Introduction to SuperKEKB
Y. Funakoshi (KEK)2023.10.23@B2GM

2023/Oct. 23rd

Inter-University Research Institute Corporation High Energy Accelerator Research Organization (KEK)

B2GM

大学共同利用機関法人 高エネルギー加速器研究機構 (KEK)1Request to this talk
• Requests• Introduction to SuperKEKB, including explanation about some important
optical parameters, nano-beam scheme, and so on.

• Contents• Luminosity formula• Nano-beam scheme• Large Piwinski angle collision• Crab waist scheme• Some important optics parameters• Emittance• X-Y coupling• Chromatic coupling• Dynamic aperture
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Luminosity formula (1)
𝐿=

𝑁− 𝑁+
2
2
2𝜋 𝜎𝑥−+ 𝜎𝑥+

𝑛𝑏 𝑓𝑟𝑒𝑣 𝑅
2
2
𝜎𝑦−
+ 𝜎𝑦+

• N-,+ : Number of paricles in a bunch (e-,e+)• nb : number of bunches -> drastically increased indouble rings• frev : revolution frequency• R : Geometrical Loss factor

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Luminosity Comparison
FCC-ee (Z-mode)(Design)

3rd generation e+/e- collider
CEPC (Z-mode) (w/ nano-beam schme)

SuperKEKB(Design)(Design)
SuperKEKB (achieved)
ILC (Design)KEKB
PEP-II
BEPC-II

LHC

2nd generation e+/e- collider (double ring)

CESR
DAFNE
VEPP-2000

SPEAR

DOTIS II

PEP
PETRA

BEPC

LEP-IITRISTANLEP

1st generation e+/e- collider

VEPP-4M
ADONE

CMS Energy [GeV]
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Luminosity formula (2)Small for the flat beam

𝜎𝑦∗
𝛾±
𝐿=
1+ ∗
2𝑒𝑟𝑒
𝜎𝑥

𝐼± 𝜉𝑦±𝛽𝑦∗𝑅𝐿𝑅𝜉±(Take ether of + or - )Not far from unity

In the energy region where the beam-beam interaction is important, this formula is commonly used.
This formula is derived with an assumption that the beam sizes at IP (sx*, sy*) are equal between two beams.
• g : Lorentz foctor• sx*, sy* : horizontan and vertical beam sizes• I : Total beam current

Luminosity is mainly determined by those
three parameters.

• by*: vertical beta function at IP• xy : vertical beam-beam parameter• Rx : Geometrical Loss factor for beam-beam parameter

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Beam-beam parameters• Beam-beam force

x/sx*

y/sy*

・Very nonlinear force-> Linear part (near bunch center) gives focusing force like quadrupoles
Δ𝑥 ′ = −2023/Oct. 23rd2𝑁𝑟𝑒𝑥
𝛾 𝜎𝑥∗ 𝜎𝑥∗ + 𝜎𝑦∗Δ𝑦 ′ = −2𝑁𝑟𝑒𝑥𝛾 𝜎𝑦∗ 𝜎𝑥∗ + 𝜎𝑦∗

B2GMTune shift66

Beam-beam parameter• Beam-beam parameter (or beam-beam tune shift)
∗
𝛽𝑦±
𝑁∓
𝑟𝑒
𝜉𝑦± =
∗
∗
∗
2𝜋𝛾± 𝜎𝑦∓
𝜎𝑥∓
+ 𝜎𝑦∓

∗
𝑟𝑒
𝛽𝑥±
𝑁∓
𝜉𝑥± =
∗
∗
∗
2𝜋𝛾± 𝜎𝑥∓𝜎𝑥∓+ 𝜎𝑦∓

𝐿𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 =
𝐿=

xy

𝐿
𝑛𝑏 𝐼𝑏𝑢𝑛𝑐ℎ,+ 𝐼𝑏𝑢𝑛𝑐ℎ,−
𝑁− 𝑁+

2
2
2𝜋 𝜎𝑥−+ 𝜎𝑥+

𝑛𝑏 𝑓𝑟𝑒𝑣 𝑅
2
2
𝜎𝑦−
+ 𝜎𝑦+

beam-beam limit
beam blowup

beam size constant2023/Oct. 23rd

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Luminosity limitation due to hourglass effectHourglass effecthourglass𝑠2
𝛽𝑦 = 𝛽𝑦0 +
𝛽𝑦0
𝜎𝑦 =

𝛽𝑦 𝜀𝑦

● Luminosity does not increase by squeezing by* down to less than ~ sz (bunch length). [ex. KEK sz: ~ 6mm, by* : 5.9mm)
・ Beam size increase in the range of bunch length (geometrical degradation).
・ Effects of beam-beam interaction is stronger at larger by position (-> additional beam-beam blowup).

