Beam-beam issues inSuperKEKB
K. Ohmi, D. Zhou
MAC2019
Thanks to Y. Funakoshi, A. Koval, H. Koiso, G. Mitsuka, A. Morita, Y. Ohnishi,
H. Sugimoto, R. Yang…, for machine experiments in my(KO) absent, June 23July 1.

Summary of Phase-2 & 3𝜎𝑧 𝜃𝑐• Collision with large Piwinski angle, ∗ ≥ 10 has been
𝜎𝑥

performed in Phase 2 & 3.
• Squeeze by* step-by-step.
• Beam-beam parameter was kept squeezing by*.
• Squeezing beta contributed the luminosity increase
𝛾𝐼± 𝜉𝑦±following 𝐿 =∗.
2𝑒𝑟𝑒 𝛽𝑦• Luminosity 1034 cm-2s-1 was achieved at the end ofPhase-3.
• Beam-beam parameter has been limited to be𝜉𝑦− =0.02 for e- beam due to blow-up of e+ beam.
• Multi-bunch effect in luminosity was weak.

Commissioning of SuperKEKB• Phase-2 (2018) Start collision installation of Belle2 detector. Squeeze bx=200-100, 200mm, by=8->6>4->3->2mm.
• Phase-3 (Mar. 2019-) Belle 2 data taking at bx=100,200mm, by=3mm.
• by=2mm, Jun.21.
bx=100mm
by=3mmbx=200mm
by=3mmLuminosity/bunch history in Phase-2Nbunch=788 (398 in July 13)
2𝑒𝑟𝑒 𝛽𝑦∗𝜉𝐿 =𝐿𝜎𝑧 𝜃𝑐=10𝛾𝐼𝜎𝑥∗q : half crossing anglebx (mm)cby (mm)Lb (1030) Ib (mA)xL

Apr,16200

8

1.55

0.417,0.367 0.0343,0.0223

May,22

200

6

1.73

0.431,0.362 0.0279,0.0190

May,28

200

4

1.73

0.431,0.362 0.0185,0.0126

Jun,8200

4,3

1.68

0.431,0.362 0.0179,0.0092

Jun,11200

3

1.33

0.406,0.336 0.0114,0.0078

Jun,12100

41.38

0.431,0.362 0.0148,0.0101

Jun,13200,10042.59

0.444,0.374 0.0264,0.0179

Jun,20200,100

3

3.30

0.431,0.362 0.0269,0.0182

July,13200,100

3

5.78

0.669,0.548 0.0299,0.0209

80,80

22019
Jun, 21R2 correction

Luminosity history in Phase-3• Increase currents• Nb=1576.

• Fire trouble• No collision• Belle-2 data taking with bx=100, 200mm, by=3mm.
• Peak Luminosity I=617, 644 mA. L=5.49x1033 cm-2s-1, ¼ of KEKB.
• The beam-beam parameter is 0.0176, 0.0295.
• Accumulate 6 fb-1.
L（KEKB) =21.1x1033 cm-2s-1

Luminosity/bunch history in Phase-3• Nbunch=1576 (788 in June,26)
𝜎𝑧 𝜃𝑐• ∗ = 10 → 15
𝜎𝑥2019bx (mm) by (mm)Lt(1034)

Lb (1030)

Ib (mA)xL

June,7200,100 3

0.549

3.48

0.408,0.391

0.0295,0.0176

June,20200,100 3

0.470

2.98

0.317,0.317

0.0325,0.0186

June,2680,80

20.6137.78

0.508,0.508

0.0353,0.0202

June,27200,200 8

0.350

2.22

0.482,0.508

0.0425,0.0231

June,27200,200 80.400

2.540.514,0.539

0.0456,0.0248

June,3080,80

2

1.03

6.54

0.457,0.457

0.0329,0.0188

July,180,80

2

1.23

7.81

0.520,0.526

0.0346,0.0195

July,13200,100 3

0.229

5.78

0.671,0.549

0.0299,0.0209

Jun,20200,100 3

0.260

3.30

0.431,0.362

0.0269,0.0182

2018

QCS
VangStudyLuminosity on the last dayLinear X-Y coupling correction• In early stage of Phase-2 commissioning, luminosity was lower
than that estimated by emittance (XSRM) at low current.
• Disagreement between sy* and 𝜀𝑦 𝛽𝑦∗Lsp(1030 cm-2s-1/mA2)

