International Task Force Joint Meeting: Discussion on
beam-beam
Demin Zhou
on behalf of the SKB-ITF-BB workgroup
Accelerator theory group, Accelerator laboratory, KEK

Acknowledgements
K. Ohmi, K. Oide, D. Shatilov, Y. Cai, C. Montag, T. Browder,
X. Bu at, Y. Ohnishi, A. Morita, K. Akai, Y. Funakoshi,
and SuperKEKB commissioning groupff

The 25th KEKB Review Meeting, Sep. 02, 2021, KEKOutline• Background- KEKB ARC meetings (2010 - 2021) [1].
- ICFA Mini-Workshop on Commissioning of SuperKEKB and e+e– Colliders, Nov. 11 - 13, 2013, KEK [2].
- 1st SuperKEKB Beam Dynamics Mini-Workshop, Jul. 17, 2019, KEK [3].
- 2nd SuperKEKB Beam Dynamics Mini-Workshop, Sep. 20, 2019, KEK [4].
- Workshop on “SuperKEKB: Challenges for the high luminosity frontier”, Jan. 30-31, 2020, KEK [5].
- Meeting of International Task Force Meeting for SuperKEKB Upgrade, Jul. 28, 2021, KEK [6].
- 1st meeting of beam-beam workgroup, Aug. 24, 2021, KEK [7].

• ITF-BB workgroup• Highlights of rst ITF-BB workgroup meeting[1] https://www-kekb.kek.jp/MAC/.
[2] https://kds.kek.jp/event/12760/.
[3] https://kds.kek.jp/event/31793/.
[4] https://kds.kek.jp/event/32065/.
[5] https://conference-indico.kek.jp/event/103/.
[6] https://kds.kek.jp/event/38899/.
[7] https://kds.kek.jp/event/39142/.

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ITF-BB workgroup• The ITF-BB workgroup was organized under the framework of International Task Force forSuperKEKB Upgrade [6] (See M. Masuzawa’s talk of this meeting)- Monthly group meeting or on demand• Currently 20 members (based on mailing list)- KEK (10), CERN (6), BINP (1), BNL (1), INFN (1), UHM (1)- Contact persons: Demin Zhou and Kazuhito Ohmi
• To join the mailing list
- Subscribe by contacting D. Zhou (dmzhou@post.kek.jp).
• The 1st meeting of beam-beam workgroup- Organized on Aug. 24, 2021 via Zoom connection.
- About 20 participants joined.
- Two talks were given: “Beam-beam e ects in SuperKEKB” by K. Ohmi and “Beam-beam simulations for SuperKEKB”

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by D. Zhou.
Following discussion was very active and fruitful.

Highlights of rst ITF-BB workgroup meeting

Y. Ohnishi• Beam-beam e ects in SuperKEKB [8]- Overview of luminosity performance with crab-

waist in 2021 (also see Y. Ohnishi’s talk in thismeeting)Speci c luminosity (Lsp) increased by ~20%
after feedback gain optimization
Rapid drop of luminosity at low bunch currents
seemed not appear (It was an issue in earlyphases).
Electron-cloud e ects were not visible whencomparing Lsp with 1174 (3-bucket spacing,blue dots) and 393 (12.25-bucket spacing,magenta dots) bunches.

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[8] https://kds.kek.jp/event/39142/contributions/194650/attachments/146581/182524/BBSKB2021ab.pdf

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Y. Ohnishi• Beam-beam e ects in SuperKEKB [8]- The obvious drop of Lsp vs bunch-current--

product disagrees with weak-strong
simulations.
At bunch current product of ~0.7 mA2 (I+/I- ratio
1.25), measurement/simulation ratio is lessthan 50%. [At ~0.4 mA2, the ratio was found tobe ~80% without BBHTI, see page.13]
With crab waist, simulated beam-beam
parameter ξy ~0.1, but achieved ξy ~0.03.

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ff[8] https://kds.kek.jp/event/39142/contributions/194650/attachments/146581/182524/BBSKB2021ab.pdf

5Highlights of rst ITF-BB workgroup meeting• Beam-beam e ects in SuperKEKB [8]- Transverse mode-coupling instability (TMCI)-

became a challenge in LER (see Ref. [9] andIshibashi’s talk in this meeting). It caused
serious blowup of vertical beam size and set alimit of luminosity performance at high bunch
currents.
With calculated impedance, ordinary TMCI
theory gives much higher threshold than
measurements.
Machine studies and following careful data
analysis showed the observed TMCI had
dependence on vertical tune. This is evidenceof TMCI caused by localized wake, while
ordinary TMCI has no dependence on νy.