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Head-on collision and Nanobeam collision• Head-on collisionσz hourglass condition: βy*>~ σz• NanoBeam collisionLhourglass condition: βy*>~ L = σzeffective
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Nanobeam collision scheme• Piwinski-angle (fp)• Luminosity
1
𝐿=
2 2𝜋

P. Raimondi

𝑁𝑒 𝑁𝑝
2 +𝜎 2𝜎𝑧 sin 𝜙𝑐 𝜎𝑦𝑒
𝑦𝑝

𝜎𝑧
𝜎𝑧
𝜙𝑝 = ∗ tan 𝜙𝑐 = 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒
𝜎𝑥𝜎

𝑓𝑐𝑜𝑙 𝑅𝐿𝑧

Luminosity enhancement factor• Beam-beam parameter𝛽𝑦𝑝 𝑁𝑒𝑟𝑒𝜉𝑦𝑝 =𝑅
2𝜋𝛾𝑝 𝜎𝑧 sin 𝜙𝑐 𝜎𝑦𝑒 𝜉𝑦𝑝

𝛽𝑦𝑒 𝑁𝑝
𝑟𝑒
𝜉𝑦𝑒 =
𝑅𝜉𝑦𝑒
2𝜋𝛾𝑒 𝜎𝑧 sin 𝜙𝑐 𝜎𝑦𝑝

Collision in boosted frame

σzeffective = σ*x / sinφc2023/Oct. 23rd

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σ*xeffective = σz sinφc φc
Projected beam shape10Machine Parameters
KEKB(LER, achieved)

SuperKEKB(LER, design)

SuperKEKB(LER, achieved)±11 mrad±41.5 mrad±41.5 mrad

bx*

1.2 m

32 mm

80 mm

by*

5.9 mm0.27 mm

1 mm (0.8 mm)

ex

18 nm

3.2 nm4.0 nmey

169 pm8.64 pm

50 pm

ey/ex

0.94 %

0.27 %

1.25 %

sx*

147 mm10.1 mm

17.9 mm-

249 mm

249 mm

sy*

~1 mm

48 nm

223 nm

sz*

~7 mm

6 mm

~6 mm

-

0.24 mm0.43 mm

0.524

24.7

13.9

Crossing angle

sx*effective

sz* effective
fPiwinski
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Nano-beam scheme= Large Piwinski angle collision11

Crab waist scheme

P. Raimondi• Collision point with the center of the other beam for a partice with a horizontal
offset• Due to large crossing angle, a parcle with horizontal offset collide with the center of theother beam at a location offset from the waist (minimum of by).
• The vertical beam-beam kick depends on the horizontal offset.
-> X-Y coupling resonances driven by the beam-beam interaction -> beam-beam blowup
Original waist points of e+• Crab waist scheme• Waist points of one beam are shifted so that there arealigned along the center of theother beam.
• The X-Y coupling resonaces can be suppressed.
Shifted waist points

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How to realize crab waist scheme
Backup plan at SuperKEKB design stage

Present scheme at SuperKEKB

K2 5.95

NX 12.5
NY 12.25

NX 13.0
NY 12.25

K2 5.95--Crab waist scheme is realized by unisg a pairof sextupole magents which have appropriate betatronphase relations with IP.
--At the design stage, crab waist scheme wasconsidered to be a backup plan.
--Problem, which was thought to be serious, wasa short beam lifetime due to narrow dynamic aperture.
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Specific luminosity w/ and w/o crab waist
Strong-Strong Beam-Beam simulation
D. Zhou

CW ratio:
LER: 80 %HER: 40%2023/Oct. 23rd

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Strong-weak simulation on crab waist
HER

LER

K. OideLER
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HER
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Summary of operation with crab waist scheme• Benefits of use of crab waist scheme• Suppression of beam-beam blowup• Specific luminosity was improved.

• Increase of the bunch currents of both beams• W/o crab waist, beam injections was limited due to beam blowup.

• Beam lifetime issue• Dynamic aperture shrinks w/ crab waist and the lifetime decrease w/ crab
waist was expected.
• But in by*= 1mm case, no lifetime decrease was observed in LER and HER, since thecollimator physical aperture is already very narrow.
• On July 1st 2021, the lifetime of LER increased with wider collimators and so lifetime seems to
be determined by physical aperture.

