Collision Tuning
Dithering system
KEK
R. Ueki, Y. Funakoshi, T. Kawamoto, M. Masuzawa, S. Nakamura, T. Oki, M. Tobiyama, S. Uehara
SLAC
A. S. Fisher, M.K. Sullivan, D. Brown
ANL

U. Wienands
LAL
P. Bambade, S. Di Carlo, D. Jehanno, C. Pang
CERN

D.El Khechen1

Contents
1. Dithering system

2. Study during Phase-2 and Phase-3 spring commissioning
1. Luminosity scan

2. Feedback test

3. Summary2

Dithering system
Beam-beam
parameterHER
LER
ξy0.0881

0.0807Beam-beam deflection

ξx0.0028

0.0012Dithering feedback

Dithering feedback system was used at SLAC for PEP-Ⅱ
By dithering LER beam,
luminosity is modulated at dithering frequency

Input

𝐴𝐵∗ 𝑐𝑜𝑠 𝐶𝛼 + cos(2𝑤𝑡 + 𝛼)
2𝐴𝑐𝑜𝑠(𝑤𝑡)B𝑐𝑜𝑠(𝑤𝑡 + 𝛼)
Lock-in Amp

・Magnitude (Voltage)
proportional to B
・Phase difference (𝛼)reference and luminosity

Output of Lock-In

Reference signal

Modulatedluminosity signal

Horizontal offset

OutputLuminosity peak

Dx

Horizontal offset

3Hardware of dithering system
・8 sets of Helmholtz coils designed and fabricated at SLAC as dithering coil
・The coils were installed in LER beam line
ZDS1LP ZDS1RP

ZDS2LPZDS4LPZDS3LPZDS3LP, ZDS4LP, ZDS3RP, ZDS4RP
Vertical dither coils

ZDS2RPZDS1LP, ZDS2LP, ZDS1RP, ZDS2RP
Horizontal and Vertical dither coils

ZDS3RPZDS4RPZDS2LPZDS3LP

4

Other hardware
TsukubaB4 control room5

Luminosity scan in the Horizontal direction
・We checked the response of the lock-in amplifier・measuring magnitude, phase and luminosity

during horizontal scanMagnitude [mV]horizontal offset was changed from -120 to 100 um

900.0004

00.0002-90luminosity

2.8×1033 cm-2s-1

Dither Amp

20 um

Freq79 Hz

Scan range-120 um → 100 um

Luminosity peaked at the point ofmagnitude minimum and phase inversion

Normalized Luminosity

2 mm

1800.0006

Condition

By*

Magnitude minimum
Phase inversion

0-150-100 -50
1.2Luminosity
peak
10Phase [degree]

・Using local bump system at HER,0.0008-180
50 100 150
・ ZDLM・ Lumibelle2

0.80.60.4-150 -100 -50

050 100 150

Horizontal offset [mm]6Luminosity degradation by hourglass effectLuminosity degradation due to horizontal offset through hourglass effect𝛽𝑦∗ = 2 𝑚𝑚Calculation1∆𝑥 = 100𝜇𝑚↓ 20 % (meas)↓ 15 % (calc)

0.80.6-150 -100 -50

050 100 150

Horizontal offset [mm]5Vertical beta function [mm]Normalized Luminosity

1.2

432

10- 200- 100

0
Horizontal offset [μm]1002007

Coupling in the vertical direction
Magnitude minimum
180
Phase inversion

Normalized Luminosity

0.003

900.00200.001-90

Phase [degree]

Magnitude [mV]

0.004

・Horizontal dither is coupling vertically・In rough estimation, vertical dither amplitude
due to coupling is ~ 0.02 um
・Possible cause is x-y coupling at IP- when vertical offset of two beams is small,

010.5
1.2

1111.5-180
12

vertical dither does not affect horizontal feedback- if vertical offset large, minimum point of the lock-in amp
magnitude does not coincide with luminosity peak1・It would be possible to cancel coupling component

0.8

applying additional vertical dither intentionally or adjusting x-y
0.6
0.4
10.5

・ ZDLM・ Lumibelle2

11coupling parameter (R1)
11.5

Vertical offset [mm]12・Vertical dither feedback may be useful for beam tuning
8Feedback test - parameter optimization Dithering feedback algorism is based on PI control→ To need optimize the feedback gain
We did 3 feedback tests changing the integral gain
Luminosity

Horizontal offset

targetMagnitude

・As a result of adjusting the integral gain,
Horizontal offset approached to target position without large overshoot.

