Overview of collective effects
Demin Zhou, Gaku Mitsuka, Takuya Ishibashi,
Shinji Terui, Ryuichi Ueki, Yukiyoshi Ohnishi, Kazuhito Ohmi

Acknowledgments
X. Wang, H. Sugimoto, K. Matsuoka, Y. Arimoto, K. Shibata,
T. Abe, Y. Funakoshi, M. Tobiyama, M. Masuzawa, Y. Suetsugu,
Y. Zhang, C. Lin, Z. Li, K. Oide, D. Shatilov, M. Zobov, P. Raimondi,
A. Blednykh, K. Bane, Y. Cai, M. Migliorati, P. Kicsiny, X. Bu at, F. Zimmermann,members of SuperKEKB and Belle II teams

ff

The 27th KEKB Accelerator Review Committee meeting, Mar. 26, 2024, KEK

2024 updates: Conditions for discussing collective effects in SuperKEKB• Breakthroughs in machine operation: Injection BG e ects on lum. measurement removed (thanks to Belle II team);Single-beam emittance ϵy<20 pm (Talks by Y. Ohnishi and H. Sugimoto); FB noises signi cantly suppressed (Talk by G.

Mitsuka); Impedance reduction by NLC installed in LER (Talk by S. Terui); Orbit control around CW sextupoles (Talk by Y.
Ohnishi); Both LER and HER can operate around design working point (.53, .57) (Talk by Y .Ohnishi).

L≈

NbN+N− f*2 + σ *22π σy+y−θc

2 + σ 2 tan
σz+
z−
2

e

Δ2y
− *2 *22(σy+ + σy−)1 γ±I± LL=ξy±2ere β*y±N∓β*y±2 tan2
*2
σz∓
+
σ
x∓
2

2
fi

σ*
y∓

θc

ff

re
ξyi± ≈
2πγ±

Collective instability mechanisms over the years [1]• …
• 1960 resistive wall instability• …
• 1969 head-tail instability• 1969 microwave instability• …
• 1971 beam-beam limit in colliders• 1971 potential well distortion• …
• 1980 transverse mode coupling instability• …
• 1990 coherent synchrotron radiation instability• …
• 1996 electron beam-ion instability• 1997 electron cloud instability• …
• 2013 interplay of multiple instability mechanisms

SuperKEKB (2021c)

L≈

NbN+N− f2π*2 + σ *2
σy+
y−

θc
2
2
σz+ + σz− tan 2eΔ2y− *2 *22(σy+ + σy−)Interplay (of multiple physics aspects) is the buzzword.
It essentially de nes the luminosity performance of SuperKEKB [2].

[1] A. Chao, “Lectures on accelerator physics”, World Scientific, 2020. [2] D. Zhou et al., PRAB 26, 071001 (2023).
fi

SuperKEKB (Final design)3On beam dynamics• “The beam dynamics is all contained in ψ.” (P. 196, [1])• Beam-beam and its interplay with other physics
aspects- For crab-waist colliders, beam-beam couples with othernonlinear problems.

- The key is looking at mνx + nνy + kνs = N, considering theTune diagram for SuperKEKB LER [2]
40% CWtunes as functions of many variablesduetoνx±,y±,s±(Ib±, Ib∓, Jx±,y±,z±, β*
,
β*
,
ϵ
,
.
.
.
)
x∓,y∓
±
±
x∓,y∓
x ,y

-

multiple beam physics aspects.
For coherent instabilities, one should look at coherent tunes.
For incoherent (weak-strong) e ects, one should look at
incoherent tunes.

• SuperKEKB is comprehensible

80% CW- At SuperKEKB, multiple dynamics and hardware problems-

couple with each other.
The key is to decouple (solve) the problems one by one.

Luminosity of crab-waist colliders [3]ff[1] A. Chao, “Lectures on accelerator physics”, World Scientific, 2020. [2] D. Zhou et al., PRAB 26, 071001 (2023).
[3] D. Shatilov and A. Valishev, Sec. 4.11.1 of “Handbook of Accelerator Physics and Engineering”, World Scientific, 2023.