• In case of lower by*, the lifetime w/ crab waist will be an issue.

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Emittance• Horizontal emittance• Determined by the balance between radiation damping and radiation
excitation.
• KEKB and SuperKEKB rings have a wide range of tunability of emittance andmomentum compaction factor.

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Radiation damping• Radiation Damping of betatron oscillation● When a particle is accelerated
by acceleration cavity, posith does
not change and angle is reduced.
-> Emittance is reduced.
●Both position and angle do notchange by emitting SR.

E
tb = 2 T
U0

Revolusion time

Energy loss / turn
Radiation damping time of betatron oscillation
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Quantum excitation

Original COD

Emit a photon with energy of u

Excited betatron
New
COD
after
emissionof a photon
New
COD
after
photonemission

When a photon is emitted at a place where dispersion is non-zero,a betatron oscillation is excited. Quantum excitation becomes weakerwith smaller dispersion.
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2.5 p cell lattice• Tunability of horizontal emittance and momentum compaction (a)●With 2.5p lattice , ex and aをcan be tuned
in a wide range

ex = 10nm
KEKB
LER

HER
LER
ex = 36nm

exとaのtunability (SuperKEKB)●SuperKEKB: lower ex is realized.
● KEKB(LER): ex 18nm,
L=0.9m -> 4m
SuperKEKB: ex 3.2nm -> 4nm (with longer bends)● Low a-> shorter bunch length
In KEKB, lower by* than PEP-II was possible
1 h
a
=
ds
with lower a.

C2023/Oct. 23rd

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KEKB
LER

òr

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Vertical emittance• Vertical emittance (single beam, zero current)2
rms
ey = kex + A (hy ) + eOA
ycoupling

dispersion

opening angle• x-y coupling• Machine errors (such as mis-alignment of Q or SX mganets. )• The coupling correction can reduce residual coupling value.

• Vertical dispersion• Machine errors (such as mis-alignment of Q or SX mganets. )• The dispersion correction can reduce residual dispersions.

• Vertical dispersion in design• Fringe field of detector solenoid, vertical bending magnets -> (small, ey ~ 0.33 pm, LER)

• Opening angle of radiation• Usually negligible ( or ultimate limit of vertical emittance)• Others• Synchro-beta emittance (a.k.a anomalous emittance)• Beam-beam blowup (large)• Instablility (TMCI, Electron clouds)

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Luminosity vs single beam vertical emittance• Ways to better beam-beam performance• Beam-beam simulations predict better beam-beam performance with••

Smaller vertical emittance in single beam (matter of optics corrections)
Higher crab waist ratio in HER (strength)• Identification of causes of discrepancy between simulations and experiments• Better working points• Beam-beam parameters• Achieved values in physics runs: : xy(LER) =0.0407 , xy(HER) = 0.0279• Achieved values in high bunch collision study: xy(LER) =0.0565 , xy(HER) = 0.0434• By increasing bunch currents in physics run, higher xy and then a higher luminosity is expected.
Pink: Nb=31, March 28th 2022
Blown: Nb = 61, April 5th 2022
Orange: Nb = 393, April 5th 2022

D. Zhou

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Luminosity vs single beam vertical emittance

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Vertical emittanceDesign Reportey< 2 pm

100 samples
w/ machine error
w/ optics corrections

Real machine
ey=~25 pm (LER, single beam, Phase 3)
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ey in Phase 1

H. Sugimoto

Large ey (~25pm) in Phase 3 may comefrom with IR for some unknown reason.

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Method of optics correction (KEKB, SuperKEKB)

Iterative method2023/Oct. 23rd

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Chromatic coupling correction in LER

Synchro-beam emittance depends on chromatic X-Y coupling and becorrected by using skew-sextupoles. Large chromatic X-Y coupling at IP
could degrade the luminosity.
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Synchro-beta emittance (LER) by* = 1mmnx –ny + ns = N
nx –ny + 2ns = N

2023/Oct. 23rd

nx = 44.527
ns = 0.02212

nx –ny + 3ns = N

Red: synchro-beta emittance command (main-trunk)
Green: particle tracking 1000 particles, 20,000 turns Rad, Fluc:ON
No machine errors
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Dynamic aperture• Dynamic aperture• Stable region in (x,x’,y,y’,DE/E,t) phase space• <-> physical aperture (usually determined by the collimator aperture)• In general, dynamic aperture shrinks with lower by*.
• By optimizing settings of sextupole magnets, dynamic aperture can be
improved.

