1. Electron cloud and ion effects in SuperKEKB and FCCee
K. Ohmi (KEK)
Beam dynamics meets Vacuum
Mar 8-10, 2017, Karlsruhe
Thanks to H. Fukuma, Y. Funakoshi, Y. Suetsugu, M. Tobiyama

2. Contents SuperKEKB FCCee Beam size blow-up due to Electron cloud
Coupled bunch instability due to electron cloud
Tune shift along bunch train in LER
Coupled bunch instability in HER
Tune shift along bunch train in HER
FCCee
Electron cloud
Ion

3. Instability simulation at SuperKEKB design stage
Using code PEHTS
re=4.2x1011 at 4000-th turn
Simulation, reth=3.8x1011 m-3.
Design target for vacuum system: re<1011 m-3 in average of whole ring

4. Beam size blow-up in LER
Beam-size blowup observed in KEKB has been seen in early stage of SuperKEKB commissioning
Threshold I~300mA in Apr 19 (Y. Funakoshi)
Electron cloud has been monitored at AL chamber w and w/o TiN coating (Y. Suetsugu).
Beast study threshold I~600mA, Nbunch=1576 in May 17 (Nakayama et al)
Aluminum bellows, which were not coated by TiN, were suspected as an electron source.
Permanent magnets were installed at the aluminum bellows.(Y. Suetsugu et al.)
The blow up was suppressed. Systematic studies in 8 July ( H. Fukuma et al.) sy
Before perm. mag installation
June 1, 2016
4 train x150 bunches, Nbunch=600
Threshold beam current
160, 200, 260,500 mA for 2, 3, 4, 6 bucket spacing
H. Fukuma et al.,

5. Simulation studies using beam study condition
Threshold of the electron density
ex=2nm, ey=15pm, sz =6mm, ns=0.019
Np=1.6x1010 Ith=160mA, 4ns spacing
Np=2.7x1010
Ith=260mA, 8ns spacing
Np=3.65x1010,
Ith=350mA, 6ns
Np=6.25x1010,
I=600mA, 8ns
Np=2.1x1010
Ith=200mA, 6ns spacing
Np=5.2x1010
Ith=500mA, 8ns spacing

6. Simulated threshold electron density (before/after permanent magnet installation)
Nb=600, ex=2nm, ey=15pm, sz =6mm, ns=0.019
Np,th
(1010)
we/2p
(GHz)
wesz/c
reth (Q=10)
(1011m-3)
reth (Q=6)
reth (Simu)
spacing
Ip,th (mA)
1.6 61
7.7
1.91
2.45
3.2
2 (4ns)
160
2.1 71
8.9
1.65
3.4
3 (6ns)
200
2.7 80
10.1
1.47
3.6
4 (8ns)
260
5.2
111
14.0
4.0
6 (12ns)
500
3.65 91
11.5
3.8
350
6.25
122
15.3
4.2
>600 6

7. Electron cloud measurement
Retarding bias, V=500V or 0V, select electrons with E>500eV or all, respectively.
Electron E=500eV, v=1.3x107m/s. R/v=3.8ns, R=5cm, density can be estimated considering volume with energy gain 500eV from a bunch. 500eV may be critical for 2 (4ns) spacing.
For V=0V, electron rate production including secondary is detected.

9. Measured electron current
Y. Suetsugu
8x10-7
　　Vr = -500 V
　　Vr = -500 V
1x10-8
Al部分
Al wo coating
Al w TiN coating
4x10-8
　　Vr = 0 V
1x10-6
　　Vr = 0 V
Al wo coating
Al w TiN coating
For V=0V, 1mA, electron production rate is 0.3x109 m-1/bunch

10. Electron density at the blow-up threshold
Simulated electron density at the threshold current
Measured threshold current and density
Only Al part r
Simple formula Q=6

11. Installation of permanent magnets produce solenoid like field
Before 2016/6/1 sy n
After : 2016/6/8
Beam size blow-up is suppressed, but remains especially in narrow bunch spacing
4/150/2
4/150/3 sy
4/150/4 r
Pressure rise is also suppressed, but still remains.

12. After installation of permanent solenoid at Al bellows
Simulated electron density at the threshold current sy
After : 2016/6/8
Ith=330 mA
Ith=200 mA
4/150/2
4/150/3
4/150/4 r
Ith>600 mA
Ith/600bunches
160mA to 200mA by 2 bucket
200mA to 330mA by 3
260mA to >600mA by 4
SuperKEKB nbunch=
Simple formula Q=6

13. Electron cloud build up simulation
Electron distribution
Electric potential electron cloud build up
10cm
Detail studies can be done-> Terui

14. Simulated electron cloud build up in Drift
Np=2.5x1010, I=240 mA for Nb=150x4=600
Np=4x1010, I=380 mA for Nb=600
1011m-3
1011m-3
re(r=0)~lex1000
Np=9.4x1010, I=900 mA for Nb=600
Beam current: Slightly higher than measured threshold
1011m-3
Ith=330 mA
2016/6/8
4/150/3
Ith=200 mA
4/150/4
4/150/2
Ith>600 mA
Y1=Photon numberx0.1x0.01

