Instabilities
simulation and observation
K. Ohmi, J. Flanagan, H. Fukuma, Y. Funakoshi, H. Ikeda,
Y. Suetsugu, S. Terui, M. Tobiyama, D. Zhou
21-th KEKB Accelerator Review Committee
KEK, 13-15 June, 2016

Contents• Beam size blow-up due to Electron cloud• Coupled bunch instability due to electron cloud• Coupled bunch instability in HER• Tune shift measurement and transverse impedance• Bunch length measurement

Beam size blow-up in LER• Beam-size blowup observed in KEKB has been seen inearly stage of SuperKEKB commissioning
1. Threshold I~300mA in Apr 19 (Y. Funakoshi)
2. Electron cloud has been monitored at AL chamber w and w/o TiN coating (Y.
Suetsugu).
3. Beast study threshold I~600mA, Nbunch=1576 in May 17 (Nakayama et al)
4. Systematic study in 1 June ( H. Fukuma et al.)
5. Permanent magnets are set at aluminum bellows.(Y. Suetsugu et al.)
6. Systematic studies in 8 July ( H. Fukuma et al.)June 1, 2016
4 train x150 bunches, Nbunch=600
Threshold beam current
160, 200, 260,500 mA for 2, 3, 4,
6 bucket spacingH. Fukuma et al.,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 averageof whole ring

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=2.1x1010,
ey=100pm

Np=2.1x1010

Np=5.2x1010

Ith=200mA, 6ns spacing

Ith=500mA, 8ns spacing

Np=2.4x1010,
ey=100pm

Simulated threshold electron density(condition before solenoid installation)• Nb=600, ex=2nm, ey=15pm, sz =6mm, ns=0.019
we/2p wesz/c reth (Q=10)(GHz)(1011m-3)

reth (Q=6)(1011m-3)

reth (Simu)(1011m-3)

1.91

2.45

3.4

8.9

1.65

2.45

3.4

80

10.1

1.47

2.45

3.8

5.2

111

14.0

1.47

2.45

5.0

500

2.0

37

5.5

2.89

2.90

4.4

600

2.4

41

6.0

2.63

2.65

4.4

spacing Ip,th(mA)Np,th(1010)

2 (4ns)160

1.6617.73 (6ns)

200

2.1

71

4 (8ns)260

2.76 (12ns)

500

3.06
3.06

6Nb=1576,
ey=100pm

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 withenergy gain 500eV from a bunch. 500eV may be criticalfor 2 (4ns) spacing.
• For V=0V, electron rate production including secondary
is detected.

Measured electron current
Vr = -500 V

Y. SuetsuguVr = -500 V

Al部分

Al wo coating

Al w TiN coating

Vr = 0 V

Vr = 0 V

Al wo coating

Al w TiN coating

For V=0V, 1mA, electron production rate is 0.3x109 m-1/bunch

8Electron density at the blow-up
threshold
Simulated electron density at the threshold current
Measured threshold current and density

Only Al part

Simple formula Q=6

After installation of permanentsolenoid at Al bellows
Simulated electron density at the threshold current

2016/6/8
Ith=200 mA Ith=330 mA
4/150/2

4/150/3
4/150/4

Ith>600 mA

Simple formula Q=6Threshold of electron cloud density
after solenoid attach
we/2p wesz/c reth (Q=10)(GHz)(1011m-3)

spacing Ip,th(mA)Np,th(1010)

2 (4ns)

200

2.1

71

8.9

3 (6ns)

330

3.5

91

11.5

4 (8ns)

>600

>6.3

3.06

500

2.0

37

5.5

3.06

600

2.4

41

6.0

reth (Q=6)(1011m-3)

reth (Simu)(1011m-3)

2.45

3.4

2.45

4.8

2.89

2.90

4.4

2.63

2.65

4.4

1.65

6 (12ns)

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

re(r=0)~lex1000

Np=9.4x1010, I=900 mA for Nb=600

Beam current: Slightly higher
than measured threshold2016/6/8
Ith=200 mA

Ith=330 mA
4/150/3
4/150/4

4/150/2

Ith>600 mA
Y1=Photon numberx0.1x0.01

electron density near beam(m-3)

E cloud buildup

CLOUDLAND, Fukuma

dmax=1.5
Np=3.13x1010,
Density R<4mm
Y1=Photon numberx0.1x0.01
quantum eff. antechamber
dmax=1.4
dmax=1.3
dmax=1.2
dmax=1.0 計算を打ち切った。
t(sec)

Coupled bunch instability caused by electroncloud• Electron cloud motion reflects coupled bunch instability mode.
• Electrons in drift, short range wake ~10ns• Electrons in solenoid, slow rotation around chamber surface.