• Beam lifetime• In SuperKEKB, Touschek lifetime is dominant. (others: beam-gas Coulomb
scattering, radiative BhaBha scattering)• Touschek lifetime is usually determined by the dynamic (or physical) aperturein horizontal-energy direction.

• Beam injection efficiency• In SuperKEKB, the injection efficiency is limited by the dynamic (or physical)
aperture mainly in the horizontal direction.
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Dynamic aperture simulation by SAD
No machine errors
CW: 80%w/ collimator

by* = 1 mm
ey = 40 pm
Ibuch = 0.62 mA

No machine errors
CW: 40%w/ collimator

Quantum excitationin dispersive region

Y. Ohnishi
by* = 1 mm
ey = 35 pm
Ibuch = 0.5 mA

Touschek scattering

No machine errors
CW: 80%w/ collimator

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by* = 0.8 mm
ey = 40pm
Ibuch = 0.62mA

B2GM

No machine errors
CW: 40%w/ collimator

by* = 0.8 mm
ey = 35 pm
Ibuch = 0.5mA30

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Touschek beam lifetime (simulation & experiment)
Y. Ohnishi▲ : experiment (by*=1mm)◆ : experiment (by*=0.8mm)▲ : experiment (by*=1mm)◆ : experiment (by*=0.8mm)◆▲▲

Same value for by*= 1 mm and 0.8 mm◆- LER lifetimes measured are consistent with simulations. HER lifetimes measured are ~ half of simulation.
- LER (CW:80%, by*:1mm): Physical aperture is slightly narrower than the dynamic aperture.
- LER (CW:80%, by*:0.8mm): Dynamic aperture is narrower than physical aperture.
- LER (CW:40%, by*:1mm): Physical aperture is narrower than the dynamic aperture.
- LER (CW:40%, by*:0.8mm): Dynamic aperture is narrower than physical aperture.
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Error of cancel coils for QC1P leakage field

Skew components
are increased.

b3(b4) and a3(b4) coils are excited by the same power supply.

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Almost no effect to beam lifetime.
Beam injection efficiency may be affected.
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QCS correction coils

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HER injection with error of cancel coilw/o error of cancel coils

w/o error of cancel coils
N. Iidaw/ error of cancel coils

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Injection efficiency (simulation and experiments)

LER

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Comparison of machine parameters
KEKB
achieved
Ibeam [A]IPAC2020
K. Shibata
SuperKEKB
2020 May 1st

IPAC2022
at present
SuperKEKB
2022 June 8th

SuperKEKB
design

LER

HER

LER

HER

LER

HER

LER

HER

1.637

1.188

0.438

0.517

1.321

1.099

3.6

2.6

# of
bunches

1585

783

2249

2500

Ibunch [mA]1.033

0.74950.55930.66030.58730.4887

1.440

1.040

by* [mm]

5.9

5.9

1.0

1.0

1.0

1.0

0.27

0.30

0.129

0.090

0.02360.02190.0407(0.0565)a0.0279(0.0434)a0.08810.0807xy
Luminosity[1034cm-2s-1]

2.11

1.57

Integrated
Luminosity [ab-1]

1.04

0.03

doubled

4.65

80

0.40

50

a) High bunch current collision study
2022/June/12th
2023/Oct. 23rd

IPAC2022

SuperKEKB

B2GMY. Funakoshi

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Fin.
Thank you for your attention.

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Inter-University Research Institute Corporation High Energy Accelerator Research Organization (KEK)

B2GM

大学共同利用機関法人 高エネルギー加速器研究機構 (KEK)37

Transverse aperture (LER)

Y. Ohnishi

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Beam lifetime estimation (at the design stage)
KEKB (design)

KEKB (operation)

SuperKEKB

LER

HER

LER

HER

LER

HER

Radiative
Bhabha

21.3h

9.0h

6.6h

4.5h

28min.

20min.

Beam-gas

45ha)

45ha)

24.5min.b)

46min. b)

Touschek

10h-

10min.

10min.

Total

5.9h

7.4h

~133min.

~200min.

6min.

6min.

Beam
current

2.6A

1.1A

1.6A

1.1A

3.6A

2.6A

Loss Rate

0.12mA/s

0.04mA/s

0.23mA/s

0.11mA/s

10mA/s
7.2mA/s
4nC@25Hz 2.9nC@25Hza) Bremsstrahlungb) Coulomb scattering, sensitive to collimator setting

As for loss rate, beam loss accompanied with the beam injection should be added.