SuperKEKB HER [2]4

CHECKLIST• MAC comments• ITF activities on collective e ects
• Potential well distortion and microwave instability• Transverse modeling coupling instability and “-1 mode instability”• Resistive wall instability• Electron cloud• IR nonlinearity• Combined e ects of beam-beam and impedances- Coherent X-Z instability- Synchrobetatron resonances- Beam-beam mode coupling• Recent beam-beam machine studies• Perspective on 1E35 luminosity

Only luminosity is of concern, impact of collective effects
on beam lifetime, injection, and detector backgroundis also important, but not covered in this talk.

ff

ff

5

MAC comments

Response:* On “IR upgrade proposal”, see M.
Masuzawa’s talk to this meeting.
* On “comprehensive simulations”:- K. Ohmi’s STCR-CUDA and Z. Li’s APEST (IHEP) are ready for strong-strong (PIC)
simulations with full lattices (KEK-IHEP
collaboration). Further efforts wished: 1)
Simpli ed SuperKEKB lattices to speed
up lattice trackings; 2) GPU parallel
computers to be managed.
- Xsuite (CERN, P. Kicsiny, X. Buffat, et al.)has been applied to SuperKEKB (beambeam + impedances, KEK-CERN
collaboration) with support of EAJADE
program. Further efforts wished: 1)
Modeling SuperKEKB lattices in Xsuite. 2)…
- Overview of collective effects (this talk).
fi

6

ITF activities on collective effects [1]• 2021-2022 (chair: M. Masuzawa)• TMCI ITF subgroup, led by T. Ishibashi and M. Migliorati-

Achievements: Detailed impedance database constructed [2], “-1 mode instability” identi ed to be an interplay of vertical
impedance e ect and BxB feedback system, accurate predictions of impedance-driven tune shifts, …

• Beam-beam ITF subgroup, led by D. Zhou and K. Ohmi-

Achievements: Comprehension of beam-beam e ects in SuperKEKB, e ective international collaborations (KEK/IHEP/CERN), …

• 2023- (chair: Y. Ohnishi [3])• Collective e ects ITF subgroup, led by G. Mitsuka, T. Ishibashi, M. Migliorati, N. Wang, D. Zhou.
-

Achievements on impedance e ects: Detailed impedance modeling w/o and w/ NLC, predictions of impedance e ects,
investigations of impedance measurements (streak camera, BPM, etc.), machine study planning, …

-Achievements on beam-beam e ects: Detailed theory/simulation investigations followed by publishing series of papers (K. Ohmi
served as a leading role), machine studies, …

• IR-Upgrade ITF subgroup, led by D. Zhou and X. Wang-

This IR-Upgrade ITF subgroup investigates IR upgrade in 2030s, not LS2 (see [4] for IR upgrade during LS2)
Achievements: Comprehension of IR complexity, challenges in IR upgrade, …

ff

fi

ff

ff

ff

ff

ff

ff

[1] https://kds.kek.jp/category/2242/. [2] https://kds.kek.jp/event/40318/. [3] Y. Ohnishi, “ITF”, Talk to this meeting. [4] M. Masuzawa, “LS2”, Talk to this meeting.

7

Potential well distortion and microwave instability• Since 2021, T. Ishibashi has been serving as “impedance manager” for SuperKEKB- Reliable impedance models (reproducing measure tune shifts very well, though plausible discrepancy inpredicting measured bunch lengthening) have been constructed and applied to simulations• Impedance modeling: SuperKEKB LER as an example- Geometric wakes by Gd dL, CST, and ECHO3D [1]; RW by IW2D [1]; CSR/CWR by CSRZ

fi[1] T. Ishibashi et al. 2024 JINST 19 P02013.

286 GHz8

Potential well distortion and microwave instability• To bridge the gap between computations

and beam-based measurements- Theories of potential-well bunch lengthening and-phase shift revisited [1]Continuous e orts on searching for overlooked
impedance sources [2]Continuous e orts on examining systematic errors
in streak camera measurements [3]• In general, the computation-experimentgap became signi cantly smaller

Measured phase shi(BPM-based) be er agrees
with simulated peak shi ,not centroid shi [1]

fi

ft

ft

ff

ff

tt

ft

[1] D. Zhou et al., NIM-A 1063 (2024) 169243. [2] T. Ishibashi et al 2024 JINST 19 P02013. [3] G. Mitsuka, https://kds.kek.jp/event/46959/.

T. Ishibashi [2] and G. Mitsuka [3] 9Potential well distortion and microwave instability

h = 45 mm, ρ = 74.7 m• SuperKEKB LER

σz0 = 4.6 mm- VFP simulations: Di erent combinations of impedance sources show-that CSR-driven MWI threshold is around 1.2 mA (< design value of
1.44 mA)
Consistent with prediction of CSR instability theory [1,2]: CSR thresholdis independent of bending radius of dipoles
CSR instability is not veri ed by experiments yet

2 1/3
24π(E/e)ησδ σzEησδ σzIth(CSR) =
S
∝
th
1/3
Z0 ρ
h

2/3

Sth ≈ 0.384ΠΠ ≡ σz ρ/h3σδ0 = 7.53 × 10−4

Chamber geometries [3]Instability analysis
fi

ff

ti

[1] Y. Cai, IPAC2011, FRXAA01. [2] A. Blednykh, D. Zhou et al., PRAB 26, 051002 (2023). [3] T. Ishibashi et al. 2024 JINST 19 P02013.