Before R2 corection

I+I- (mA2)• 0mA, sy0=0.3mm, 0.4mm, Lsp=35• 200x80mA, sy0=0.5mm, 0.6mm, Lsp=23• 285x340mA, sy0=1.5mm, 0.6mm, Lsp=11
Lsp disagrees with geo value at low current

1𝐿𝑠𝑝 =
2𝜋𝜎𝑥𝑐 𝜎𝑦𝑐 𝑒 2 𝑓0

IP coupling and beam distribution at IP
R1yyR2,hsy

syxxyysyx'syx’
sdd=Dp/p

Relation of R and skew strength ofQC1 in a simple model• Transformation of R2,∆𝜙 =𝜋2∆𝜙 =𝐻 = −𝑅2 𝑝𝑥 𝑝𝑦𝐻 = ±𝑅2 𝑝𝑥 𝑝𝑦𝜋2

𝐻 = 𝑅2 𝑝𝑥 𝑝𝑦𝑦 = 𝑦 ± 𝑅2 𝑝𝑥• Assume p/2 for phase difference between IP to both QC1.
𝐻=±𝑅2𝛽𝑥∗ 𝛽𝑥,1 𝛽𝑦∗ 𝛽𝑦,1𝑥𝑦 ≈ ±𝑅2 𝑥𝑦• Skew quad at QC1 is B’L/Br=R2, which is independent of b*.
• Deviation from p/2 induces R3.
• Control of inside of p section is hard from outside. It should becorrected by both side of skew. (like waist correction)

𝐻 = 𝑑𝑠𝑝𝑦2waist shift

Vertical Beam size measurement
using collision scan ∗• Beam size is larger than 𝜀𝑦 𝛽𝑦 for existing R1, R2.
• After R2 correction, sy*=1.25mm->0.33mm• R1,R2 is measurable .

R scan in the simulation• Required tuning range R1 O(mrad),R2 O(mm), R3 O(1m-1),R4 O(0.1)

TbT measurement• y motion in X mode.
𝒙 = 𝑅𝐵𝑿𝑅=

𝑟4 −𝑟2
𝑟0 00 𝑟0 −𝑟3 𝑟1−𝑟1 −𝑟2 𝑟0 0−𝑟3 −𝑟4 0 𝑟0

ri=Ri
𝐵=

𝐵𝑋 =𝐵𝑋00𝐵𝑌

𝛽𝑋

0−𝛼𝑋 / 𝛽𝑋

1/ 𝛽𝑋

r1: cos component of y for x betatron motion ,r2: sin component𝑎𝛼𝑦 = −𝑟1 𝑥 − 𝑟2 𝑝𝑥 = −𝑟1 𝑎 cos 𝜙 𝑠 + 𝑟2 sin 𝜙 𝑠 +𝑎 cos 𝜙 𝑠𝛽𝛽
𝜙 𝑠 = 2𝜋𝑛𝜈𝑥 + 𝜙𝑥= 𝑐 cos(2𝜋𝑛𝜈𝑥 + 𝜙𝑦 )𝑐𝛼𝑐𝑟2cos(𝜙𝑦 −𝜙𝑥 ) = −𝑟1 + 𝑟2sin(𝜙𝑦 −𝜙𝑥 ) =𝑎𝑎𝛽𝛽
r3: cos component of y for px betatron motion ,r4: sin component
𝑎𝛼𝑝𝑦 = 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 + 𝑟4𝑎𝛽

𝑑𝑟4sin(𝜙𝑞 −𝜙𝑥 ) = −𝑎𝛽FFT of BPM data
• Small yIP, but enough pyIP=qIP.
• R1,R2 are y for x and px. R3 and R4 are py for x and px.
• R1 and R2 are hard to be measured.

LER• R1, R2 are ambiguos, but R3, R4 are well determined.

