Luminosity performance for
Crab waist operation inSuperKEKB
K. OhmiJuly, 15,2020
MAC2020

SuperKEKB in 2019

Slide by Y. Ohnishi

by* is squeezed to 1mm in 2019.
Specific luminosity is lower than expectedvalue (~9x1031)at even low current.
The beam-beam parameter is limited at 0.02
(HER is lower, due to LER blowup).

Try Crab waist in SuperKEKB• Specific luminosity and beam-beam parameters were limited atlower values than expectation.
• Optics aberrations at IP (ex. Chromatic coupling) seems todegrade the luminosity performance, but the correction was notstraightforward.
• 𝐿𝑠𝑝 = 40 − 50 × 1030 cm-2s-1mA-2, while the geometrical value
estimated by beam size measurement is 𝐿𝑠𝑝 = 90 × 1030 .

• Then we decide to try the crab waist.
• Crab waist can be realized in both of LER and HER by detuningof SLY (non-interleaved local chromaticity correction) strength.
• We expect improvement of luminosity using the crab waist.
1𝐿𝑠𝑝 =2𝜋Σ𝑥 Σ𝑦 𝑒 2 𝑓0

Σ𝑦 = 0.2𝜇m, 𝐿𝑠𝑝 = 89 × 1030 cm-2s-1mA-2

Crab waist component• 𝜃𝑐 : half crossing angle, 41.5mrad.
𝐻∗ =1 ∗ ∗2𝑥 𝑝𝑦 = 6.0𝑥 ∗ 𝑝𝑦∗24𝜃𝑐• Required crab waist term (80%)
𝐻 ∗ = 5𝑥 ∗ 𝑝𝑦∗2

• The component can be created by local chromaticity correction
sextupoles.
𝐾2 3𝐻𝑠 =𝑥 − 3𝑥𝑦 26𝑖 ∗𝑖 ∗𝑥𝑖 (𝑥 ∗ , 𝑝𝑥∗ ) = 𝑇11
𝑥 + 𝑇12𝑝𝑥
𝑁𝐿

Ti is transfer matrix for IP to i-th sextupole.
𝑖 ∗𝑖 ∗𝑦𝑖 (𝑦 ∗ , 𝑝𝑦∗ ) = 𝑇33
𝑦 + 𝑇34𝑝𝑦

1 ∗ ∗2𝐾2,𝑖 3𝐻∗ =𝑥 𝑝𝑦 = ෍(𝑥𝑖 − 3𝑥𝑖 𝑦𝑖2 )4𝜃𝑐6𝑖=1

Betatron phase difference from IP is required np
for x, (½+n) p for y to produce xpy2 term at IP.

Betatron Phase variation
Comparison between LER and HER
bx*=80mm, by*=1mm
LER
AX

BYNYAX

BX

NX

AY

0.47977 32.53525

524.960.75059-0.60132

6.507640.467998.26539675.0993

0.749895.664310.97977 -33.0733

524.961.25059-0.96485

6.507640.96799-8.2618675.0993

1.24989

94.01306

1.1518 -1.90277 11.46071

1.855217.8604451.47830

1.28484-4.2009016.84147

1.8839094.01306

1.65182.35521-7.86044

51.47830

1.78484

6.30734

16.84147

2.38390

BXNX-0.57066

5.66431

SLYL2 -0.75034
SLXL1 12.54136
SLXL2 -9.22825

SLYL1

bx*=60mm, by*=1mm
HER
AY

0.71045 11.46071

BYNY

8.47988

65.82581 -1.77001-3.64419.2571 -2.35147-5.29293 135.30740-1.74499

0.34348

1.13724-2.49426

SLXR2 -9.32224

65.82581 -1.27001

3.75568

19.2571 -1.85147

5.24070 135.30740-1.24331

0.402521.13724-1.99426

SLXR1

SLYR10.65861

5.516 -0.97574 38.76399 521.2173 -1.24865-0.01475

3.79083-0.98869

79.7672-701.63-1.25022

SLYR20.66937

5.516 -0.47574 -39.2803 521.2173 -0.74865

0.673843.79083-0.48869-79.767701.63-0.75022

0.08-0.00011

0.06

45.53302-0.002090.001

43.57037

IP044.53

00.00146.5912Crab waist (FCCee type, K. Oide et al., PRAB) can be tried using the local chromaticity correction
sextuples in both of LER and HER, though the phase variation is not perfect especially in x.