400 f01000 f0

KEKB

Unstable mode (before solenoid
M. Tobiyamainstallation)• Typical signal of coupled bunch instability causedby drift electrons

1000 f0
400 f0Fast,
strong

400 f0Mode spectrum
By 2 ver

300mA

400mA

Solenoid origin

By 4 ver 350mA

Drift origin

600mA
Solenoid origin

Solenoid origin

Unstable mode (after solenoidinstallation)• Typical mode caused by electrons in solenoid is seen.
• Mode seems to change to those of drift origin at highcurrent.
Solenoidmodes

540 f0Fast,
strong

400 f0700 f0

Coupled bunch instability in electron ring (HER)
M. Tobiyama• Ion?

Fast,strong

𝑀𝑜𝑑𝑒 = 5120 −

𝜔𝑖,𝑥𝑦
𝜔0CO

Resistive wall
5120-1=5119

Impedance estimation- transverse• Tune shift as function of bunch current
1 𝑁𝑟𝑒 𝐿 𝑖𝑍𝑒𝑓𝑓Δ𝜈𝑥 = 3/2
𝛾 𝜈𝑥 𝜎𝑧 𝑍0
4𝜋𝑖𝑍𝑒𝑓𝑓 = 31 𝑥

LER x

53 𝑦 𝑘Ω/𝑚HER yΔ𝜈𝑥
HER
𝐼(𝑚𝐴)

Δ𝜈𝑥
LER𝐼(𝑚𝐴)= 58.2𝑖𝑍𝑒𝑓𝑓 = 43 𝑥

145 𝑦 𝑘Ω/𝑚𝑖𝑍𝑒𝑓𝑓 (𝑘Ω) = 33.3

Collimatordependence

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

Longitudinal impedance issueBunch length measurement•L

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

Summary• Beam size blow-up has been observed since early stage ofSuperKEKB commissioning.
• Electron density at Al bellows part (5% of circumf.) is high(re>1012m-3). Simulations show the electrons can cause
fast head-tail instability.
• Coupled bunch instability caused by electron cloud has
also been observed as is predicted.
• Installation of Permanent solenoid reduced the blow up. It
is possible to operate with 1A, 4 bucket spacing at presentcondition.
• Tune shift as function of bunch current was measured toestimate transverse impedance. It was 30-50kW/m, similar
as KEKB.
• Bunch length was measured by a streak camera. Bunch
lengthening, which was similar as KEKB, was observed, 7-8mm at the design current, while no bunch lengthening inprediction.

Thank you for your attention

Rough estimation of Electron density• Electron current, Ie=1mA.
• Acceptance of the electron detector, Smon=1 cm2.
• Number of electron absorbed (=produced) at chamber
wall, d=10cm.
10−6 × 0.1𝜋
16 𝑚−1 𝑠 −1
𝑛𝑒 ==2×10
1.6 × 10−19 × 10−4

• Electron stay time in the chamber, te=100ns. Electrondensity
2 × 1016 × 10−7𝜌𝑒 == 2.5 × 1011 𝑚−3
20.05 𝜋

Emittance dependence• Vertical emittance knob

by=67mDesign current & spacing
Np=9.4x1010, I=3600 mA

金澤氏の式を使った電子密度の算出*＊PAC2005, p.1054

nb = バンチ数
pA = 通過確率 = 0.0003x1/4 = 7.5E-5
Vb = グリッド電圧 [V]Nb = バンチ内のe+の数
INb =I = ビーム電流 [A]nbfrevee = 1.602E-19 [C]frev = 1E5 [s-1]re = 2.818E-15 [m]me = 9.109E-31 [kg]c = 3.0E8 [ms-1]
まとめると、
D = 2.630E13 x

IobsnbVb
I2

例えば、2/150/3 Vr = -30 V, I = 200 mA, Iobs = 1E-7 A の場合 (平均で)nb = 600, Vb = 30

D = 1.18E12 [e- m-3]

26

Simulated electron cloud build up in Bend
Np=2.5x1010, I=240 mA for Nb=600bucket
Np=9.4x1010, I=900 mA

Np=4x1010, I=380 mA

bucketIth=200 mA
4/150/2

Ith=330 mA
4/150/3
4/150/4

Ith>600 mA
bucketMultipactoring arises Y2max>=1.5 at the threshold beam currents.

KEKBx 10

Solenoid-Off
Experiment

4Simulation

5

Horizontal

0.4

Horizontal

40.3

320.2

10.1

00x 10200400600

800

1000 1200 1400

0Mode3Vertical

30.8

10.40200

400

600

800

Mode2001.22001000 1200 1400

0400600

800

1000 1200 1400

800

1000 1200 1400

Mode

Vertical

0200

400600Mode

Su Su Win et al,(EC2002)