Lesson from linear x-y couplingcorrection• We have to always confirm that the beam size at IP
equal to 𝜀𝑦 𝛽𝑦∗ estimated by XSRM.
• R3,R4 are well determined by TbT measurement, butR1,R2 are not.
• R1,R2,hy at IP can be measured by collision scan.
• R3,R4 are measurable. The tolerance for luminosity
degradation in simulation is O(1). Insensitive formonitor rotation. R3,R4 are well managed.
• All linear coupling parameters are well managed.

Vertical angle at IP, June 20, 2019
• Vertical angle scan was limited due to heating on HER Vangle change (done in KEK without problem).
• Change of LER V-angle vertical has induced verticaldispersion at IP.
• V angle scan with dispersion correction was done in 20,June 2019.

H.Koiso,Nakayama

Vertical crossing angle• Correction of full crossing angle 2qV=0.5mrad
contributed 20% luminosity up (June 20, 2019).
𝜃𝑉 𝜎𝑧 = 1.5 𝜇𝑚

𝜃𝑉 : half V-angle
Side view

Overlap area

by=3mm,500x500mA, 1576b
Lmes=4.7x1033

𝜎𝑦= 0.8𝑚𝑚
𝜃𝑉
𝜎𝑥= 0.5𝑚𝑚
Comparable with𝜃𝑐

by=3mm• For V angle 0.5mrad, luminosity loss is small for I+I<0.2mA2. It is 20% at I+I-=0.4mA2. Initial condition ey(S)=40nm, ey+(W)=40nm.
• For initial condition ey-(S)=20nm, ey+(W)=8nm, 20%lumi loss at I+I-=0.15mA2, but Lsp is very high.
• Accuracy of vertical angle is ~0.1mrad at I+I-=0.4mA2.

by=3mmey-(S)=20nm, ey+(W)=8nm

Present beam-beam performance

Y. OhnishiIR magnets and their nonlinearity
studied at early stage• There are many nonlinear field components in IRmagnets.
• Chromatic coupling are induced at IR.
D. Zhou,
SKEKB MAC
2015
BBWS : arc expressed by simple transfermatrix
SAD: complex lattice structure

Luminosity for H=c10px2py andchromatic Twiss, design parameter

Skew sext
ChromaticSumSAD• The luminosity degradation due to Skew sext component andchromatic Twiss almost explains that of beam-beam simulation
with SAD.
• The strength of px2py term is 0.072.
• Study of Space charge force is next.

SAD simulation for detuned lattice :studied at early stage• by=2.2, 2.4mm• No difference between SAD and BBWS(simplearc+optics aberrations)Temporal detuned designSpecific Luminosity and Beam-Beam (Phase 2)

2 stage blow-up of LER beam
（１）Very small bunch current, I+I=0.01mA2.
（２）High bunch current I+>0.5 mA

（２）

（１）

HER beam I->0.2mA.
24

Chromatic, nonlinear aberrations• Possible errors to explain measured luminosity• R1’=12rad• R2’=3m
100 times larger for the early• C(px2py)=8m
estimation (page 22)
Weak strong simulation with nonlinear IP aberrations

Measurement of IP chromatic aberrations• Effect on vertical beam size of the aberrations
𝜎𝑦 = 0.3𝜇𝑚
𝜀𝑥 =3 nm, 𝜀𝑦 = 0.03 nm• d=Dp/p=0.17%.
𝛽𝑥 = 0.2 𝑚• R1(d)=20.4mrad∆𝜎𝑦 = 𝑅1 (𝛿)𝜎𝑥 = 0.50 𝜇m
𝑅2 (𝛿)• R2(d)=5.1mm
R1’=12rad∆𝜎𝑦 =• 𝐻 = 8𝑝𝑥2 𝑝𝑦𝛽𝑥∆𝜎𝑦 = 8 𝑝𝑥2 =𝜎𝑥 = 0.62 𝜇m

8𝜀𝑥= 0.12𝜇𝑚 = 0.4𝜎𝑦𝛽𝑥R2’=3mC(px2py)=8m• Aberrations with clear vertical beam size increase as
synchroton/betatron amplitude affect luminosity
performance.
• Errors, which affect luminosity performance, are visible
ones.
• Linear coupling, which gives 0.1-0.2sy, affect luminosityperformance.