Magnet configuration
SLYTLP2SLYTRE1SLYTLP1

SLYTRE2
IP

Dfx=0.5x2p
Dfy=0.75x2p

SLYTLE1SLYTLE2SLYTRP2

bx*=80mm, by*=1mm

K2(m-2)SLYTRP1

K2(m-2)K2(m-2)K2(m-2)SLYTLE.1

9.5213 SLYTLP.1

1.4349SLYTRE.1-7.9251 SLYTRP.1

0.9978SLYTLE.2

8.0697 SLYTLP.2

3.7171SLYTRE.2-9.7211 SLYTRP.2

3.3356K2(m-2)K2(m-2)K2(m-2)K2(m-2)SLYTLE.1

9.1304SLYTLP.11.341

SLYTLE.2

7.6788SLYTLP.2

3.6239Design b

SLYTRE.1-8.1626

SLYTRP.1

1.1294SLYTRE.2-9.9586

SLYTRP.2

3.4679Polarity Check for the final hardware arrangement
SLYTLP2SLYTLP1x

Top view
IP

SLYTLE1SLYTLE2SLYTRE1
SLYTRE2

Dfx=0.5x2p
Dfy=0.75x2p

SLYTRP2SLYTRP1• LER beam travels right to left.
• For X>0, Sextupole SLYTRP2 with larger K2(>0), focus/defocus in x/y direction.
• Phase of Ｘchanges 180 degree.
• Y waist shifts away from IP.

• HER beam travels left to right• The same condition as LER.

3rd order terms at IP in LER Crab waist• LeftK2(m-2)

xpy2

pxpy2

xy2

pxy2

by*=1mm
xypy

pxypy

SLYTLP.1

1.43493.1435-0.032143.8484-0.4484-23.4807

0.2401SLYTLP.2

3.7171-8.1435

0.0833-113.594

1.161660.8292-0.622SLXTLP.1

0.6621-0.0469-0.0053-28368.2-3199.25

72.9414

8.226

SLXTLP.2

0.6621

0.04690.005328368.17

3199.251-72.9414-8.226-50.0512-69.7455

0.713237.3485-0.3819

Sum• RightK2(m-2)

xpy2

pxpy2

xy2

pxy2

xypypxypy

SLXTRP.1

0.297-0.0066-0.0042-3644.36-2306.72-9.8402-6.2284

SLXTRP.2

0.297

0.00660.00423644.363

2306.719

9.8402

6.2284SLYTRP.1

0.9978-2.134-0.0262-153.026-1.880936.14170.4442SLYTRP.2

3.33567.134

0.0877511.5711

6.288-120.823-1.485150.0615358.5452

4.4071-84.6811-1.0409Sum• Uninvited parasitic terms appears due to imperfection of betatron phase, but
their contributions are small (10% in normalized coordinates, PxPy2.

rd
3 order terms at IP in HER Crab waist• LeftK2(m-2)

xpy2

xy2

pxy2

xypy

pxypy

SLYTLE.1

9.521332.7962-0.401215.9549-0.195245.7498-0.5597SLYTLE.2

8.0697-27.7962

0.34-13.5225

0.1654-38.775

0.4744SLXTLE.1

2.8507

0.0568-0.016376893.09-22145.7-132.13838.0567SLXTLE.2

2.8507-0.0568

0.0163-76893.1

22145.72

132.1384-38.0567

5-0.0612

2.4328-0.0292

6.9748-0.0853sum• Rightpxpy2

b*=(80,1)mm

K2(m-2)

xpy2

pxpy2

xy2

pxy2

xypy

pxypy

SLXTRE.1-3.4726-3.86E-6

7.33E-6-2957.06

5610.141-0.2138

0.4056SLXTRE.2-3.4726

3.86E-6-7.33E-6

2957.06-5610.14

0.2138-0.4056

SLYTRE.1-7.9251

22.06280.094210.74

0.0459-30.7866-0.1315SLYTRE.2-9.7211-27.0628-0.1156-13.174-0.0563

37.7637

0.1613-5-0.0214-2.4341-0.0104

6.97710.0298

Sum• Uninvited parasitic terms appears, but their contributions are small(10% in normalized coordinates, PxPy2.