9

Feedback Test - stability of feedback Converged to the optimal orbit
X @ QC1LE [mm]-1.1

Feedback on-1.15

Feedback lost40 um-1.2

target position(luminosity peak)Stable state05

10150.008

1800.006

900.00400.002-9000510

Phase [degree]

Magnitude [mV]

-1.25

・The cause is not understood yet
・We are checking algorism of system-18015Time [min]10Luminosity degradation due to offset at each beta y*𝛽𝑦∗ = 2 𝑚𝑚 (Phase3 spring commissioning)∆𝑥 = ±20 𝜇𝑚
degradation is small𝛽𝑦∗ = 1 𝑚𝑚(next step)∆𝑥 = ±20 𝜇𝑚↓ 5%𝛽𝑦∗ = 0.3 𝑚𝑚 (design)∆𝑥 = ±20 𝜇𝑚↓ more 50 %Simulation of luminosity degradation
by Ohmi-san11

Summary
・All components of dithering system were prepared before Phase-2 commissioning
・We checked lock-in amplifier response and did dithering feedback test
Luminosity scan・We successful found Luminosity peak from magnitude and phase of Lock-in Amp

・Horizontal dither is coupling vertically
Feedback test
・by adjustment of integral gain, horizontal orbit converged to the optimal orbit
・Dithering feedback system does not operate now.
・When beta is squeezed and luminosity degradation due to horizontal offset become remarkable,
dithering system will be needed in order to keep high luminosity
12

13

14

Trend graph of current and luminosity

15

Feedback algorism• Beam-beam deflection (SLC, KEKB vertical)
Dy at IP=~5nm ~1/10sy*

BPM
Dy at BPM= ~1.3mm

LER

HER

垂直（ξy）

0.08810.0807水平（ξx）

0.00280.0012IPBPM

Luminosity• Luminosity feedback (dithering)(PEP-II)
When we shake the beam at around the peak of theluminosity (dithering), the dithering frequency in theluminosity is minimized and there appears twice of they the dithering frequency.
16Horizontal bump

2 mmluminosity

2.8×1033 cm-2s-1

Dither Amp

20 um

Freq79 Hz

Scan range-120 um → 80 um

Luminosity peaked at the point ofmagnitude minimum and phase inversion

Normalized Luminosity

By*

0.008

1800.006

900.00400.002-900-150-100 -50
1.20-180
50 100 150
Luminosity
peak

10.80.6

・ ZDLM・ Lumibelle20.4-150 -100 -50

050 100 150

Horizontal offset [mm]Magnitude minimum
Phase inversion

Phase [degree]

Condition

Magnitude [mV]Luminosity scan in the horizontal direction (LumiBelle2)

Luminosity scan to Horizontal direction
Input ZDLM
Magnitude minimum 1800.0004

00.0002-90

Normalized Luminosity

Magnitude [mV]

900-150-100 -50
1.2
Luminosity
peak

0-18050 100 150
・ ZDLM・ Lumibelle2

10.80.6-150 -100 -50

0Phase [degree]

0.000650 100 150

Horizontal offset [mm]Input LumiBelle2

0.006

900.00400.002-900-150-100 -50
1.20-18050 100 150
Luminosity
peak

10.80.6

・ ZDLM・ Lumibelle20.4-150 -100 -50

050 100 150

Horizontal offset [mm]Magnitude minimum
Phase inversion

180

Phase [degree]

Phase inversion

Magnitude [mV]0.008

Normalized Luminosity

0.0008

Lock-in output with vertical offset
Vertical offset of LER and HER beam
→ The point of magnitude minimum and phase inversion shift from luminosity peak
→ Horizontal feedback dose not work properly
・It’s important to maintain good vertical collision point
for accurate horizontal feedback
・High frequency fluctuation can be not collected,
・Slow drift during long time can be collectedusing vertical dither20

Luminosity scan to Vertical direction180
900.002-90010.5
1.2

Normalized Luminosity

01111.5

Phase [degree]

Magnitude [mV]

0.004

Input

LumiBelle2

Dither Amp

20 um

Freq79 Hz-180
12

Vertical Dither ON
1Dither Amp

0.8
0.6
0.4
10.5

1111.5120.07 um

Feedback test
-1.1

Feedback on
-1.15

40 um
-1.2

-1.25

target position(luminosity peak)
0100

Stable state
200

300

-1.198

400
300

-1.2
250
-1.202200-1.204-1.206

0100

200

300

150
400
22

Luminosity degradation by horizontal offset
Continuous Injection mode∆𝑥 2
𝐿 𝑥 /𝐿0 = exp(− 2 )
2Σ𝑥

