Electron cloud simulations for SuperKEKB - PowerPoint Presentation

Slide1

Electron cloud simulations for SuperKEKB

Y.Susaki,KEK-ACCL

13 Jan, 2010

Low Emittance Rings 2010, CERNSlide2

Positron beam emits synchrotron radiation

Electrons are produced at the chamber wall by photoemission

Electrons are attracted and interact with the positron beamElectrons are absorbed at the chamber wall after several 10 nsSecondary electrons are emitted according the circumferencesElectrons are supplied continuously for multi-bunch operation with a narrow spacing Electron cloud is built up

Electron cloud built-up K.Ohmi, Phys.Rev.Lett,75,1526 (1995)

e

-

γ

Secondary e

-

e

+

beam

y

xSlide3

Wake field is left behind in the electron cloud by advanced bunches

The wake field induced by the electron cloud affect backward bunches

Coherent instability occurs when there is resonance between the wake field and the backward bunches Coupled bunch instabilitySingle bunch instability

Coherent instabilities due to electron cloud

e

-Slide4

Coupled bunch instability

The wake filed causes

correlation among bunchesThreshold is determined by balance with some damping effects Independent of emittance, momentum compaction Depends on electron cloud density, distribution and motion

e

-Slide5

Single bunch instability

The wake filed causes correlation among positrons

within a single bunchThreshold is determined by the balance with Landau damping due to the momentum compaction factorDepends on emittanceDepends on only local electron cloud density 

e

+

e

+

e

-Slide6

List of parameters

Unit

SuperKEKBLER

SuperB

LER

E+

GeV

4

4

I+

Amp

3.6

2.70

Np

×10

10

6.25

4.53

Nbun

2500

1740

I

bunch

mA

1.4

1.6

β

x,y

ave

m

12

12

ν

s

Hz

0.012

ε

x

nm

3.2

2.8

ε

y

pm

33

7

σ

x

mm

0.2

0.18

σ

y

μm

20

9.1

σ

z

mm

6

L

m

3016

1400

radiation damping time

ms(turn

)

60(6000)Slide7

Number of produced electrons

Number of

the photon emitted by one positron per unit meterSuperKEKB-LER γ=8000　→　Yγ=0.17 m-1 Bunch populationSuperKEKB-LER design (3.6A) Np

=1011 Quantum efficiency for photoelectron (np.e./nγ)　

η=0.1

Energy distribution 10±5 eV

Number of electrons produced by one positron per unit meterSuperKEKB-LER Y

p.e=0.017 m-1

Yp,eNp

=1.7x109 m-1

Quantum efficiency for secondary electrons

d2,max=1.0-1.2

α= 1/137 (fine structure const.) Slide8

Increase of electron density r

e

with multi-bunch (simulation results) d2,max=1.2 Yp,eNp=1.7×109 (h=0.1) Yp,eNp=1.7×108 (h=0.01) Yp,eNp=1.7×107 (h=0.001)

 Yp,e

Np

=1.7×107 (h=0.001)

d

2,max=1.2 d

2,max=1.1 d

2,max=1.0 Slide9

Electron density

r

e as functions of quantum efficiencies (h and d2,max)d2,max=1.2  Yp,eNp=1.7×107 (h=0.001)

η

=0.003

w/ antechamber

ρ

eth

=1.1

✕

10

11

m

-3

Together with solenoid it is expected to reduce

η to 0.001 (Suetsugu)Slide10

Antechamber

©

SuetsuguSlide11

Electron distribution and electric potential with

d

2,max=1.2AntechamberCylindrical chamber Slide12

Electron distribution and electric potential with

d

2,max=0AntechamberCylindrical chamberSlide13

Reduction factor

Averaged electron density

Ratio of the densities at the beam pipe of ante-chamber and cylindrical-chamber The ratio ≈0.03 for δ2,max=0The antechamber reduces η in 3% effectivelySlide14

Wake field induced by electron cloud and beam stability

EOM for the beam and the cloud in the

y direction (coasting beam model)F becomes linear near the beam

ysSlide15

Wake field induced by electron cloud and beam stability

The eq. for the cloud can be solved as

The eq. for the beam becomeswake force

wake fieldSlide16

Wake field induced by electron cloud and beam stability

Fourier trans. of the eq. for the beam leads

Growth rate of instability = Im ω Slide17

Wake for bunch correlation

Y

1eNp=1.7×109 m-1(h=0.1)1.7×108 m-1(h=0.01)1.7×107 m-1(h=0.001)Slide18

Unstable modes and growth rate

Growth rate for

ηGrowth rate is 0.02 for η=0.001not so severe that it could be controlled by the feedbackY1eNp=1.7×109 m-1(h=0.1)

1.7×108 m-1(h=0.01)1.7×107 m

-1(

h=0.001)

corresponding to the threshold of the SBISlide19

Stability condition for the single bunch

instability

Landau dampingCoherence of the transverse oscillation is weakened by the longitudinal oscillation associated with momentum compactionStability condition for ωeσz/c>1Balance of growth and Landau dampingSlide20

Threshold of the single bunch instability

Threshold of the electron cloud density

Qnl depends on the nonlinear interactionK characterizes cloud size effect and pinchingωeσz/c>10 for low emittance ringsWe use K=ωeσz/c and Qnl

=7 for analytical estimation Slide21

Threshold for

SuperKEKB

and SuperB UnitSuperKEKBLER

SuperB

LER

L

m

3016

1400

γ

8000

8000

I+

Amp

3.6

2.70

Np

×10

10

6.25

4.53

I

bunch

mA

1.4

1.6

β

x,y

ave

m

12

12

ν

s

Hz

0.012

σ

x

mm

0.2

0.18

σ

y

μm

20

9.1

σ

z

mm

6

Q

7

ω

e

σ

z

/c

10.9

ρ

e

threshold

×10

11

m

-3

1.13Slide22

Simulation with Particle In Cell

Method

for the single bunch instabilityElectron clouds are put at several positions in a ringBeam-cloud interaction is calculated by solving  two-dimensional Poisson equation on the transverse planeA bunch is sliced into 20-30 pieces along the longitudinal direction

e

+

e

-Slide23

Simulations for instability threshold for

SuperKEKB

Profiles of the beam size ηy=0.2ηy=0ρe,th≈2.4×1011

m-3 ρe,th≈2.2×10

11m

-3 Slide24

Bunch and

e

-cloud profiles at 4000 turn Coherent motions (SuperKEKB)ηy=0.2η

y=0Slide25

FFT spectra below and above the threshold

Unstable modes of the instability (

SuperKEKB)stablestableunstableunstable

η

y

=0.2η

y=0Slide26

Simulations for instability threshold for

SuperB

Profiles of the beam sizeηy=0ηy=0.2ρe,th≈4.4×1011m

-3 ρe,th≈2.6×1011

m

-3 Slide27

Bunch and

e

-cloud profiles at 4000 turn Coherent motions (SuperB)ηy=0.2ηy=0Slide28

FFT spectra below and above the threshold

Unstable modes of the instability (

SuperB)stablestableunstableunstable

η

y

=0.2η

y=0Slide29

Summary

Multi-bunch numerical simulation

The effective quantum efficiency η should be reduced to 0.001The antechember alone seems not to be sufficient for achieving η=0.001, but together with solenoid it is expected to cure the situation (Suetsugu) The CBI seems not to be severe with η=0.001Single bunch numerical simulationThe threshold of the electron cloud density for the stability has been estimated for SuperKEKB, SuperB