Measurement of Crabbing waist• Apply x orbit at SLYTLP1 and SLYTRP2.
• Measure vertical beta at QC1 using K modulation.
• Measure vertical beta using orbit response.
• Check IP waist shift.
𝛿𝑥𝑆𝐿𝑌 = 1𝑚𝑚 @𝛽𝑥,𝑆𝐿𝑌 = 5.66𝑚

𝛿𝑥 ∗𝛿𝑠 == 1.4𝑚𝑚
2𝜃𝑐𝛿𝑥 ∗ = 0.12𝑚𝑚 @𝛽𝑥∗ = 0.08𝑚
SLYTLP2

Measure by* using K modulation or orbit response

SLYTLP1
QC1LPxQLB1LPIPQLC3LP

QC1RP
QLC3RP

Y-waistDfx=0.5x2p
Dfy=0.75x2p SLYTRP2SLYTRP1QLB1RPClosed bump to create crabbing
SLYTLP1waist
IH. Koiso
SLYTLP2PV-offset scan• Σy measured by
V-offset scan.

12

Crab Waist measurement
For different LER IP orbit offsetdx(SLY), HER waist position changed andΣy/sqrt(2) measured.
0102

LER crab waist
HER no crab waist
Waist scan changing HER waist,
then search LER waist• LER waist changes for LER IPorbit: crab waist
HER waist
dscol=dx*/2q=1.45mm
LER waist
0.1mm
13q: half crossing angle

1

K modulation• QC1 s=L*=900mm, waist shift ds=1mm.
2𝑠𝛽 𝑠 = 𝛽∗ + ∗𝛽𝛽 𝑠 + 𝛿𝑠 − 𝛽 𝑠 − 𝛿𝑠 =Δ𝐾1 𝛽∆𝜈 =4𝜋𝑑𝛽 𝑠4𝑠𝛿𝑠2𝛿𝑠 = ∗𝑑𝑠𝛽

𝛽 𝑠 + 𝛿𝑠 − 𝛽 𝑠 − 𝛿𝑠4𝛿𝑠≅𝛽 𝑠𝑠𝛽𝑦 𝑠 = 900𝑚𝑚 = 745𝑚
Δ𝐾1 𝛿𝛽𝛿∆𝜈 =4𝜋∆𝜈 = 0.01

𝛽 𝑠 + 𝛿𝑠 − 𝛽 𝑠2𝛿𝑠
≅𝛽 𝑠𝑠𝛽 𝑠 + 𝛿𝑠 − 𝛽 𝑠 − 𝛿𝑠 = 3.6m
𝛿∆𝜈 𝛿𝛽=∆𝜈𝛽Δ𝐾1= 2 × 10−4𝐾1
𝛿∆𝜈 = 0.5 × 10−4 too small to be measured.

• It seems to be difficult to measure crab waist using K modulation.
• Beam-beam scan is only possible way now.

Vertical orbit error in SLY• Vertical orbit in SLYTLP/E
induces
R1*atIP𝑁𝐿1 ∗ ∗2
𝐾2,𝑖 3∗𝐻 =𝑥 𝑝𝑦 ≈ ෍(𝑥𝑖 − 3𝑥𝑖 𝑦𝑖2 )4𝜃𝑐6𝑖=1𝑖∗𝑖 ∗𝑖 ∗𝑦𝑖 𝑦 ∗ , 𝑝𝑦∗ = 𝑇33
𝑦 + 𝑇34
𝑝𝑦 + 𝑦𝑖,0 𝑦𝑖,0 = 𝑇34 𝑝𝑦,0𝑆𝐿𝑌1𝑆𝐿𝑌2𝑇𝑘𝑙= −𝑇𝑘𝑙

