosity loss: ~1% at peak of luminosity• Expected event rate in case of measuring lostparHcles– ~ 2MHz @ 1035 cm‐2 s‐1

S. Uehara

Summary•

Algorism of orbit control– VerHcal: beam‐beam deﬂecHon based on BPM measurement– Horizontal: dithering method or beam size feedback•QCS vibraHon issues– We found that coherency of QC1 and QC2 for electron and positron is almost
complete on both sides of IP.
– Further suppression of the vibraHon (~ 50%) is possible by using high dampingmaterial.
– The coherence of vibraHon of the two rings may help.

• Dithering for horizontal orbit control– We just started considered the dithering method for horizontal orbitcontrol.
– Our study is on a primiHve stage. We have conducted somesimulaHons on the event rate of fast luminosity monitor.

Spare slides

Ground motion data created byusing Ornstein-Uhlenbeck process
τ= 0.2, c = 1 x 28^‐10, Δt=1/53/50HistogramTime domain

PSD of O‐U processOrnstein-Uhlenbeck process
・Measurement on ground moHon‐consistent with Brownian moHon in low frequency region（S. Takeda）
・Brownian moHon‐ Explained by Einstein using diﬀusion equaHon (1905)‐ Analyzed by P. Langevin using conHnuous Markov process(1908)
・ Ornstein‐Uhlenbeck process (sort of conHnuous Markov process) )‐ Used in analysis of Brownian moHon
1/2

X (t + dt ) = X (t ) ! ! !1 X (t ) dt + c1/2 n ( dt )n : sample value of radom variable N=N(0,1)
N(0,1) is Gaussian distribution with mean=0, ! =1.
1/2# c!
"(1/! )!t"(2/! )!t &X (t + !t ) = X (t ) e+ % (1" e)(' n (<- Exact update formula)$2

X (t ) = x0 e!(t!t0 )! " 0 (t " #), var{X (t )} =Power spectrum density SX ( f ) =c!
c!
!2(t!t0 )!
1!
e"(t " #)()2
22c! 2
1+ ( 2"! f )~21f2

S. Takeda

System of harmonic oscillator withdamping and external force
・Modeling of magnet vibraHons
ny = ! yi (i: each resonant mode)
i=1・EquaHon for yi..

2 .
y i+ ! yi + !i2 y = Ci F
i! i : damping time (determine Q value of resonance)!i : angular resonant frequency
Ci : coupling between floor vibration and magnet
F : external force (substitute floor vibration data for this force)・SoluHon of equaHon‐ ωi = 2π x (3Hz, 36Hz, 53Hz) : solve with Runge‐Kuoa method‐ Coupling and damping Hme were chosen so that the resonances are reproduced.
‐ Sum up three soluHonsSummary of MAC in 2011••

The IP orbit control at SuperKEKB is much more diﬃcult than that at KEKB.
Major diﬃculty comes from the mechanical vibraHon of IR quadrupoles.
– SimulaHon on the quads of SuperKEKB has given a beoer result than KEKB.
– Further suppression of the vibraHon may be possible.
– The coherence of vibraHon of the two rings may help.

• In parallel to the eﬀorts to suppress the quadrupole vibraHon,
we will develop the orbit feedback based on the beam‐beamdeﬂecHon.
• BPM requirement– ResoluHon: 1µm is enough. 5µm is tolerable?
– Bandwidth: ~ 1kHz

• Horizontal orbit feedback– We need to develop a method other than the beam‐beam deﬂecHonsuch as luminosity feedback or beam size feedback.

IP machine parameters
KEKB

SuperKEKB

LER

HER

LER

HER

εx

18nm

24nm

3.2

5.0

εy

0.15nm0.15nm8.6pm

13.5pmκ

0.83 %

0.62%

0.27%

0.25%

βx*

120cm

120cm

32mm

25mm

βy*

5.9mm

5.9mm

0.27mm0.31mm ~1/4.5σx *

150µm

150µm

10µm

11µm

σx’*

120µrad120µrad450µrad320µradσy*0.94 µm

0.94µm

48nm

56nm

σy’*

0.16mrad0.16mrad0.18mrad0.22mradiBump horizontal oﬀset+/‐ 500µm+/‐ 30µm?

iBump verHcal oﬀset+/‐ 150µm+/‐ 7.5µm?

iBump verHcal angle+/‐ 0.4mrad+/‐ 0.4mrad?

~1/4~1/20

Measurements by ZDLM
Luminosity measurements(1) CounHng rate variaHon with conHnuous measurement(2) Bunch‐by‐bunch Luminosity – Hme criHcal measurementin rather short terms
ZDLM

PMT
amp.

constant‐fracHon

CF Discri.

Integr.circuit(f‐V conv.)

Digi.Vol

LogicAnalyzer
PowerUP!
Computernetwork

TOT Discri.
Hme‐over‐threshold

KEKB revoluHon signal as areference to bunch posiHon

ZDLM-1 in KEKB Commissioning"Real-time luminosity monitor for a B-factory experiment"
T.Hirai, S.Uehara and Y.Watanabe, Nucl. Instr. Meth. A458 (2001) 670-676.

The ﬁrst collision signal of KEKB
Before installaHon of BelleZDLM-5@KEKB/Belle in 2010
• Quartz Cherenkov radiatoron the deﬂected e‐ region (low eﬃciency)(The photons were blocked by thick beamchamber (~ 15 r.l. Cu)
Can obtain the Hming informaHon
 bunch‐by‐bunch luminosity measurement.
σt = 0.5 ns using a CF discriminatorContributions from other magnets• IP verHcal orbit change due to 0.1µm posiHonchange– QC1LP (βy ~ 2519m, K1 ~ 1.68) ‐> 69nm @ IP
– QC5LP (βy ~ 1570m, K1 ~ 0.15) ‐> 4.9nm @ IP
– Q (typical in arc) (βy ~ 20m, K1 ~ 0.2) ‐> 0.75nm @ IP

• CollecHve eﬀects of many Q magnets– Number of Q magnets per ring: ~400
– Assume no correlaHon of movements of the magnets:‐> expected oﬀset at IP ‐> 0.7 x Sqrt(400) ~ 15 nm

Effect of BPM resolution
Beam size
1 µm resoluHon is enough.

BPM resoluHon = 0 µm

BPM resoluHon = 1 µm

5 µm resoluHon is tolerable?

BPM resoluHon = 5 µm

BPM resoluHon = 10 µm