HER

250 mA (-1% Auto injection)

LER

250 mA (-1.5% Auto injection)

Fill pattern

6.12 spacing 1train, 789 bunches∗𝑒𝑓𝑓2

Σ𝑥2 = 𝜎𝑥+TU

Normalized Luminosity

1.2Input ZDLM

y = m1+exp(-(M0-m2)^ 2/(2*(m...
値エラー
m1-0.0042074
0.0024503
m2-1.1823 0.00057764
m3-0.13657
0.0013125
カイ２乗
0.093666
NAR
0.97648
NA1

By fitting parameter= 𝜎𝑧 𝑠𝑖𝑛∅𝑐

By bunch length and half crossing angles

Σ𝑥𝜎𝑧−𝜎𝑧+Σ𝑥0.13657

5.64 mm4.99 mm0.312

0.15201

0.8

y = m1+exp(-(M0-m2)^ 2/(2*(m...
値エラー
m1 -0.033087
0.0024198
m2-1.174 0.00072517
m30.15201
0.0017362
カイ２乗 0.096792
NAR0.96847
NA

0.6

0.4-1.35

∗𝑒𝑓𝑓

𝜎𝑥±

∗𝑒𝑓𝑓2+ 𝜎𝑥−-1.3 -1.25-1.2 -1.15

QC1LE [mm]-1.1 -1.05∆𝑥 = 100 𝜇𝑚
𝐿 𝑥→= 20 %
𝐿0𝐿 𝑥∆𝑥 = 100 𝜇𝑚 →=5%
𝐿0

0.00200.001

-90

010.5
1.2

1111.5

0.8

0.4
10.5

・ ZDLM・ Lumibelle2

1111.5

Vertical offset [mm]12180900.002

0-90010.5
1.2-180
1210.6

Magnitude [mV]90

Normalized Luminosity

Magnitude [mV]Normalized Luminosity

0.003

0.004

1111.5

10.8
0.6
0.4
10.5

・ ZDLM・ Lumibelle2

1111.5Phase [degree]

180

Phase [degree]

0.004-180
12𝐿 𝑦 = 1 − 𝑎 𝑦 − 11.3 2𝐿 11.7 = 0.8 → 𝑎 = 1.25𝑑𝐿(𝑦) = −2.5 𝑦 − 11.3
𝑑𝑦𝑑𝐿
11.7 = −1.0𝑑𝑦𝑑𝐿
12 𝑀𝑎𝑔𝐷𝑖𝑡ℎ𝑒𝑟𝑦 𝑦 =𝑦 × Δ𝑦𝑑𝑦

𝑀𝑎𝑔𝐷𝑖𝑡ℎ𝑒𝑟𝑦 11.7 = −1.0 × Δ𝑦

Luminosity scan to Horizontal direction (LumiBelle2)

Normalized Luminosity

1800.006

900.00400.002-900-150-100 -50
1.20-18050 100 150

10.8

Phase [degree]

Magnitude [mV]

0.008

Input

LumiBelle2

Dither Amp

20 umFreq

79 Hz

CCCONiBump FB

ON𝐿 𝑥 = 1 − 𝑏 𝑥 − 20 2
𝐿 −75 = 0.8 → 𝑏 = 2.2 × 10−5𝑑𝐿(𝑥) = −4.4 × 10−5 𝑥 − 20𝑑𝑥
𝑑𝐿−550=−1.3×10𝑑𝑦𝑑𝐿

0.6

・ ZDLM・ Lumibelle2

0.4-150 -100 -50

050 100 150

Horizontal offset [mm]𝑀𝑎𝑔𝐷𝑖𝑡ℎ𝑒𝑟𝑥 𝑥 = 𝑑𝑥 𝑥 × Δ𝑥
𝑀𝑎𝑔𝐷𝑖𝑡ℎ𝑒𝑟𝑦 50 = −1.3 × 10−3 × Δ𝑥
𝑀𝑎𝑔𝐷𝑖𝑡ℎ𝑒𝑟𝑦 11.7 = −1.0 × Δ𝑦
𝑀𝑎𝑔𝐷𝑖𝑡ℎ𝑒𝑟𝑦 50 = 𝑀𝑎𝑔𝐷𝑖𝑡ℎ𝑒𝑟𝑦 11.7
−1.0 × Δ𝑦=1.3 × 10−3 × 20𝜇𝑚 −> Δ𝑦=0.026 𝜇𝑚