- Small-gap collimators dominate the sources ofvertical impedance driving TMCI.

[8] https://kds.kek.jp/event/39142/contributions/194650/attachments/146581/182524/BBSKB2021ab.pdf
fiff[9] https://kds.kek.jp/event/39138/

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Highlights of rst ITF-BB workgroup meeting• Beam-beam e ects in SuperKEKB [8]- Collision o set noise is a candidate source ofluminosity degradation.
Weak-strong simulations show drop of Lsp,
similar to observations.
In realistic machine operation, the amplitude ofcollision o set noise is unknown. It is to beinvestigated in the future.

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[8] https://kds.kek.jp/event/39142/contributions/194650/attachments/146581/182524/BBSKB2021ab.pdf

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Highlights of rst ITF-BB workgroup meeting• Beam-beam e ects in SuperKEKB [8]- High-bunch current collision (HBCC) machine-

study reveals rich information of beam-beam
e ects (see the talks and memo of Ref. [7]).
Asymmetric blowup of the two beams in bothhorizontal and vertical planes were observed.

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[8] https://kds.kek.jp/event/39142/contributions/194650/attachments/146581/182524/BBSKB2021ab.pdf

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Highlights of rst ITF-BB workgroup meeting• Beam-beam e ects in SuperKEKB [8]- Coherent beam-beam head-tail instability(BBHTI) (discovered by K. Ohmi in 2016 andobserved at SuperKEKB in 2018 duringmachine study) is one candidate to explain thehorizontal blowup.

fiff[8] https://kds.kek.jp/event/39142/contributions/194650/attachments/146581/182524/BBSKB2021ab.pdf

9Highlights of rst ITF-BB workgroup meeting• Beam-beam e ects in SuperKEKB [8]- With the current parameter regime of-SuperKEKB (β*y = 1 mm), BBHTI appears
frequently in simulations. But it does not cause
large luminosity degradation.
There is inconsistency between simulation andexperiment: Simulated BBHTI show
simultaneous σx blowup of the two beams. But
in HBCC machine study, blowup of LER beam
was obvious but HER beam was not.

- Ohmi-san’s remark-1: If head-tail signal, which-

synchronizes the two beams, is observed, it isthe evidence of BBHTI.
Ohmi-san’s remark-2: Optics aberrations at IP(such as chromatic coupling), collision o set
noise, and BBHTI are candidates to be
counted in beam-beam simulations tounderstand the present luminosity limit.

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[8] https://kds.kek.jp/event/39142/contributions/194650/attachments/146581/182524/BBSKB2021ab.pdf

10• Beam-beam simulations for SuperKEKB [10]- D.Z. gave an overview of beam-beam simulations with-nal design con gurations (β*y = 0.27/0.3 mm for LER/HER,
w/o crab waist).
The source of the luminosity loss seen in beam-beamsimulations (weak-strong model plus design lattice) wasinterplay of beam-beam resonances and nonlinearity of theIR.

fi[10] https://kds.kek.jp/event/39142/contributions/194651/attachments/146544/182494/20210824_BB_Simulations_SKB.pdf
fifiHighlights of rst ITF-BB workgroup meeting11

Highlights of rst ITF-BB workgroup meeting• Beam-beam simulations for SuperKEKB [10]- Observations in Phase-2 commissioning without crab waist:-

Peak luminosity lower than predictions of simulations; Easy
blowup of one beam; Small area in tune space for goodluminosity; Unexpected high Belle-2 background; No or small
gain of luminosity via squeezing β*x,y; Hard to approach to thedesign working point (.53, .57); …
Weak-strong simulations showed that the beam-beamresonances of ± νx + 4νy + α = N (they appear without crab
waist) can be important.

Machine parameters ofPhase-2 for beam-beamsimulationsfi[10] https://kds.kek.jp/event/39142/contributions/194651/attachments/146544/182494/20210824_BB_Simulations_SKB.pdf

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Luminosity history panel seen in SuperKEKB control room

Highlights of rst ITF-BB workgroup meeting• Beam-beam simulations for SuperKEKB [10]- Strong-strong simulations with crab waist (use parameter set of2021.05.14 which was typical for 2021ab physics run) weredone to compare experimental observations in Phase-3.

- With single-beam ϵy of 22.5 pm, BBSS simulations predict lum.
of ~3.75e34 cm-2s-1 without obvious BBHTI. This is comparedto the achieved luminosity of ~3.0e34 cm-2s-1 in 2021ab run.

- In simulations, the crab waist and the single-beam ϵy werevaried, showing that these parameters are essential indetermining the luminosity performance.