𝑦𝑆𝐿𝑌1,0 = − 𝑦𝑆𝐿𝑌2,0𝐾2,𝑆𝐿𝑌1 ≠ 𝐾2,𝑆𝐿𝑌2 crab waist

𝑁𝐿𝐻𝑅∗ = − ෍ 𝐾2,𝑖 𝑦𝑖,0 𝑥𝑖 𝑦𝑖 = −∆𝐾2,𝑆𝐿𝑌 𝑦𝑆𝐿𝑌1,0 𝑥𝑖 𝑦𝑖
𝑖=1= −∆𝐾2,𝑆𝐿𝑌 𝑦𝑆𝐿𝑌1,0𝑅1∗ = ∆𝐾2,𝑆𝐿𝑌𝛽𝑥,𝑆𝐿𝑌𝛽𝑥∗

𝛽𝑥,𝑆𝐿𝑌𝛽𝑦,𝑆𝐿𝑌 𝛽𝑦∗ 𝑥 ∗ 𝑝𝑦∗ = −𝑅1∗ 𝑥 ∗ 𝑝𝑦∗∗𝛽𝑥bx, by=(80,1)mm

𝑦𝛽𝑦,𝑆𝐿𝑌 𝛽𝑦∗ 𝑦𝑆𝐿𝑌1,0 = 10.4 𝑦𝑆𝐿𝑌1,0 = 10−3 𝑆𝐿𝑌1,0𝜎𝑦,𝑆𝐿𝑌𝜎𝑦,𝑆𝐿𝑌 = 72.5μ𝑚

V Orbit at SLY - Fluctuation of R1HER
𝛿𝑅1∗ = ∆𝐾2,𝑆𝐿𝑌 𝛿𝑦𝑆𝐿𝑌1,0𝛽𝑥,𝑆𝐿𝑌𝛽𝑥∗𝛽𝑦,𝑆𝐿𝑌 𝛽𝑦∗𝛿𝑦𝑆𝐿𝑌𝐸 = 0.08𝑚𝑚
CW40%∆𝐾2,𝑆𝐿𝑌𝐸𝛽𝑥,𝑆𝐿𝑌𝛽𝑦,𝑆𝐿𝑌 𝛽𝑦∗ = 6∗𝛽𝑥∗
𝛿𝑅1,𝐸= 0.5𝑚𝑟𝑎𝑑

LER𝛿𝑦𝑆𝐿𝑌𝑃 = 0.09𝑚𝑚
CW60%∆𝐾2,𝑆𝐿𝑌𝑃𝛽𝑥,𝑆𝐿𝑌𝛽𝑦,𝑆𝐿𝑌 𝛽𝑦∗ = 10.4
∗𝛽𝑥∗
𝛿𝑅1,𝑃= 0.9𝑚𝑟𝑎𝑑

Not large but visible

Luminosity performance in the crab waist operation• Specific luminosity is almost constant at higher current 0.03mA.
• Convoluted beam size in single beam is Sy=0.2mm (by*=1mm), the131-2-1-2
𝐿=corresponding Lsp=8.9x10 cm s mA𝑠𝑝2𝜋Σ Σ 𝑒 2 𝑓• Specific luminosity degrade at very low current <0.03mA.

𝑥 𝑦

Σ𝑦 = 0.2𝜇m,
𝐿𝑠𝑝 = 8.9 × 1031 cm-2s-1mA-2

20190

Status of crab waist operation• Crab waist did not improve the luminosity performance
drastically.
• Lsp degraded at low bunch current as the same as before.
• There were some improvement on the beam back ground andlife time.
• At high bunch current, the gain seems to be clear.

Beam size blowup at very low bunch current collisionobserved since the early stage of commissioning• by=3mm• Two stage blow-up ofLER beam
1. Very small bunch
current, I+I-=0.01mA2.
2. High bunch current
I+>0.5 mA• Single stage in HER• HER beam I->0.2mA.

（２）

（１）

Possible source of the beam size blow up at low
current collision
K. Ohmi, retire seminar at Apr. 2019
• Chromatic, or nonlinear aberrations• R1’=12rad• R2’=3m
100 times larger for the early estimation.
2• C(px py)=8m
Weak strong simulation with nonlinear IPaberrations

by=3mm

TbT optics (coupling) measurement at IR• Search for the optics aberrations which
degrades the luminosity performance.

|y|=0.1|x|• Excite x mode using injection kicker.
• Measure y oscillation with nx.
• R1: y motion with in-phase of x motion.
• R2: y motion with p/2 deviation of x motion.
• Strong vertical signal (30% of x) was seen insome BPM’s.