If a chromatic beam size variation are seen, it
can be source of luminosity degradation
Df=400Hz → d=0.17%
hy

R1’R2’+0.5mm-400Hz

Df=0400Hz-400Hz

Df=0400Hz-400Hz+0.6mm

Df=0Measure the beam size using beam-beam scan
(Luminosity.)

400HzVertical offset scan with different
RF frequency

Δf = +400Hz

Δf = +200Hz

Δf = ±0Hz

Δf = -200Hz

Y. Funakoshi
One cycle injection by Kaji.

Δf = -400Hz
beam loss at the scan

Vertical offset shift for frequency shift：IP vertical dispersion
Vertical size variation for frequency shift beam energy：IP chromatic couplingDispersion at IP• Df=400Hz, IP Knob ON
hy=+1mm hy=-1mm

Y position shift and size increase due to dispersion
are seen.

Latest data June 25,2019
Beam size variation for energy change wasobserved. 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 can exist.
∆𝜎𝑦 = 𝑅1 (𝛿)𝜎𝑥 = 0.50 𝜇m
R1’=12rad𝑅2 (𝛿)
R2’=3m∆𝜎𝑦 =𝜎 = 0.62 𝜇m
𝛽𝑥 𝑥

by=3mmSimulated luminosity
degradation due tononlinear dispersion.

Chromatic and nonlinear couplingcorrection• Chromatic coupling knob for HER was available. The tuning
range was R1’~0.8rad (req.12rad), R2’~0.1m (3m).
• LER sextupole hardware rotation system is prepared, but nottried yet.
• Measurement showed no big aberrations, but 8-10 times
wider range is desirable.
• Squeezing by* further, wider range is required.
• Correction of Chromatic aberrations has started.
• Nonlinear coupling correction has started. It affects Dynamicaperture.

by=2mm• Lmes.=1.24x1034 cm-2s-1, xL=0.02 was achieved.
• ey=12, 18pm, ey=6mm.
• 820mAx820mA, 1576bunch• Simulation shows 2 times higher luminosity, 2.3x1034 .

Beam-beam limit• Beam-beam parameter has been limited to be𝜉𝑦− =0.02 for e- beam due to blow-up of e+ beam.
• The tune shift limit 0.02 does not depend on by=4,3, 2mm. The limit is somewhat high 0.025 at
by=8mm.
• The low tune shift is caused by difficulty related to
the large Piwinski angle, if the limit is independentof by?
• The tune shift limit at by=8mm

What determines the low beambeam limit?
• Key parameters• 𝛽𝑦∗ , chromatic effects𝜎𝑧 𝜃𝑐• Piwinski angle𝜎𝑥∗𝜎𝑥∗• Hour glass effect𝜃𝑐 𝛽𝑦∗

bunch length/overlap area

ratio of overlap area and 𝛽𝑦∗𝜎𝑥∗𝜃𝑐𝜃𝑐 : half crossing angle

Choice of bx, Hour glass effectq : Half crossing anglec• Key parameter sx/(qcby), characterize hour glass effect.
• Vertical tune shift increase as function of horizontal
amplitude. (Crab waist effect).
• Synchro-beta resonance in head-on collision => x-y
resonance in large crossing collision• sx/(qcby)=0.16 (2018-2019, by=3mm, bx=100/200mm)•=0.16-0.23 (by=2mm, bx=80/80mm)• sx/(qcby)=0.9 (design by=0.27/0.3mm, bx=32/25mm)• Enough margin for the hour glass effect at present.
• If we see such Hour glass effect, crab waist must benecessary in SuperKEKB.

Summary• Squeezing by was very successful. Luminosity
increased twice, L=1.23x1034 cm-2s-1, in the last one
week, 23 June - 1 July.
• Beam-beam parameter did not change for squeezing.
𝛾𝐼± 𝜉𝑦±Luminosity increases as 𝐿 =∗.
2𝑒𝑟𝑒 𝛽𝑦• This is fortunate result, because squeezing by makes
sensitive for errors.