15. Coupled bunch instability caused by electron cloud
Electron cloud motion reflects coupled bunch instability mode.
Electrons in drift, short range wake ~10ns
Electrons in solenoid, slow rotation around chamber surface.
KEKB
400 f0
1000 f0

16. Electron distribution and Wake field
drift space Weak Solenoid
positive
negative
Slow freq. corresponds to electron rotation along chamber.
Higher Q~>10
Electrons oscillate 1 or 2 period, low Q=1

17. Unstable mode (before solenoid installation)
M. Tobiyama
Typical signal of coupled bunch instability caused by drift electrons
1000 f0
400 f0
Fast, strong
400 f0

18. Mode spectrum (after solenoid installation)
positive modes for W(z~0)<0
negative modes W(z~0)>0
By 2 ver 300mA 400mA By 4 ver 350mA 600mA
Solenoid origin
Drift origin
Electrons in drift space dominate for narrow bunch spacing and high current
Solenoid origin
Solenoid origin

19. Unstable mode (after solenoid installation)
Typical mode caused by electrons in solenoid is seen.
Mode seems to change to those of drift origin at high current.
Solenoid modes
400 f0
540 f0
700 f0
Fast, strong

20. Tune shift measurement along bunch train
Tune shift along bunch train in LER （Ohmi,Tobiyama,Fukuma）
∆ 𝜈 𝑥 =∆ 𝜈 𝑦
Δ𝜈 𝑦 = 𝜌 𝑒 𝑟 𝑒 𝛽 𝑦 2𝛾 𝐶
Δ𝜈 𝑦 =0.005 より
𝜌 𝑒 =8× m-3
∆ 𝜈 𝑥 =0
∆ 𝜈 𝑦 = 𝜌 𝑒 𝑟 𝑒 𝛽 𝑦 𝛾 𝐶
𝜌 𝑒 =4× 𝑚 −3
∆ 𝜈 𝑦 =0.005
Agree with density measurement

21. Ion effects in SuperKEKB

22. Coupled bunch instability in electron ring (HER)
M. Tobiyama
Ion?
Fast, strong
𝑀𝑜𝑑𝑒=5120− 𝜔 𝑖,𝑥𝑦 𝜔 0
Resistive wall
5120-1=5119 CO
fi/f0(measure)=30(x)-60(y)
fi/f0=220(y)

23. Ion production Produced ion for a bunch(population：Ne) pass through 1m
dm: molecular density, sm: ion cross-section
𝑛 𝑖 =𝑑 𝑚 𝜎 𝑚 𝑁 𝑒
𝑑 𝑚 ( m −3 )=2.42× 𝑃 𝑚 (Pa)
𝜎 𝐶𝑂 7𝐺𝑒𝑉 =190× 10 −24 𝑚 2
𝜎 𝐻2 7𝐺𝑒𝑉 =32× 10 −24 𝑚 2
𝑛 𝐶𝑂 ( 𝑚 −1 )=0.045 𝑁 𝑒 𝑃 𝑚 (Pa)
𝑛 𝐻2 ( 𝑚 −1 )= 𝑁 𝑒 𝑃 𝑚 (Pa)
For 𝑁 𝑒 =6.3× mA bunch 𝑃 𝑚 = 10 −7 Pa
𝑛 𝐶𝑂 =283 m-1
𝑛 𝐻2 =48.5 m-1
𝑁 𝑒 =2× 10 10
𝑛 𝐶𝑂 =90 m-1

24. Tune shift measurement along bunch train in HER Ohmi,Tobiyama,Fukuma
Dnx>Dny
pilot bunch 23 bucket after the train end
𝑁 𝑒 =2× 10 10
What we know from these facts.
𝛽 𝑥,𝑦 =12m
∆ 𝜈 𝑥 +∆ 𝜈 𝑦 = 𝜌 𝑖 𝑟 𝑒 𝛽 𝑥,𝑦 𝛾 𝐶
𝜌 𝑖 =2.8× 𝑚 −3
2𝜋 𝜎 𝑥 𝜎 𝑦 𝜌 𝑖 =5.3× 𝑚 −3
Number of ions (CO) at the train end
Beam size
𝑁 𝑖 =90×1576=1.4× 𝑚 −1
𝜎 𝑒,𝑥 =0.25𝑚𝑚
Ion cloud size
𝜎 𝑖,𝑥 =0.28𝑚𝑚
𝜎 𝑖,𝑦 =0.53𝑚𝑚
𝜎 𝑒,𝑦 =0.012𝑚𝑚

25. Ion distribution in simulation
Feedback OFF at 1000 turn
fi/f0=5120/(3x8)=210
fi/f0(measure)=30(x)-60(y)
78-th bunch
780-th bunch
1576-th bunch
Ion cloud increases, but unstable frequency is kept fast.

