10 February 2003
The 8th KEKB Accelerator Review

S. S. Win, H. Fukuma, K. Ohmi, S. Kurokawa

ELECTRON CLOUD IN LER

TRANSVERSE COUPLED-BUNCH INSTABILITY BY2)

1)

by computer simulation presuming electron cloud (EC) instability.

experimentally from the positron bunch oscillation data anddistribution of electrons around the beam.

results in order to understand the mechanism of EC formation and

The experimental observations were compared with the simulation

Transverse Coupled-Bunch Instability (TCBI) was studied

In this work,

Energy (GeV)
Circumference (m)Revolution frequency (kHz)RF frequency (MHz)Harmonic number
Beam current (mA)
No. of train/No. of bunches
Bunch spacing (ns)Transverse tune, νx/νy
Inner dia. of vacuum chamber (mm)3.53016.2699.39
508.8875120
300 ~ 900
1/1153845.51/43.56
94 (circular)

Machine parameters of LER in TCBI experiments

Recorder with and without solenoid field.
 From the experimental data, the TCBI is characterized by the mode
spectrum and the growth rate of oscillation amplitudes.

 Positron bunch oscillation data were taken by Bunch OscillationEXPERIMENTS (1)Amplitude (ADC count)30080130180230500

Figure 2: Snapshots at 6 ms
(700 mA, horizontal)

1000 1500 2000 2500 3000 3500 4000
Turn number-300-20-1001020200

400

600
800
Bunch id1000

1200

Figure 1: Bunch oscillation recorded by BOR(700 mA, horizontal, Bunch #31)

EXPERIMENTAL OBSERVATION OF TCBI (2)Amplitude (arbitrary unit)Mode0200

800 1000 1200

Mode400 6000

Beam current: 600 mA

Figure 4: Mode spectra in verticalplane at 600 mA beam current

0Fill pattern: 1 train/1153 bunches/8 ns bunch spacing

Figure 3: Mode spectra in horizontal
plane at 600 mA beam current

000625350

10.4

200 400 600 800 1000 1200

1250

700

1.22Solenoids on
Solenoids off

2500

0.8

1400

Vertical

1875

x104
41050

Solenoids on
Solenoids off

Horizontal

31.6x 104

Mode Spectra

EXPERIMENTAL OBSERVATION OF TCBI (3)00123400

600

800

Beam current (mA)

200

25%72%100%(solenoids on), Jul01(solenoids off), Jul01(solenoids on), Nov01(solenoids on), Dec01a) Horizontal

100000123b) Vertical

400600800

Beam current (mA)

200

20%

74%100%(solenoids on), Jul01(solenoids off), Jul01(solenoids on), Dec01

Growth rates

Figure 5: Observed growth rates when solenoid-off andsolenoid-on in a) horizontal and b) vertical planes.

Average growth rate (/ms)

EXPERIMENTAL OBSERVATION OF TCBI (4)Average growth rate (/ms)

1000

3.53016
1/11530.52
3.3×1010
10/10
18/0.3645.52/43.57
10±5 (Gaussian)
0.1
1.5/300

Assuming 2 cases:
Case I: Electrons are mainly produced at the illumination pointwith 30% reflection
Case II: Electrons are produced uniformly over the surface

Beam energy (GeV)
Circumference (m)No. of train/No. of bunches
Bunch current (mA)
No. of positrons per bunch
Average βx/βy (m)Emittance εx/εy (nm)
Betatron tune νx/νy
Initial energy of photoelectrons(eV)Photoelectron yield
Secondary electron yield of copper δmax/Emax (eV)

Simulation parameters:

PEI model was used. (PEI was originally developed by K. Ohmi ,KEK).

Simulation study of TCBI caused by electron cloud (1)00.05x (m)b)y (m) -0.05 -0.050b)

x (m)

00.05

Figure 6: Electron distribution over cross-section of beam chamberassuming that photoelectrons are produced a) at illumination point with30% reflection and b) uniformly on the surface of beam chamber.

y (m) -0.05 -0.05

00.05

00.05

0300a)

Electron distribution 2
Electrons
600

2500

Electrons
5000

Electron distribution 1

Electron Distribution

LER SIMULATION STUDY - SOLENOID-OFF (2)200 400

VerticalMode

600 800 1000 1200

Mode

200 400 600 800 1000 1200

Horizontal

Figure 7: Mode spectra when solenoid-off
assuming photo-electrons are produced atthe illumination point with 30% reflection00

1200

12Production of electrons at illumination point

0120ModeMode

200 400 600 800 1000 1200

Verticalx 103

200 400 600 800 1000 1200

Horizontal

x104001234Experiment

SIMULATION STUDY - SOLENOID-OFF (3)00Mode200 400 600 800 1000 1200

Vertical800 1000 1200

Mode

200 400 600

Horizontal

Figure 8: Mode spectra when solenoid-off
assuming photo-electrons are produced
uniformly on chamber wall

00.5

100.40.8

Uniform production of electrons

0120ModeMode

200 400 600 800 1000 1200

Verticalx103

200 400 600 800 1000 1200

Horizontalx10400

1234

Experiment

SIMULATION STUDY - SOLENOID-OFF (4)

6000

6000

(a)

00.05

3000

Y0-0.05-0.05-0.05-0.05

X0X

0(e)

0.05 0.05(b)0.05 0.05-0.05-0.05-0.05-0.05

30 G

Y0Y

05G0X

X

0(f)

0.05 0.05(c)

0.05 0.05-0.05-0.05

Y

0-0.05-0.05

40 G

Y

010 G0X

X

00.05

0.05

Figure 9: Projection of electrons over the cross-section of the vacuum
chamber due to various solenoid fields in Case I. (X and Y in m)

(d)

00.05

300020 GY00G

Production of electrons at illumination point [Solenoid-OFF & ON] (5)Electrons

Electrons

0Mode200 400 600 800 1000 1200 1400

Solenoid-40 G

Mode200 400 600 800 1000 1200 1400

Solenoid-5 G

Horizontal0Mode

200 400 600 800 1000 1200 1400

Solenoid-ONExperiment

Mode

Solenoid-10 G200 400 600 800 1000 1200 1400

x 104

00.5

11.5

200246The mode spectrum due to 10 G solenoid field is consistent with the experimental observation.