For beam-beam parameter andluminosity performance• Beam-beam parameter increases for luminosity
increasing due to e+ current up. Somewhat morebeam-beam parameter may be possible.
• However in present condition, higher e+ current thantransparency condition was better. It seems e+ beam
has some problem.
• We have factor 2 discrepancy between simulation andachieved luminosity.
• The discrepancy was factor 2 in crab crossing.
• Choice for near future
1. We continue to search and correct error sources toexplain the discrepancy.
2. In parallel, we go crab waist. Not decided yet.

Coherent Beam-Beam-Head-Tailinstability study in Phase II• Typical condition• bx=0.2m, 0.1m, by=3mm• Itot=270mA (e+)x 225mA (e-), Nb=395,• Ib=0.68mAx0.57mA (design 1.44mAx1.04mA)• Np=4.3x1010, 3.6x1010. (design 9.04x1010x 6.53x1010)• ns (e+)=0.022, ns (e-)=0.026

Horizontal beam size measurement• 16:50 (instability start) & 16:57 (peak), data taking
using streak camera x-z and BOR.
• Tune scn, ns (e+)=0.022, ns (e-)=0.026
300mAx250mA
strong signal
270x225
weak

0.554,0.5435

0.552,0.5435

Beam oscillation at the horizontal
size blowup

BackupR. Yang, A. Koval

Vertical offset noise, slow
• ~Hz component

Luminosity degradation for Collisionoffset• Luminosity vs yoffset (BBWS simulation)• L decreases for vertical offset at high bunch current.

εy0+-=40pm
σy0+-=0.36μm

44Vertical offset scan with RF phaseoffset+5 degree (4.2mm offset)

0 degreeRF phase offsetによるvertical offsetの変化は小さい
逆方向にscan11 -> 5 mm (他は5 ->11mm)-5 degree (-4.2mm)

Vertical beam size/offset variationfor z• Low and high bunch current because beam tilt may
be caused by impedance asymmetry.

Top view

Side viewBeam-beam scan
Measure offset as function of z
Measure Bunch length, z-profile

K. OhmiPhase scan
• Equivalent to pan cake collision with projectedlongitudinal distribution

Luminosity integral∞

𝐿 = 𝑁𝑒 𝑁𝑝 𝑓𝑐𝑜𝑙

𝑧𝑝 − 𝑧𝑒𝑑𝑥𝑑𝑦𝑑𝑧𝑒 𝑑𝑧𝑝 𝑑𝑠2𝑥 − 𝜃𝑐 𝑧 2𝑦2𝑧2
exp −− 2− 222𝜎𝑥2𝜎𝑦 2𝜎𝑧

𝜌𝑒 𝑥, 𝑦, 𝑧𝑒 ; 𝑠 𝜌𝑝 𝑥, 𝑦, 𝑧𝑝 ; 𝑠 𝛿 𝑠 −−∞

𝜌𝑒 𝑥, 𝑦, 𝑧; 𝑠 =132𝜋 2 𝜎𝑥 𝜎𝑦 𝜎𝑧

𝜎𝑦 s =

𝜀𝑦 𝛽𝑦 (𝑠)2∞𝑥 − 𝜃𝑐 𝑧𝑝𝑥 − 𝜃𝑐 𝑧𝑒 2exp −−222𝜋𝜎𝑥,𝑒 𝜎𝑥,𝑝 −∞2𝜎𝑥,𝑒2𝜎𝑥,𝑝1𝑧𝑒 − 𝑧𝑝 𝜃𝑐2
exp −2Σ𝑥22𝑑𝑥 =4𝜋Σ𝑥22 + 𝜎2
Σ𝑥2 = 𝜎𝑥,𝑒𝑥,𝑝2𝑧𝑒 − 𝑧𝑝 𝜃𝑐2𝑧𝑝2𝑧𝑒2
exp −− 2 − 2 𝑑𝑧𝑒 𝑑𝑧𝑝 =22𝜎𝑧 2𝜎𝑧2Σ𝑥−∞∞2𝜋Σ𝑥 𝜎𝑧
Σ𝑥2 + 2𝜎𝑧2 𝜃𝑐2

Luminosity in nano-beam collision• Luminosity- collision is done in area sx/qc<<sz at s*.
𝜎𝑥∗
< 𝛽𝑦∗
𝜃𝑐