• IP coupling is interpolated from QC1L-R
monitors|y|=0.3|x|IR optics and BPM’sLER

HER

COD, TbT

x-y coupling TbT measurement• y motion in X mode.
𝒙 = 𝑅𝐵𝑿

𝑅=𝐵=𝑟4 −𝑟2𝑟0 00 𝑟0 −𝑟3 𝑟1−𝑟1 −𝑟2 𝑟0 0−𝑟3 −𝑟4 0 𝑟0𝑦 = −𝑟1 𝑥 − 𝑟2 𝑝𝑥 = −𝑟1 𝑎 cos 𝜙 𝑠 + 𝑟2

𝐵𝑋 =𝐵𝑋00𝐵𝑌𝛽𝑋0−𝛼𝑋 / 𝛽𝑋

1/ 𝛽𝑋𝑎𝛼sin 𝜙 𝑠 + 𝑎 cos 𝜙 𝑠𝛽𝛽

= 𝑐 cos(2𝜋𝑛𝜈𝑥 + 𝜙𝑦 )𝑐𝛼cos(𝜙𝑦 −𝜙𝑥 ) = −𝑟1 + 𝑟2𝑎𝛽

𝜙 𝑠 = 2𝜋𝑛𝜈𝑥 + 𝜙𝑥𝑐𝑟2sin(𝜙𝑦 −𝜙𝑥 ) = −𝑎𝛽𝑎𝛼𝑝𝑦 = −𝑟3 𝑥 − 𝑟4 𝑝𝑥 = −𝑟3 𝑎 cos 𝜙 𝑠 + 𝑟4 sin 𝜙 𝑠 + 𝑎 cos 𝜙 𝑠𝛽𝛽
= 𝑑 cos(2𝜋𝑛𝜈𝑥 + 𝜙𝑞 )𝑑𝛼cos(𝜙𝑞 −𝜙𝑥 ) = −𝑟3 + 𝑟4𝑎𝛽𝑑𝑟4sin(𝜙𝑞 −𝜙𝑥 ) = −𝑎𝛽𝛽 = 𝛽𝑥𝛼 = 𝛼𝑥𝑐|𝑌|=in the figure𝑎|𝑋|

LER, Mar. 9, 2020
• Very large x-y coupling exists in IR.

BPM +:Left -:Right
1 QC1
2 QC2
4,5 SLY (Local Chrom y)
6,7 SLX (Local Chrom x)
Large y signal for x excitation

HER, Mar. 5, 2020
• Very large x-y coupling exists in IR.

Beam-beam simulations considering the IR
coupling at SLY• Crab waist is realized by detuning of chromatic correction
sextupole.
• X-y coupling at SLY may affect the crab waist.

• Beam-beam simulation considering SLY coupling• Chromatic coupling at IP induced in IR area is not considered.

Weak-strong Simulation for the crab waist
using detuned SLY w/o SLY coupling• 1567 bunches, 0.9x1.1A, b=80, 1mm.
• Detuned SLY’s.
SLYR1 K2=0.9978
twiss= 0.65861, 5.51600,-0.97574, 38.76399, 521.21731,-1.24865,
R=0.0133, 0.0766, 0.0138, -0.219
SLYR2 K2=3.3356
twiss= 0.66937, 5.51600,-0.47574, -39.28025, 521.21731,-0.74865,
R= 0.0261, -0.123, 0.0051, -0.00087
SLYL1 K2=1.4349
twiss= -0.57066, 5.66431, 0.47977, 32.53525, 524.96002, 0.75059,
R=0.052, -0.698, 0.003, -0.0967
SLYL2 K2=3.7171
twiss= -0.75034, 5.66431, 0.97977, -33.07327, 524.96002, 1.25059,
R= 0.075, -0.822, 0.0059, -0.0665

Effect (on momentum) of linear coupling at SLY is negligible in thecrab waist collision. Parasitic terms also does not affect.

Chromatic coupling at IP in LER• SLY is rotated small
angle as a test.
• Optics measurement
W/O SLY rotation• R1 and R2 are hard tomeasure, while R3 andR4 are easy, due to betasqueezing.