Figure 10: The mode spectra in horizontal plane due to various solenoid fields in Case I.

Mode0200 400 600 800 1000 1200 1400

0022600244Solenoid-20 G

Mode200 400 600 800 1000 1200 1400

Solenoid-0 G

46000.511.526Production of electrons at illumination point [Solenoid-OFF & ON] (6)0Mode00Mode

200 400 600 800 1000 1200 1400

Solenoid-ONExperiment

Figure 11: The mode spectra in vertical plane due to various solenoid fields in Case I.
The mode spectrum due to 5 ~10 G solenoid field is consistent with experimental observation.

Mode200 400 600 800 1000 1200 1400

000200 400 600 800 1000 1200 1400

0.5

21.5ModeSolenoid-10 G

200 400 600 800 1000 1200 1400

x 103

002

Solenoid-40 G

Mode

200 400 600 800 1000 1200 1400

241.0

60024Solenoid-5 G

64Solenoid-20 G

Mode

200 400 600 800 1000 1200 1400

Solenoid-0 G

646000.5

11.5

2

Vertical

Production of electrons at illumination point [Solenoid-OFF & ON] (7)-0.05Y

0-0.05

20 G

Y

00G

-0.05

-0.05

X0X

00.05
0.05

0.05 0.05

Y0-0.05

-0.05

30 G

Y

05G-0.05

-0.05

X

0X

00.05

0.05

0.05 0.05-0.05

Y0-0.05

40 GY010 G-0.05

-0.05

X0X

00.05

0.05

Figure 12: Projection of electrons over the cross-section of the vacuum
chamber due to various solenoid fields in Case II. (X and Y in m)

00.05

200

400600Electrons

00.05

200

400600Electrons

Uniform production of electrons [Solenoid-OFF and Solenoid-ON] (8)00Mode200 400 600 800 1000 1200 1400

Solenoid-40 G

Mode

200 400 600 800 1000 1200 1400

Solenoid-5 G

00.51

1.5

20Mode200 400 600 800 1000 1200 1400

Solenoid-ONExperiment

Mode

Solenoid-10 G

200 400 600 800 1000 1200 1400

x 104000.511.522.5

Figure 13: The mode spectra in horizontal plane due to various solenoid fields in Case II.
The mode spectrum due to 10 G solenoid field is consistent with the experimental observation.

Mode200 400 600 800 1000 1200 1400

0.5

0.5

00

112

2.5

00

0.5

1

1.5

2

1.5

Solenoid-20 G

Mode

200 400 600 800 1000 1200 1400

Solenoid-0 G

2.5

1.5

2

2.500

0.2

0.4

0.6

0.8

Horizontal

Uniform production of electrons [Solenoid-OFF & ON] (9)Mode

200 400 600 800 1000 1200 1400

Mode

200 400 600 800 1000 1200 1400

Solenoid-40 G000.51.0

Mode

200 400 600 800 1000 1200 1400

Solenoid-ONExperimentMode

200 400 600 800 1000 1200 1400

31.5 x 100

Solenoid-10 G

Figure 14: Mode spectra in vertical plane due to various solenoid field in Case II.
The mode spectrum due to 10 G solenoid field is consistent with the experimental observation.

00Mode0.5

0.5

200 400 600 800 1000 1200 1400

12

2.5

00

0.5

0.5

1.5

22.5

11

Solenoid-20 G

Mode

200 400 600 800 1000 1200 1400

Solenoid-5 G

Vertical

11.5

21.50

Solenoid-0 G

2.5

1.5

22.500.51Uniform production of electrons [Solenoid-OFF & ON] (10)0515

Solenoid field (G)1020

Case I
Case II
Experiment (Solenoid-off)Experiment (Solenoid-on)

25

00.3

0.6

0.9

1.2

1.5

05

101520
Solenoid field (G)Case I
Case II
Experiment (Solenoid-off)Experiment (Solenoid-on)b) VerticalFigure 15: Average growth rate of bunch oscillation with and without solenoid
fields assuming Case I and Case II in (a) horizontal and (b) vertical plane.

00.5

1.0

1.5

2.02.5a) Horizontal

Growth rates

25Case I. Photoelectrons are produced at the illumination point with 30% reflection.
Case II. Photoelectrons are produced uniformly over the surface of vacuum chamber.

Growth rate (/ms)

SIMULATION STUDY - SOLENOID-OFF and ON (11)Growth rate (/ms)

z From the experiment, the transverse coupled bunch
instability observed in the KEKB-LER is caused by theelectron cloud.
z From the comparison between experiment and simulation
results, it is suggested that the electrons are produced
uniformly over the surface of the vacuum chamber.
z The effective solenoid field is not less than 10 G to explain
the observed mode spectra and the growth rates of thecoupled bunch instability.

The results show that:

We performed
z experimental study of the TCBI with solenoid off/on andz simulation study of the coupled bunch instability due to theelectron cloud without and with applying various solenoid fields.

Summary