- Weak blowup in ϵx (hint of BBHTI) was observed in the control
room, but not well-con rmed.

Operation parameter
set

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[10] https://kds.kek.jp/event/39142/contributions/194651/attachments/146544/182494/20210824_BB_Simulations_SKB.pdf

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Luminosity history panel seen in SuperKEKB control room

Highlights of rst ITF-BB workgroup meeting• Beam-beam simulations for SuperKEKB [10]- Simulations showed that the machine seemed to operate roundthe BBHTI threshold: The blowup of positron σ*x in experimental
data occurred around the simulated BBHTI threshold.

- The observed blowup of σ*y of both electron and positron beams
were complicated (see 24 hours’ history of ϵy). BBSS
simulations cannot reproduce the trends of σ*y blowup.

- Simulations showed the same working point (.53,.57) for bothrings is better: Higher BBHTI threshold and weaker beam-size
blowup.

Operation parametersetfi[10] https://kds.kek.jp/event/39142/contributions/194651/attachments/146544/182494/20210824_BB_Simulations_SKB.pdf

Electron σ*xElectron σ*yPositron σ*x

Positron σ*y14Highlights of rst ITF-BB workgroup meeting

Luminosity history panel seen in SuperKEKB control room

• Beam-beam simulations for SuperKEKB [10]- On Jul. 1st, 2021, a machine study was done with high bunchcurrents for collision. Strong blowup in LER σ*y and obvious
blowup in LER σ*
x were observed in experiment.

- BBSS simulations were done to compare the experimental

observations. With strong BBHTI and assumed bunch
lengthening, the simulated slope of speci c luminosity seemed
to agree with experimental data. [This was an accidental
agreement. See discussions of the following slides.]- Parameters such as ϵy, σz, and νx,y were varied in simulations.
The design working point (.53,.57) has weaker BBHTI, giving
high luminosity. BBHTI seemed to play an important role.

Operation parameter
sets

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[10] https://kds.kek.jp/event/39142/contributions/194651/attachments/146544/182494/20210824_BB_Simulations_SKB.pdf

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Highlights of rst ITF-BB workgroup meeting

Luminosity history panel seen in SuperKEKB control room

• Beam-beam simulations for SuperKEKB [10]- BBSS simulations showed BBHTI threshold threshold issensitive to σz and νx, not sensitive to ϵy and νy.

- Simulations showed that BBHTI makes vertical emittance-

growth more severe.
Experiment phenomena are quite complicated. It was hard todetermine the BBHTI threshold (suppose the horizontal blowup
was due to BBHTI). Blowup of σ*y was much di erent fromsimulations. The two beams had unbalanced blowup.
Electron σ*xElectron σ*yOperation parameter
sets

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[10] https://kds.kek.jp/event/39142/contributions/194651/attachments/146544/182494/20210824_BB_Simulations_SKB.pdf

Positron σ*x

Positron σ*y16Highlights of rst ITF-BB workgroup meeting• Discussion on beam-beam- [Question/Comment] (D. Shatilov): In BBHTI, σx of bothbeams should blow up. But in HBCC study, we only see
blowup of LER beam. The observed instability might not
be coherent BBHTI, but just synchro-betatron resonancenear half-integer. Scan of νx should help identify this e ect.
One ring (LER) might touch the νx − kνs = N/2 and it
caused σx blowup. Of course, it can be synchro-betatronresonance driven by beam-beam.

- [Discussion] In HER, we also see small growth of σx, it is-

not trivial to exclude BBHTI. In SuperKEKB operation, νx,y,s
are di erent for both rings. Around the current working
point, there was no σx blowup for single beam (nocollision).
[Discussion] The two rings operated between resonancesof νx − νs = N/2 and νx − 2νs = N/2. The footprint of thebeam may overlap with these lines, causing blowup.

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Highlights of rst ITF-BB workgroup meeting• Discussion on beam-beam- [Question/Comment] (Y. Funakoshi): The asymmetric blowup of
σx is inconsistent with the simulated BBHTI. Blowup of LER σx
might not be due to BBHTI.

- [Discussion]: Ohnishi-san showed clear correlation of LER σx

blowup as function of HER bunch current (also see Onishi-san’s
talk in this meeting). This can be a hint of instability driven by adi erent mechanism.

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Highlights of rst ITF-BB workgroup meeting• Discussion on beam-beam- [Discussion]: Because simulated vertical beam sizes are

di erent from measurements, the agreement of simulated andmeasured luminosity was accidental.