Measurement of chromatic coupling for R1 and R2• If a chromatic beam size variation are seen, it can be sourceof luminosity degradation
Df=400Hz → d=0.17%hy
R1’=dR1/dd
R2 ’+0.5mm-400Hz

Df=0-400Hz
400Hz

Df=0400Hz -400Hz+0.6mm

Df=0400Hz• Measure the beam size using beam-beam scan (Luminosity.)

Vertical offset scan with different RF frequency

Δf = +400Hz

Δf = +200Hz

Δf = ±0Hz

Δf = -200Hz

Δf = -400Hz
beam loss at the scanY. Funakoshi
One cycle injection by Kaji.

Vertical offset shift for frequency shift：IP vertical dispersion
Vertical size variation for frequency shift beam energy：IP chromatic couplingLatest data June 25,2019
Beam size variation for energy change was observed. Chromatic coupling
exists at IP.
Nonlinear dispersion also exist at IP.

Chromatic beam size enlargement∆𝜎𝑦 = 0.28 𝜇A half strength of the Chromatic coupling, which candegrade the luminosity, exists.
∆𝜎 = 𝑅1 (𝛿)𝜎𝑥 = 0.50 𝜇m
R1’=12rad 𝑦𝑅 (𝛿)R2’=3m ∆𝜎𝑦 = 2
𝜎 = 0.62 𝜇m
𝛽𝑥 𝑥

by=3mmSimulated luminosity
degradation due tononlinear dispersion.

Weak-strong simulation for crab waist withchromatic coupling• Lsp worsens in the low bunch current (<0.3mA) and then changes
slowly for a large R1’=6, 12.
• Lsp somewhat increase/decrease for Crab waist ON/OFF for
I>0.5mA.
by=1mmWe are here now.

SKB20/skb801c*,wc*

R1’ correction using rotatable sextupoles• SLY’s contribute R1’ dominantly. Target R1’=+-12.
• 1st trial R1’+=3, mainly using SLY in June 15, 2020.
• Emittance increase in single beam.
• Luminosity performance does not change remarkably, decrease 10%.

• 2nd trial R1’+=0.5 using all sextupoles since June 18 (H, Koiso).
• Luminosity performance does not change remarkably.

• There is no clear evidence, in which R1’ affects luminosity
performance, yet.

Effects of imperfection of compensation solenoids
Left side• R’=dR/dd vs Bz(ESLR)• Change Bz uniformlywith a factor.
• S: ESL, ESR are changed
the same value.
• O: Opposite value.
• dp=+-0.1%,• No large chromatic
coupling appears for theimperfection of 4%.

How to continue the crab waist operation• Further high bunch current, squeezing further• Specific luminosity is almost constant at higher current 0.03mA.
• Luminosity and beam-beam parameter increase if higher bunch current is available.

• Specific luminosity degradation at very low current.
• Study of the degradation source, chromatic or nonlinear optics aberrations.
• Correction of the aberrations• For smaller beta, dynamic aperture may shrink due to IR nonlinearity.
Simulation
Σ𝑦 = 0.2𝜇m,
𝐿𝑠𝑝 = 8.9 × 1031 cm-2s-1mA-2
We are here now.

Why beam-beam blowup in low bunch current
collisionParameters and beam size at the best condition

Horizontal orbit• Inside of SLY pairSLYTLP2SLYTLP1
Y-waistInsidex• Outside of SLY pairSLYTLP2SLYTLP1x

QLB1LP

Dfx=0.5x2p
Dfy=0.75x2p SLYTRP2

OutsideIP

QLC3LPSLYTRP1

Y-waist
QLC3RPSLYTRP1QLB1RP
Dfx=0.5x2pDfy=0.75x2p SLYTRP2

Horizontal orbit fluctuation at SLY• HER• LER• Waist fluctuation

𝛿𝑥 ∗ = 𝛿𝑥𝑆𝐿𝑌𝛿𝑥 ∗ = 0.1mm

𝛽𝑥∗

𝛽𝑥∗

𝛽𝑥,𝑆𝐿𝑌𝛽𝑥,𝑆𝐿𝑌~13𝛿𝑥 ∗𝛿𝑠 == 0.25mm < 𝛽𝑦∗𝜃𝑐Not serious now