26. Comments on Ion instability
Modeling of ion instability is quite insufficient.
Mode spectrum is consistent, if ion cloud with 𝜎 𝑖,𝑦 =40 𝜎 𝑒,𝑦 moves correctively.
How ions are cleared at the abort gap
NSLSII E=3GeV, C=792m, h=1320, ex~1nm, ey<8pm.
Hor. FB ON, V FB gated OFF
fx,y/f0=15,47 at 100mA
Weixing Cheng (BNL)
fy/f0(measure)=15
Dny=0.0026
𝜌 𝑖 =6.8× 𝑚 −3
𝑁 𝑖 =1× 𝑚 −1
2𝜋 𝜎 𝑥 𝜎 𝑦 𝜌 𝑖 =4.3× 𝑚 −3
I=100mA

27. FCCee works

28. Electron cloud effects in FCC-ee
Photons are emitted by positron/electron beam.
Number of photon per revolution
Critical energy
Electrons are produced at the chamber wall due to photo-emission. Quantum efficiency Y1=
Electron production by a bunch per m passage.
ne,pri= Ng Y1 Np (m-1)
Secondary electron
𝑁 𝛾 = 5𝜋 3 𝛼𝛾
𝑢 𝑐 = 3ℏ𝑐 2 𝛾 3 𝜌 𝑏𝑒𝑛𝑑

29. Synchrotron radiation
Number of photon per meter, proton
rbend=11.3km(TLEP), 6km(CEPC)
Critical energy
Quantum efficiency of electron production, Y1=
Electron production by a bunch per m passage.
Chamber cross section m-2 (tentative)
Electron density exceeds re,th=7.8x109 m-3 even in a bunch passage.
Antechamber and other cures are necessary.
ne,pri= Ng Y Np (m-1)

30. Simulation of electron cloud build up in TLEP
FCCee-Z
FCCee-W
FCCee-H
FCCee-t

31. Electron cloud effects in FCC-ee
FCCee-Z
Nb=90300, Lb-b=1.1m
Np=3.3x1010, <b>=100m, sx=95mm, sy=10mm
we=2px127GHz, wesx/c=13
re,th=7.8x109 m-3. Threshold is very weak density.
KEKB 5x1011, SuperKEKB 1x1011

32. Parameters related to EC instabilitiy
CEPC
TLEP-Z
TLEP-W
TLEP-H
TLEP-t
Circumf
C (km) 54
100
Energy
E (GeV)
120
45.5 80
175
No. bunches Nb 49
90300
5162
770 78
Bunch pop
Np (1011)
3.8
0.33
0.6
0.8
1.7
Beam l-density
l (1010m-1)
0.74
3.0
0.3
0.06
0.0013
Beam size (av.)
sx/sy (mm)
583/32
95/10
164/10
247/11
360/16
Bunch length
sz,tot(mm)
2.6
5.0
2.4
2.5
Synch. tune ns
0.18
0.015
0.037
0.056
0.075
g prod. rate
Ng (/m/e+)
0.28
0.059
0.10
0.16
0.23
e- prod. rate
ne,prod (1010m-1)
1.1
0.020
0.062
0.12
0.39
Electron freq.
we/2p (GHz)
137
127
171
174
Electron osci.
wesz,tot/c
7.5 13 11
8.7
9.0
Thr. density
re,th (1010m-3)
104
0.78
3.4
7.7 15
Tune shift
Dn at re,th
0.034
0.0025
0.0061
0.0092
0.012

33. Simulation for FCCee-Z
Growth of emittance Coherent motion in
y+(z), y-(z),sy+(z)
Threshold is re,th=0.8x1010 m-3 , agree with the analytic formula 0.78x1010.

34. Ion instability in FCCee -Z
Nb=90300, Lsp=0.75m(2.5 ns)
Ne=3.3x1010,<b>=50m, sx=67mm, sy=7mm
Dispersion increases sx , assume 21/2 times controlled by ex in simulation.
ex =0.09nm, wi=2px103MHz, weLsp/c=1.61<- critical for trap in the bunch train,
ex =0.18nm, wi=2px88MHz, weLsp/c=1.38
Ion production rate for CO, ni =0.045 Ne P(Pa),
ni (10-8 Pa)= 14.9 (/(m.e-)).

35. Simulation results for P=10-8 Pa
Ions are trapped partially for ex=0.09nm
Growth does not depend on train length.
Bunch-by-bunch Feedback G=0.1(10 turn) is necessary.

36. Summary
Commissioning of SuperKEKB (Phase I) had started at Feb without collision point.
Beam-size blow-up caused by fast head-tail instability due to Electron cloud had been observed.
Aluminum bellows without TiN coating are suspected as electron source.
Installation of permanent magnets on the bellows worked to suppress the instability.
It is good for Phase II (1A 3-4 spacing).
Furether cures are necessary for Phase-III (>2A).
Ion instability and tune shift were observed. The instability is less serious and ion density near the beam is weak.
Horizontal tune shift is bigger. Ion seems to distributes si,x<si,y.