𝑁𝑒 𝑁𝑝 𝑓𝑐𝑜𝑙 ∞𝐿=
𝜌𝑒 𝑦, 𝑧; 𝑠 ∗ 𝜌𝑝 𝑦, 𝑧; 𝑠 ∗ 𝑑𝑦 𝑑𝑧
𝜃𝑐−∞• When e+ bunch shift in longitudinal
𝑁𝑒 𝑁𝑝 𝑓𝑐𝑜𝑙 1𝑧02
𝐿(𝑧0 ) =exp − 22𝜋𝜃𝑐 Σ𝑦 Σ𝑧2Σ𝑧𝜌𝑝 𝑦, 𝑧 =1∗2𝜋𝜎𝑦,𝑝𝜎𝑧,𝑝exp −𝑦2(𝑧 − 𝑧0 )2−∗2
22𝜎𝑦,𝑝2𝜎𝑧,𝑝Top viewΣ𝑧 is measurable.

• Non-Gaussian longitudinal profile∞𝐿(𝑧0 ) ∝• Tilt beam in y-z

𝜌𝑒 𝑧; 𝑠 ∗ 𝜌𝑝 𝑧, 𝑧0 ; 𝑠 ∗ 𝑑𝑧−∞(𝑦 − 𝑎𝑧 − 𝑏)2 (𝑧 − 𝑧0 )2
𝜌𝑝 𝑦, 𝑧 =exp −−∗∗222𝜋𝜎𝑦,𝑝𝜎𝑧,𝑝2𝜎𝑦,𝑝2𝜎𝑧,𝑝12 𝑏 2 + 𝜎 2 (𝑎𝑧 + 𝑏)2
1 Σ𝑦2 𝑧02 + 𝜎𝑧,𝑝𝑧,𝑒0𝐿(𝑧0 , 𝑏) ∝ exp −222Σ𝑦2 Σ𝑧2 + 𝑎2 𝜎𝑧,𝑒𝜎𝑧,𝑝HERHER• F0=100kHz

Impedance estimation- transverse• Tune shift as function of bunch currentΔ𝜈𝑥 =1 𝑁𝑟𝑒 𝐿 𝑖𝑍𝑒𝑓𝑓
4𝜋 3/2 𝛾 𝜈𝑥 𝜎𝑧 𝑍0𝑖𝑍𝑒𝑓𝑓 = 31 𝑥

LER x𝑖𝑍𝑒𝑓𝑓 (𝑘Ω) = 33.3

Δ𝜈𝑥𝐼(𝑚𝐴)

53 𝑦 𝑘Ω/𝑚LER𝑖𝑍𝑒𝑓𝑓 = 43 𝑥

HER y= 58.2

Δ𝜈𝑥𝐼(𝑚𝐴)

145 𝑦 𝑘Ω/𝑚Collimatordependence

KEKB-LER: -0.0034mA-1, 81kW/mcoll. open 33-46 kW/m T. Ieiri, EPAC00

HERBunch length measurement• H.Ikeda

Measured by a Streak camera
The behaviors are similar as KEKB for both of LER andHER.
Bunch lengthening is stronger than that of simulation.

RF phase scan

このデータからバンチ長を評価できるはず->まだやってない• set IP knob
• Df=-400Hz0Hz+400Hz

Beam-beam scan with DfRF

• IP knob off• Df=-400Hz0Hz400Hz2018/7/6 Swing HBC tune scan
• One of the Crab waist
effect• Is resonance nx+4ny=0seen?

L>20x1032

nx+4ny=0• bx=200/100mm
Dangerous line
nx=0.5+1.5ns=0.539

57

sx of both beam increases

LER tune scan 2019/3/31• nx+4ny=int is seen. bx=200/200mm

58

LER tune scan 2019/3/31• Shift of sy peak for nx.
nx =0.57

nx =0.552

59

nx =0.56

nx +4 ny =2.998 n = (0.57,0.607)
3.012 =(0.56,0.613)
3.000 =(0.552,0.612)

LER tune scan 2019/5/13• No resonance is seen at nx+4ny=int at bx=100(H),200(L)mm.
• The resonance appeared for bx=200,200mm (2019/3/31)
but does not for 100(H),200(L)mm• This crab waist effect, (1,4) resonance, is weak.