VFP simula ons
10

Transverse modeling coupling instability and “-1 mode instability”• TMCI in LER [1]- Tune shift and TMCI simulated by PyHEADTAIL (T. Ishibashi and M. Migliorati)- With machine con gurations of β*y =1 mm: Simulations using impedance models well reproduced the measured
tune shifts. Simulated TMCI threshold is 1.8 mA.

fi[1] T. Ishibashi et al. 2024 JINST 19 P02013.

11

Transverse modeling coupling instability and “-1 mode instability”• TMCI in HER [1]- Tune shift and TMCI simulated by PyHEADTAIL (T. Ishibashi and M. Migliorati)- With machine con gurations of β*y =1 mm: Simulations using impedance models well reproduced the measured
tune shifts. Simulated TMCI threshold is 3.5 mA.

fi[1] T. Ishibashi et al. 2024 JINST 19 P02013.

12

Transverse modeling coupling instability and “-1 mode instability”• “-1 mode instability” in LER [1,2,3,4]-

Observed instability threshold is signi cantly lower than TMCI threshold. Both vertical impedance e ects (tune shift in 0 mode, dνy /dI~-0.01/mA)and bunch-by-bunch (BxB) feedback (FB) (excitation of -1 mode) play important roles in this phenomenon.

-

Simulations using PyHEADTAIL consider resistive damper and show ITSR (Imaginary Tune Split and Repulsion) instability [5]. Simulations by K. Ohmi
consider multi-tap scheme of BxB FB and show that BxB FB can reactively drive -1 mode [2]. However, FB gain much higher than operation setting isrequired to reproduce the observed instability [2].

-Countermeasure: Noise suppression and ne tuning of FB system (see [6] for details). Another countermeasure (proposal): The “easiest” way toescape from this instability is increasing νs of LER.

2024 [4]2022 [3]Courtesy of S. Terui

Need to con rm if BxB FB s ll excites -1 mode
ff

fi

fi

ti

fi

[1] T. Ishibashi et al. 2024 JINST 19 P02013. [2] K. Ohmi et al., eeFACT2022, WEXAT0102. [3] S. Terui, “Collimator challenges at SuperKEKB and their countermeasures using nonlinear
collimator”, submitted to PRAB. [4] S. Terui, Talk to this meeting. [5] E. Metral and M. Migliorati, Phys. Rev. Accel. Beams 23 (2020) 071001. [6] G. Mitsuka, talk to this meeting13

Resistive wall instability• Transverse coupled-bunch instability driven by low-frequency resistive wall impedance [1,2]- For SuperKEKB LER, by theory (counting RW impedances of normal chambers, IR chamber and collimators) thegrowth time is τyTheory=1.0 ms at Ibeam=600 mA; by experiment, it is τyExp=3.8 ms.

- For SuperKEKB HER, by theory (counting RW impedances of normal chambers, IR chamber and collimators) the
TheoryExp
growth time is τy=0.5 ms at Ibeam=600 mA; by experiment, it is τy =1.6 ms.

[1] D. Zhou et al., IPAC’23, WEPL187. [2] D. Zhou, Talk to mini-impedance workshop at KEK, 2022.

14

Electron cloud• Electron cloud in SuperKEKB LER [1]- “No signi cant electron cloud e ect has been observed in the LER after installing solenoids in drift spaces in2017 which apply magnetic elds in the beam direction.”

ff

fi

fi

[1] Y. Suetsugu et al., “SuperKEKB vacuum system operation in the last 6 years operation”, PRAB 26, 013201 (2023).

15

IR nonlinearity: converged understandings• Complicated interaction region (IR) [1][1] K. Shibata, “Overview of SuperKEKB IR”.

16

IR nonlinearity: converged understandings• Complicated interaction region (IR) [1]- Large crossing angle (required by collision scheme) and limited spaces for hardwares increase the complexity of
optics.

[1] Y. Arimoto, “Current QCS magnet system”.

Overlap of solenoids and FF quads

17

IR nonlinearity: converged understandings• Complicated interaction region (IR): Side e ects from beam physics viewpoint- Extremely small β*
y → Nonlinear e ects from kinematic term of IP drift and fringe elds of nal focus (FF)quadrupoles [1] → Fundamental limit on dynamic aperture and lifetime [1,2,3] → Poor injection e ciency [4] andhigh detector background [5].