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Highlights of rst ITF-BB workgroup meeting• Discussion on beam-beam- [Suggestion] (Y. Cai): Try to get a consistent and predictablemodel for beam-beam simulation. This task should be the rst
priority. The beam-beam simulation codes should have thepredictability power when comparing with observations ofmachine. One of the model can explain the luminosity, but it
cannot explain the vertical beam sizes. So the current beambeam model is not consistent. Try to get the model t themachine and then make predictions.

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Highlights of rst ITF-BB workgroup meeting• Discussion on beam-beam- [Question/Comment] (D. Shatilov): For the current working point,
νx is set between νx − νs = N/2 and νx − 2νs = N/2. There might

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be not enough room for the tune footprint of the beam, and thismay be the reason of observing BBHTI easily in simulations.
Moving νx to be between νx − 2νs = N/2 and νx − 3νs = N/2 (alsoneed to move up νy) might be useful: This will make the working
point be far away from νx − νs = N/2 and help mitigate the
BBHTI.
[Discussion]: In Phase-2 and early Phase-3, the machine wasoperated around (.57,.61) without crab waist. At that time,
beam-beam resonances ± νx + 4νy + α = N set constraints. Thenthe working point was moved to around (.53,.57) where
simulated luminosity is the best.
[Discussion]: With crab waist, the constraints from± νx + 4νy + α = N is removed, it is possible the operate themachine around (.57, .61). With beam-beam parameterξy < 0.04, there is room to avoid lattice resonances from theupper side.

Highlights of rst ITF-BB workgroup meeting• Discussion on beam-beam- [Question/Comment] (D. Shatilov): Now SuperKEKB operates

with di erent synchrotron tune νs. Why is it not possible to havethe same νs for the two rings?

- [Discussion]: Same νs is good to avoid BBHTI. There are two

ways to change νs: Changing RF voltage or changing
momentum compaction factor of optics. The feasibility can bechecked with experts of RF and optics.

- [Discussion]: Equalizing νx,y,s is good for avoiding BBHTI.
- [Discussion]: It is possible to change νs by changing momentum
compaction. But it will result in many side e ects (such as
rematching the arc cells and straight sections, change ofemittance, extra commissioning time, etc.).

- [Discussion]: Gains of equalizing νs should be well clari ed
before discussing its feasibility.

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Highlights of rst ITF-BB workgroup meeting• Discussion on beam-beam- [Question/Comment] (D. Shatilov): Now SuperKEKB operates-

with di erent synchrotron tune νs. Why is it not possible to havethe same νs for the two rings?
[Discussion]: To equalize the nu_s of the two rings, we can increase LER
Vc from 9.15 MV to 12.3 MV, or decrease HER Vc from 14.2 MV to 10.6
MV.

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[Discussion]: Lowering Vc of HER from 14.2 to 10.6 MV will change thebucket height from 0.0203 to 0.0166. With the nominal energy spread of
6.3e-4, the resulting bucket height is no problem for momentum
acceptance and dynamic aperture.

-[Discussion]: At a higher beam current with the lower Vc, stability of theaccelerating mode can be deteriorated due to heavy beam loading, inparticular for the case of SCC.

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[Discussion]: As a compromise, changing both Vc and momentum
compaction at the same time has advantages. One reason is thatlowering Vc without changing alpha_p increases bunch length. Anotherreason is that the demands for Vc or alpha_p would be less stringent
compared to the case of only changing either one.

-[Conclusion]: To justify the necessity of equalizing νs, detailed analysis(theory and simulations) is required. The possibility can be checked bymachine studies at low beam currents. The nal step is to discuss thetechnique challenges to RF and optics design.

Contributions from Y. Funakoshi, Y. Ohnishi, and K. Akai

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Highlights of rst ITF-BB workgroup meeting• Discussion on beam-beam- [Question] (C. Montag): Can we swap the working point of-

the two beams? This may swap the σx blowup and thencan be evidence of BBHTI.
[Discussion] In machine operation, it’s not trivial to swap
tunes. We can try changing working point in futuremachine studies.

- [Question] (Y. Cai): The observed ξy was about 0.03, what’s
the simulated value?

- [Discussion] Simulated value (both weak-strong and

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strong-strong) was 0.077 for machine parameters of2021.07.01 without coherent BBHTI.
[Question] (Y. Cai): In beam-beam simulations, what’s themap for lattice?
[Discussion] Simple matrix map was used. D.Z. tried
beam-beam simulations using SAD (lattice included), forthe current machine condition, no di erence between
simple map and using lattice.

Highlights of rst ITF-BB workgroup meeting• Discussion on beam-beam- [Question] (X. Bu at): Why are the wake elds localized but not distributed in the TMCI study since the collimators are
distributed?