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Machine parameters at highest luminosity

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41

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Dynamic aperture with sextupoles for crab waist (LER)

0%

50%

100%

with optimization

with optimization

50%

100%

before optimization

before optimization

by* = 0.27mm

At the design stage, crab waist scheme was thought to be unusable due todynamic aperture decrese.
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H. Koiso44

Synchro-beta emittance (HER)
by* = 1mm
Red: synchro-beta emittance command (main-trunk)
Green: particle tracking 1000 particles, 15,000 turns Rad, Fluc:ON
No machine errors
Blue: experiment (use lattice model tune in horizontal axis)

nx = 45.533
ns = 0.0270

nx –ny + ns = N

2023/Oct. 23rd

Oct. 2021

nx –ny + 2ns = N

Present working point
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Layout of LINAC, BT, Injection to MRe+ beam is injected into the LER via DR:
The injection BG is not almost affected by thebeam condition at upstream of the DR.

e- beam directly injects into HER:
The injeciton BG is directly affected by thecondition of RF-gun, LINAC, and BT.
Injection Points

LINAC
1.1GeV Damping Ring (DR)for positron

Jarc

primary e- for e+: Thermionic Gun
e- : RF Gun
Sector B Sector A
Sector C

Sector1

BCS
Sector2

Beam Transport line (BT)
Arc4
BT2
ECS
for e+

LTR

ECS

BT1

Sector3

Sector4

Slope2Arc2-3

Sector5e+ target

BT1 and BT2: Wire scanners(WSs), MSE.10:OTR
BCS: Bunch Compression System (for e+)rd
ECS:
EnergyCompression System (for e+) B2GM
MDI, 19.Oct.2023,
Injection,N.
2023/Oct.
23Iida

Arc0

BT1

Arc1

MSE.10(OTR)(=BT1.5)

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Bunch length (measurement by streak camera)

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Luminosity improvement [1/4] Crab waist• Introduction of crab waist at SuperKEKB• Motivations• The beam-beam performance was poor in spite of all of knob tunings for
improving it.

• Method• FCC-ee type scheme: use of imbalance sextupoles in the vertical local
chromaticity correction section.

• Time table• 2020 March 16th : LER crab waist (40%)• 2020 March 24th : LER crab waist (60%)• 2020 April 24th : HER crab waist (40%)• 2030 June 1st : LER crab waist (80%)
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Injection efficiency (simulation and experiments)

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Beam LifetimeTime• Lifetime model𝜏 𝑇𝑜𝑢𝑠𝑐ℎ𝑒𝑘
𝑛𝑏
= 𝐶𝑇
𝜀 𝜀 𝜎
𝐼𝑏𝑒𝑎𝑚 𝑥 𝑦 𝑧
1𝜏𝑉𝑎𝑐𝑢𝑢𝑚 = 𝐶𝑉𝐼𝑏𝑒𝑎𝑚
1

𝜏𝑇𝑜𝑡𝑎𝑙=1

𝜏𝑇𝑜𝑢𝑠𝑐ℎ𝑒𝑘+

Ibeam[mA]

Ibunch [mA] nb

Tau [min]emity [pm]emitx [nm]sig_z [mm]2021/12/20/8:56

227.3

0.5784

393

8.35

22.3

3.1

5.67

2021/12/20/10:01

225.1

0.1643

1370

21.8

21.1

2.9

4.58

𝐶𝑇 = 𝐶𝑇 (physical aperture, dynamic aperture)
𝐶𝑉 = 𝐶𝑉 (dP/dI, physical aperture, dynamic aperture)𝜏𝑇𝑜𝑢𝑠𝑐ℎ𝑒𝑘
𝜏𝑉𝑎𝑐𝑢𝑢𝑚∝ 𝑛𝑏

𝐶𝑇 = 1.973*1011 [sec A /m3]
𝐶𝑉 = 7622 [sec A]

1

𝜏𝑉𝑎𝑐𝑢𝑢𝑚• Result of analysis
Time

Ibeam
[mA]

2021/12/20/
227.3
8:56
2021/12/20/
225.1
10:01

nb

Tau
[min]

sig_z
[mm]

Touschek Vacuum[min.][min.]

sig_z Touschek Vacuum[mm][min.][min.]

393

8.35

5.67

8.48

558.9

4.58

9.46

70.9

1370

21.8

4.58

22.7

564.3

4.58

31.3

71.6
51