- Overlap of solenoid and FF quadrupoles, o sets of FF quadrupoles, etc. → Vertical emittance growth (single-beam)
due to local linear and chromatic couplings [6] → Vertical emittance growth (two-beam) from interplay of beam-beamand lattice nonlinearity [7,8] → Imperfect crab waist due to nontransparent IR [2].

[1] K. Oide and H. Koiso, Phys. Rev. E 47, 2010 (1993). [2] SuperKEKB TDR. [3] Y. Suetsugu, et al., PRAB 26, 013201 (2023). [5] A. Natochii, et al., “Beam background expectations for Belle II at SuperKEKB”.

ffi

fi

fi

ff

ff

ff

[6] M. Masuzawa, IPAC’22. [7] D. Zhou et al., “Beam Dynamics Issues in the SuperKEKB”. [8] K. Hirosawa et al., J. Phys.: Conf. Ser. 1067 062004 (2018).

18

IR nonlinearity: converged understandings• Implementation of crab waist at SuperKEKB- Crab waist [1] was optional in SuperKEKB nal design, because it signi cantly reduces dynamic aperture and lifetime-(from optics design with a realistic IR) [2].
Beam commissioning experienced severe emittance blowup and poor luminosity, forcing implementation of crab
waist (Oide’s scheme [3]).
Crab waist is e cient in suppressing beam-beam blowup (at high bunch currents), but cause signi cant loss ofdynamic aperture and lifetime at SuperKEKB with β*y =1 mm [4]. Careful machine tunings might be necessary to
improve the e ciency of CW (this talk).
No crab waist

80% crab waist

fi

fi

fi

ffi

ffi

[1] M. Zobov et al., Phys. Rev. Lett. 104, 174801 (2010). [2] SuperKEKB TDR. [3] K. Oide et al., Phys. Rev. Accel. Beams 19, 111005 (2016). [4] Y. Ohnishi, “Dynamic Aperture for Crab Waist in LER”.

19

IR nonlinearity: converged understandings• High detector background- The short lifetime and poor injection e ciency cause high background to Belle II [1,2], requiring tight con gurations of-collimation system [3].
Small-gap collimators contribute large impedance (especially after head damages) and caused vertical emittance
blowup (“noise” in bunch-by-bunch feedback, interplay with beam-beam, etc.) [4].

[1] A. Natochii, et al., “Beam background expectations for Belle II at SuperKEKB”. [2] A. Natochii et al., PRAB 24, 081001 (2021).

20
fi

ffi

[3] T. Ishibashi et al., PRAB 23, 053501 (2020). [4] T. Ishibashi et al. 2024 JINST 19 P02013.

Beam-beam related topics in crab-waist colliders• Mechanisms of pure beam-beam e ects

‣ Horizontal: (coherent two-beam) X-Z instability [Ohmi 2017 (PRL), Kuroo 2018 (PRAB)] and (single-beam)‣

synchrobetatron resonances [Zhou 2023 (PRAB)]
Vertical: Nonlinear X-Y resonances [Ohmi 2004 (PRST-AB), Ohmi 2007 (PRST-AB), Zobov 2010 (PRL)]• Mechanisms of interplay between beam-beam and impedances‣ Horizontal: modi ed X-Z instability [Lin 2022 (PRAB), Zhang 2020 (PRAB), Migliorati 2021 (EPJP)] (key issue: potential‣

distortion and synchrotron tune spread due to impedance)
Vertical: TMCI-like head-tail instability [White 2024 (PRAB), Zhang 2023 (PRAB), Zhou 2023 (PRAB), Ohmi 2023
(PRAB)] (key issues: spread of synchrotron and vertical betatron tunes due to impedance)• Mechanism of interplay between beam-beam and other problems (Zhou 2023 (PRAB))‣ BxB feedback: “-1 mode instability” [Ohmi 2022 (eeFACT), Ishibashi 2023 (JINST)]‣ Linear IP X-Y couplings [Ohmi 2018 (eeFACT)]‣ Chromatic IP X-Y couplings [Zhou 2009 (PRST-AB)]‣ Nonlinear IP X-Y couplings [Zhou 2015 (ICFA BDN)]‣ Non-perfect crab waist [To be investigated]

The recent papers of K. Ohmi, Y. Zhang et al. showcase full collaborations.
More papers triggered by collaborations on SuperKEKB are expected.
ff

fi

21

Combined effects of beam-beam and impedances• Simulated νx-dependent horizontal instability in SuperKEKB-

Strong coherent X-Z instability around resonance νx − kνs(Jz) = N/2 and weak blowup due to synchrobetatron (SB) resonances [1]-Mitigation: Squeezing β*
x [2][1] D. Zhou et al., PRAB 26, 071001 (2023). [2] K. Ohmi et al., PRL 119, 134801.