- [Discussion] The collimators are located with integer of π phase advance, therefore their e ects can be simply-

summed up.
[Question] (Y. Cai): About settings of collimators, are their gaps narrow both in vertical and horizontal?
[Discussion] Vertical collimators (minimum full gap < 2 mm) have much smaller gaps than horizontal ones. This
explains only the vertical blowup (related to TMCI) is serious.
[Question]: TMCI threshold is tight on both rings?

- Only LER is tight.
- [Question]: Are there speci cations (noise level) about collision o set noise? Are there measurements about BPM

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noise or estimate on the movement of magnets.
Discussion: The beam-beam simulations consider turn-by-turn noise. It is fast noise, therefore not relevant to magnet
movement. So far there are no measurements on noise level.

Highlights of rst ITF-BB workgroup meeting• Discussion on beam-beam- [Question/Comment] (Y. Cai): Currently machine is limited by-

lifetime and background, can the beam-beam simulations
calculate beam-beam lifetime and background?
[Discussion] Beam-beam drives beam tail that hits thecollimators. This e ect should change the lifetime.
[Discussion] Belle-2 group studied the background, and did notobserve strong e ect from beam-beam. Currently the main
limits of lifetime are from Touschek and beam-gas scattering.
[Discussion] The gaps of vertical collimators are small, but still
about 40 sigma. The beam-beam driven tail does not hit thecollimators. This is mostly the current situation.

- [Question/comment] (Y. Cai): For the resonance driving terms,

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which machine is worse? LER or HER?
[Discussion] LER is always worse.

Highlights of rst ITF-BB workgroup meeting

Luminosity history panel seen in SuperKEKB control room

• Discussion on beam-beam- [Question/Comment] (T. Browder): Is there any explanation for

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beam sizes extracted from X-ray monitors. This is evidence ofgood collision condition at low bunch currents. Low bunchcurrent study was done long time ago, good agreement wasseen.
[Discussion] The luminosity was optimized around 0.4 mA2, andthen the HBCC study started. At low bunch current products,
the collision condition was not re-optimized. This could be areason to explain the di erence between simulation andmeasured luminosity. (BUT, this scenario is plausible.)

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the Lsp at low bunch current products?
[Discussion] At low bunch current products, beam-beam e ects
are weak except dynamic beta/emittance. The simulated
luminosity is close to geometric one.
[Discussion] Experimental data showed good agreement in
*2
*2
σ*
=
σ
+
σ
y
y+
y− calculated from measured luminosity and from IP

Summary• Potential sources for luminosity limit (K. Ohmi)- Optics aberrations at IP, such as chromatic coupling- Collision o set noise- Coherent beam-beam head-tail instability• Discussion on beam-beam- The observed horizontal blowup might not be due to coherent BBHTI, but just synchro-betatron resonance-near half-integer driven by beam-beam.
The agreement of simulated and measured luminosity in HBCC study was accidental.
The current beam-beam simulations cannot predict vertical emittance growth. A consistent andpredictable model for beam-beam simulation is necessary.
With crab waist applied and beam-beam parameter < 0.04, it might be better to move working point fromaround (.53,.57) to around (.57,.61).

- Equalizing νx,y,s of the electron and positron beams should be useful.
• Outlook- Collaborative studies are very welcome.
- Strong interactions with other subgroups are essential.

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Highlights of rst ITF-BB workgroup meeting• Discussion on beam-beam- [Question] (K. Oide): Are the strong-strong simulations-

consistent with D. Zhou’s simulations?
[Discussion] They should be consistent. The simulation
results with occurrence of BBHTI are sensitive to chosenparameters.
[O ine check by D.Z.] Parameters sets of 2021.05.14 and2021.07.01 used by K.O. and D.Z. are slightly di erent.
Because BBHTI is very sensitive to σz and νs, the behaviorof beam blowup was somehow di erent.

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[8] https://kds.kek.jp/event/39142/contributions/194650/attachments/146581/182524/BBSKB2021ab.pdf

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Highlights of rst ITF-BB workgroup meeting• Beam-beam e ects in SuperKEKB [8]- Analysis of mode coupling for localized wake-showed betatron tune a ects the TMCI
threshold.
TMCI threshold with localized wake is lower
than prediction of ordinary theory.
The above ndings agree with measurement.
Localized wake from collimators is so far themost convincing explanation for single-beam
blowup in LER.

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[8] https://kds.kek.jp/event/39142/contributions/194650/attachments/146581/182524/BBSKB2021ab.pdf

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