Electron σ*xElectron σ*yPositron σ*x

Positron σ*y22Combined effects of beam-beam and impedances• Simulated νx-dependent horizontal instability in SuperKEKB- Beam-beam driven SB resonances have been investigated since 1970s.
- Investigations are ongoing to study the SB resonances in the presence of impedance e ects [1, 2].

[1] D. Zhou et al., PRAB 26, 071001 (2023). [2] P. Kicsiny et al., paper under preparation.
ff

23

Combined effects of beam-beam and impedances• Simulated vertical TMCI-like instability in SuperKEKB- First found by K. Ohmi in simulations, followed by detailed investigations [1,2,3].
- Beam-beam mode coupling theory reproduces the results of the beam-beam simulation [3].

[1] D. Zhou et al., PRAB 26, 071001 (2023). [2] Y. Zhang et al., PRAB 26, 064401 (2023); [3] K. Ohmi et al., PRAB 26, 111001 (2023);

24

Recent beam-beam machine studies
Crab waist is a MUST

• HBCC studies compared- w/ CW, 2024.03.22- w/ CW, 2024.03.21- w/o CW, 2024.03.12- w/ CW, 2022.04.05
Better geometric luminosity in 2024a
Specific Lum. [1031cm-2s-1/mA2]

12

ECL, Physics run (May. 16-17, 2022)
ECL, HBCC experiment (Apr. 05, 2022)
ECL, HBCC experiment (Mar. 12, 2024) w/o CW
LER νy scan, ECL, HBCC experiment (Mar. 12, 2024) w/o CW
ECL, HBCC experiment (Mar. 21, 2024) w/ CW
ECL, HBCC experiment (Mar. 22, 2024) w/ CW
BBSS simulation w/ ZL w/ CW (HER:40%, LER:80%)

11
10
9
8
7

Interplay of multiple dynamics

6
5
4
3
2

0

0.2

0.4

[νy+]=.575, LER injection OK
0.6

0.8
+
2
Ibunch(e )×Ibunch(e ) [mA ]11.2[νy+]=.567, LER injection trouble[νy+]=.59, LER injection impossible at hight bunch currents

25

Recent beam-beam machine studies
Crab waist is a MUST

• HBCC studies compared- w/ CW, 2024.03.22- w/ CW, 2024.03.21- w/o CW, 2024.03.12- w/ CW, 2022.04.05

30

26

11
10
9

0.45

20
18

0.4
0.35
0.3

16

0.25

14

0.2

12

0.15
0

0.2

0.4

0.6

0.8
+
Ibunch(e )×Ibunch(e ) [mA2]

1

e-

0.5

22

10

ECL, Physics run (May. 16-17, 2022)
ECL, HBCC experiment (Apr. 05, 2022)
ECL, HBCC experiment (Mar. 12, 2024) w/o CW
LER νy scan, ECL, HBCC experiment (Mar. 12, 2024) w/o CW
ECL, HBCC experiment (Mar. 21, 2024) w/ CW
ECL, HBCC experiment (Mar. 22, 2024) w/ CW
BBSS simulation w/ ZL w/ CW (HER:40%, LER:80%)

0.55

σy [µm]σx [µm]24

ECL, Physics run (May. 16-17, 2022)
ECL, HBCC experiment (Apr. 05, 2022)
ECL, HBCC experiment (Mar. 12, 2024) w/o CW
LER νy scan, ECL, HBCC experiment (Mar. 12, 2024) w/o CW
ECL, HBCC experiment (Mar. 21, 2024) w/ CW
ECL, HBCC experiment (Mar. 22, 2024) w/ CW
BBSS simulation w/ ZL w/ CW (HER:40%, LER:80%)

0.1

1.2

0

0.2

0.4

0.8
Ibunch(e )×Ibunch(e ) [mA2]
+

0.6

-

1

1.2

Horizontal blowup will be the next BIG problem

8
40

7

Interplay of multiple dynamics

3
0

0.2

0.4

[νy+]=.575, LER injection OK
0.6

0.8
+
2
Ibunch(e )×Ibunch(e ) [mA ]

1

20

0.5
0.4
0.3

15

0.2

1.2

[νy+]=.567, LER injection trouble

e+

0.6

25

10

ECL, Physics run (May. 16-17, 2022)
ECL, HBCC experiment (Apr. 05, 2022)
ECL, HBCC experiment (Mar. 12, 2024) w/o CW
LER νy scan, ECL, HBCC experiment (Mar. 12, 2024) w/o CW
ECL, HBCC experiment (Mar. 21, 2024) w/ CW
ECL, HBCC experiment (Mar. 22, 2024) w/ CW
BBSS simulation w/ ZL w/ CW (HER:40%, LER:80%)

0.7

σy [µm]σx [µm]

4

2

e+

30

5

0.8

ECL, Physics run (May. 16-17, 2022)
ECL, HBCC experiment (Apr. 05, 2022)
ECL, HBCC experiment (Mar. 12, 2024) w/o CW
LER νy scan, ECL, HBCC experiment (Mar. 12, 2024) w/o CW
ECL, HBCC experiment (Mar. 21, 2024) w/ CW
ECL, HBCC experiment (Mar. 22, 2024) w/ CW
BBSS simulation w/ ZL w/ CW (HER:40%, LER:80%)

35

6

0

0.2

0.4

0.8
+
Ibunch(e )×Ibunch(e ) [mA2][νy+]=.59, LER injection impossible at hight bunch currentsfi

Specific Lum. [1031cm-2s-1/mA2]

12

e-

28

Better geometric luminosity in 2024a

0.6

ECL, Physics run (May. 16-17, 2022)
ECL, HBCC experiment (Apr. 05, 2022)
ECL, HBCC experiment (Mar. 12, 2024) w/o CW
LER νy scan, ECL, HBCC experiment (Mar. 12, 2024) w/o CW
ECL, HBCC experiment (Mar. 21, 2024) w/ CW
ECL, HBCC experiment (Mar. 22, 2024) w/ CW
BBSS simulation w/ ZL w/ CW (HER:40%, LER:80%)

0.6

1

1.2

0.1

0

0.2

0.4

0.8
Ibunch(e )×Ibunch(e ) [mA2]
+

0.6

-

1

1.2

Vertical blowup is complicatedMultiple factors to be identi ed
HER emittance knobs used to achieve balanced collision 26

Recent beam-beam machine studies• LER vertical tune scan compared- β*y =1 mm, w/o CW, 2024.03.12- β*
y =1 mm, w/ CW, 2024.03.22

10
9

240

σy-, Tune scan experiment (Mar. 12, 2024) w/o CW
σy+, Tune scan experiment (Mar. 12, 2024) w/o CW
σy-, Tune scan experiment (Mar. 22, 2024) w/ CW
σy+, Tune scan experiment (Mar. 22, 2024) w/ CW

200160
εy [pm]8
εx [nm]σy-, Tune scan experiment (Mar. 12, 2024) w/o CW
σy+, Tune scan experiment (Mar. 12, 2024) w/o CW
σy-, Tune scan experiment (Mar. 22, 2024) w/ CW
σy+, Tune scan experiment (Mar. 22, 2024) w/ CW

7

120

6

80

5

40

4
0.55

0
0.55

0.56
0.57
0.58
0.59
0.6
Fractional νy+ (Measurement, pilot bunch)

0.61

0.56
0.57
0.58
0.59
0.6
Fractional νy+ (Measurement, pilot bunch)

Escaping from resonance νx + 4(νy + ξy) = N

0.61

27

Recent beam-beam machine studies• LER horizontal tune scan compared- β*y =8 mm, w/o CW, 2024.02.26- β*
y =1 mm, w/o CW, 2024.03.12- β*
y =1 mm, w/ CW, 2024.03.22

14
13
12

νx − 1.5 | νs | = N/2

360

σx+, Single-beam experiment (Mar. 12, 2024) w/o CW
σx+, Collision experiment (Mar. 22, 2024) w/ CW
σx+, Single-beam experiment (Feb. 26, 2024) w/o CW
σx+, Collision experiment (Feb. 26, 2024) w/o CW

320
280
240

10
9
8
7

εy+ [pm]εx+ [pm]11

νx − 2 | νs | = N/2

νx − νy + 2 | νs | = N

160
120
80

5

40

4
0.52

0
0.52

0.56

νx − νy + 2 | νs | = N
νx − 2 | νs | = N/2

νx − 1.5 | νs | = N/2

200

6

0.53
0.54
0.55
Fractional νx+ (Measurement, pilot bunch)

σy+, Single-beam experiment (Mar. 12, 2024) w/o CW
σy+, Collision experiment (Mar. 22, 2024) w/ CW
σy+-60, Single-beam experiment (Feb. 26, 2024) w/o CW
σy+-60, Collision experiment (Feb. 26, 2024) w/o CW

0.53
0.54
0.55
Fractional νx+ (Measurement, pilot bunch)

0.56
28

• 1E35 luminosity is achievable, if crab waist works well. Factors a ecting luminosity:-(2) Beam-beam-driven fth-order betatron resonances νx ± 4(νy + ξy) = N → Cured by crab waist(3) Vertical TMCI-like instability driven by the interplay of beam-beam and vertical impedance [1,2](4) Dynamic beta and dynamic emittance caused by linear transverse beam-beam force (β*y ↘ , ϵy ↗ )(5) Crab waist (CW) suppresses the fth-order beam-beam resonances(1)&(4)post-LS1 1E35
HER
LER

Ib+ = 0.89 mA
Ib− = 0.63 mA

Ibunch (mA)# bunchεx (nm)(1)&(3)&(4)(2)&(5)

Comments

0.89

σz0 (mm)

4.6
30
60
0.8
5.1

4.0
30
60
0.8
4.6

νx

45.53244.5242022a operation value

νy43.57446.5892022a operation valueνs0.02720.0222

Calculated from latticex,y (ms)

58.0

53.1

Transverse damping time (w/ NLC)

z (ms)

29.0

26.6

Longitudinal damping time

Crab waist

80%

80%

Lattice design

εy (pm)(2)&(5)

0.63

Achieved in 2024a run:* ϵy <20 pm* [νy+] =0.57

2022a operation value
w/o IBS
Single-beam emittance
Lattice design value
Lattice design value
Natural bunch length (w/o MWI)

βx (mm)βy (mm)2345[1] Y. Zhang et al., PRAB 26, 064401 (2023); K. Ohmi et al., PRAB 26, 111001 (2023).
ff-(1) Bunch lengthening and synchrotron tune spread caused by longitudinal impedance → Unavoidable

fi

-

fi

𝛕

𝛕

Perspective on 1E35 luminosity29SuperKEKB as a demonstrator of crab-waist colliders:* After years of investigation, SuperKEKB has become comprehensible from the perspective of collective effects.
* Collaborations within the collider community have accelerated the learning curve of understanding collective effects.

2019
2022
2024?
1.23x1034 4.71x1034 1x1035

2019
2022
1.23x1034 4.71x1034

e
rv
cu
ng
ni
ar
Le
≈
y
or
st
hi
ity
os
in
m
Lu
Op cs correc ons
Linear IP aberra ons
X-Z instability

BB resonances

Crab waist
Chroma c coupling“-1 mode instability”
Collimator impedances

FB noise

SBLs
FB noise
Collimator damages Collision tunings
SB resonances
BB mode coupling

ti

ti

ti

ti

https://www-superkekb.kek.jp/

NLC
CW tuning
SBLs

30

WISHLIST• Send young accelerator physicists (domestic and international) to SuperKEKB• EAJADE project is excellent• Manage GPU computers for strong-strong (PIC) simulations with full lattices• A model including everything has been a dream 30 years ago, but feasible now• Beam time for machine studies• Experiments tell more than theories and simulations (?)• Plan nonlinear optics tunings/optimizations (see H. Sugimoto’s talk to this meeting)• The crab waist concept: brilliant, yet challenging (see crab cavity experience in KEKB)• AI/ML techniques have become trendy• Plan NLC studies (See S. Terui’s talk to this meeting)
Y. Ohnishi, EPJP 136:1023 (2021)• Less BG and impedances• Think of global parameter optimizations, such as increasing νs of LER• Big ideas are written in the Handbook, though requires lots of R&D work
• ……
31

WISHLIST

2013

2023

Many exci ng updates relevant
to crab-waist colliders!

To Frank: Send a few copies toSuperKEKB control room?

ti

32

Backup33

Status and activities of ITF-BB sub-group and ITF-IR sub-group[1] https://kds.kek.jp/event/45407/.

• Beam-beam sub-group[2] https://kds.kek.jp/event/46663/- Re-organized under the collective e ects sub-group.
- Two ITF-BB meetings organized: Feb. 7, 2023 [1]; Jul. 1, 2023 [2].
- More activities under private collaboration mode (to be reviewed in this talk).
- Presentations••••[3] https://kds.kek.jp/event/45534/.
[4] https://kds.kek.jp/event/45877/.
[5] https://kds.kek.jp/event/46026/.

K. Ohmi, “SCTR-CUDA” [1].
D. Shatilov, “Computation of Complex Error Function, comparison of accuracy and speed” [1].

[6] https://kds.kek.jp/event/46234/.

K. Ohmi, “Beam-beam mode coupling” [2].

[7] https://kds.kek.jp/event/46574/.

D. Zhou, “Beam-beam simulations for post-LS1 target luminosity 1E35” [2].

• IR upgrade sub-group- Focus on investigations of “Much Larger scale modi cation” of SuperKEKB IR in 2030s [3].
- Should not be confused with the existing IR upgrade team (investigating “Moderate scale modi cation around 2027” and “Larger scale modi cation” [3]).
- Five ITF-IR meetings organized: Feb. 17, 2023 [3]; Mar. 7, 2023 [4]; Mar. 28, 2023 [5]; Apr. 18, 2023 [6]; May. 23, 2023 [7].
- Presentations
Y. Ohnishi, “Opening remark” [3].
K. Shibata, “Overview of SuperKEKB IR” [3].
D. Zhou, “Discussions on tasks/goals of ITF-IR subgroup in 2023” [3].
M. Koratzinos, “A proposal for the upgrade of the nal focus system of SuperKEKb” [4].
P. Raimondi, “Final Focus beam dynamics studies” [4].
Y. Arimoto, “Current QCS magnet system” [5].
D. Zhou, “Constraints on investigations of SuperKEKB IR-Upgrade under the ITF-IR framework” [5].
A. Natochii, “Beam-induced background status and expectation in Belle II” [6].
Y. Ohnishi, “Dynamic Aperture for Crab Waist in LER” [6].

Mainly understanding thechallenges in IR.
So far, no activities of IR
optics design for upgrade.

F. Forti, “Comments on detector constraints on IR design” [7].
D. Zhou, “Tentative parameter table for post-LS2 SuperKEKB and strategy for ITF-IR workgroup” [7].

fi

fi

fi

fi

34
ff

•
•
•
•
•
•
•
•
•
•
•

Crab waist applied to SuperKEKB• SuperKEKB nal design (β*y = 0.3/0.27 mm) with ideal crab waist• Tune scans using BBWS
• Crab waist creates large area in tune space for choice of working pointfi

35Crab waist applied to SuperKEKB

Lum. w/o crab waist in LER• SuperKEKB 2021b run (β*y = 1 mm) with ideal crab waist- Tune scan using BBWS showed that 80% crab waist ratio in LER ise ective in suppressing vertical blowup caused by beam-beamresonances (mainly νx ± 4νy + α = N).

2021.07.01
HER
LER
Ibunch (mA)

0.80

1.0
1174

# bunchComments

Assumed value

εx (nm)4.6

4.0

w/ IBSεy (pm)23

23

Estimated from XRM dataβx (mm)60

80

Calculated from latticeβy (mm)1

1

Calculated from lattice

σz0 (mm)

5.05

4.84

Natural bunch length (w/o MWI)νx45.53244.525

Measured tune of pilot bunch

νy43.58246.593

Measured tune of pilot bunchνs0.02720.0221

Calculated from lattice

Crab waist

40%

80%

Lattice design

Lum. w/ 80% crab waist in LER

ff36

Crab waist applied to SuperKEKB

Lum. w/o crab waist in HER• SuperKEKB 2021b run (β*y = 1 mm) with ideal crab waist- Tune scan using BBWS showed that 40% crab waist ratio (current
operation condition) in HER is not enough for suppressing vertical
blowup caused by beam-beam resonances (mainly
νx ± 4νy + α = N).

Lum. w/ 80% crab waist in HER
Lum. w/ 40% crab waist in HER

37

Beam-beam viewpoints on achieving higher luminosity

=
β*
=
β*
ϵ
=
ϵ
=
ϵ
,
and
the
hourglass
e
ect
is
not
• Assume balanced collision: β*
y−
y
y+
y−
y
y+
strong, we can look into the formula of beam-beam parameter and discuss the challenges• Note that we have to respect the constraints of real machines.

ξy ≤ 0.1

i
ξy± ≈

fi

Crossing angle:
1) IR layout (constraints fromoptics design)
2) Reducing θc does not createa gain of luminosity if there thebeam-beam limit exists.

To keep ξy ≤ 0.1, higher
currents requires smaller β*
y

re

Ib∓

θc σ
2πef0γ± tan 2 z∓

If we must accept ξy ≤ 0.1, thensmaller β*y is always preferred

β*
y
ϵy

Impedance effects
Longer σz0 can be bene cial

We achieved ϵy0 < 20 pm
ξy ≤ 0.1 sets a lower limit on theachievable ϵy (at a given β*y ).
It is not feasible to achieve ϵy ≈ 10 pm
at β*
y = 1 mm38
ff

Beam-beam limit requires:

Beam-beam viewpoints on achieving higher luminosity• Speci c luminosity only depends on the geometric parameters (beam sizes and crossing angle).

We achieved ~11 × 10

31

−2
−2
−1
cm s mA with β*y = 1 mm
31
−2
−2 −1

The baseline design is ~21 × 10

cm

Lsp ≈

s

mA

1
*2 + σ *2
2πe 2f σy+y−

The fundamental limit lies in vertical beam sizes
Challenges: High currents, beam-beam, crab waist, latticeimperfections, …

θc

2 + σ 2 tan
σz+
z−
2

Impedance effects
modify the synchrotron motion,
indirectly playing a role in many issuesfi39