1. Electron Cloud Effects in SuperB
T. Demma, INFN-LNF
SuperB Workshop
LAL, Orsay , 15-18/02/2009

2. PLAN OF TALK Electron Cloud Effects
Electron Cloud Single Bunch Instability
Linear Theory
Simulations
Electron Cloud Build-Up
Straight
Solenoid
Dipole
Quadrupole
Mitigation Techniques
Work in progress
Conclusions

3. Electron Cloud Effects
The electron cloud develops quickly as photons striking the vacuum chamberwall knock out electrons that are then accelerated by the beam, gain energy, and strike the chamber again, producing more electrons.
The peak secondary electron yield (SEY) of typical vacuum chamber materials is >1 even after surface treatment, leading to amplification of the cascade.
The interaction between the electron cloud and a beam leads to the electron cloud effects such as single- and multi-bunch instability, tune shift, increase of pressure and so on.

4. Linear Theory of Single Bunch Instability K. Ohmi, et Al. , Phys. Rev
Linear Theory of Single Bunch Instability K.Ohmi, et Al., Phys.Rev.E65,2002.
The oscillation frequency of electrons under a bunch population (Nb= 5.52×1010 ) is given by
The number of oscillations is:
The threshold of electron cloud density for a given bunch population is given by
where 4

5. Input Parameters for HEADTAIL
SuperB LER (june ‘08)
Beam energy
E[GeV] 4
circumference
L[m]
1800
bunch population Nb
5.52x1010
bunch length
σz [mm] 5
horizontal emittance
εx [nm rad]
2.8
vertical emittance
εy [pm rad] 7
hor./vert. betatron tune
Qx/Qy
43.57/21.59
synchrotron tune Qz
0.017
hor./vert. av. beta function
<βx>[m]/ <βy>[m]
20/20
momentum compaction 
3.2e-4

6. Emittance growth due to fast head-tail instability
Head-Tail (CERN)
june’08 param.s
The interaction between the beam and the cloud is evaluated at 10 different positions around the SuperB ring for different values of the electoron cloud density.
The threshold density is determined by the density at which the growth starts:

7. Emittance growth due to fast head-tail instability
Head-Tail (CERN)
june’08 param.s
The interaction between the beam and the cloud is evaluated at 10 different positions around the SuperB ring for different values of the electoron cloud density.
Electron in the cloud moves only vertically.
The threshold density is:

8. Electron cloud buildup simulation
Cloud buildup was calculated by code “ECLOUD” developed at CERN.
Assumptions:
- Round or elliptical Chambers
- Uniform production of primary electrons on chamber wall.
- A reduced number of primary electrons is artificially used in order to take into account the reduction of electron yield by the ante-chamber.

9. Build Up Input Parameters for ECLOUD
Bunch population Nb
5.52x1010
Number of bunches nb
500
Bunch spacing
Lsep[m]
0.6
Bunch length
σz [mm] 5
Bunch horizontal size
σx [mm]
0.3
Bunch vertical size
σy [mm]
0.012
Chamber hor. Aperture
hx [mm] 50
Chamber vert. aperture
hy [mm]
Photoelectron Yield
Yeff
0.1
Primary electron rate
dλ/ds
0.0024
Photon Reflectivity R
100%
Max. Secondary Emission Yeld
δmax
Energy at Max. SEY
Εm [eV]
250
SEY model
Cimino-Collins ((0)=0.5)

10. Build Up in Drift Space (95% antechamber protection)

11. e-cloud Density at Center of Beam Pipe
95% prot.
δmax=1
δmax=1.1
δmax=1.2
δmax=1.3
The central e-cloud density is always above the threshod th.=5*1011 m-3

12. Build Up in Drift Space (99% antechamber protection)
For δmax=1.2 the central e-cloud density is below the threshod th.=5*1011 m-3

13. Electron Cloud Buildup in a 50G Solenoidal Field

14. Build Up in the SuperB arcs: Dipoles
For δmax=1.3 the central e-cloud density is below the threshod th.=6*1011 m-3

15. Build Up in the SuperB arcs: Quadrupoles

16. Mitgation Techniques
Preliminary simulations indicate that a peak secondary electron yield close to 1.2 and an antechamber protection of 99% results in a cloud density close to the instability threshold.
Planned use of NEG coatings and solenoids in SuperB free field regions (~75% of LER cirmumference, no wigglers) can help.
In magnetic field region, external solenoid field are not effective in build-up of electron cloud. In SuperB all chambers would be TiN coated inside the beam channel to reduce the SEY.
Studies of mitigation techniques (grooves in the chamber walls, clearing electrodes) are in progress for other accelerators, we can profit of these studies to plan mitigation in SuperB.

17. Mitigation Techniques: SEY reduction
M. Pivi et. al, SLAC

18. Mitigation Techniques: SEY reduction (cont.)
M. Pivi et. al, SLAC

19. Mitigation Techniques: Clearing Electrodes

20. Clearing Electrode Test chamber was installed into a wiggler magnet
Y. Suetsugu, KEK
Test chamber was installed into a wiggler magnet
Beam current (Ib) ~1600 mA
Bunch spacing (Bs) 4 ~16 ns
Wiggler magnet.
Magnetic field: 0.77 T
Effective length: 346 mm
Aperture (height): 110 mm
Placed at the center of pole
SR: 2x1017 photons/s/m
Test chamber
Electrode
Gate Valve
Gate Valve
Inside view
Beam 20
Monitor
2018/6/9
2008/12/10 INFN
2008/12/10 INFN

21. Clearing Electrode Effect of electrode potential
Y. Suetsugu, KEK
Effect of electrode potential
Drastic decrease in electron density was demonstrated by applying positive voltage.
1585 bunches
(Bs ~ 6 ns)
~1600 mA
Vr = 1.0 kV
B = 0.77 T
[Logarithmic scale]
Vr = -1 kV
~1x1012 e-/m3
Electron density decreased to
1/10 at Velec = ~ 200 V
1/100 at Velec = ~ 400 V
-500 V
Velec = 0 V
Velec [V]
Ie [A]
+500 V
Collectors 21
2018/6/9
2008/12/10 INFN
2008/12/10 INFN

22. Conclusions and Outlook
Simulations indicate that a peak secondary electron yield of 1.2 and 99% antechamber protection result in a cloud density below the instability threshold in free field regions.
Planned use of coatings (NEG, TiN..) and solenoids in SuperB free field regions (~75% of LER cirmumference, no wigglers) can help.
Studies on mitigation techniques offers the opportunity to plan activity for SuperB.
• Work is in progress to:
estimate other effects: multi-bunch instability, tune-shift.
compare the results with other codes (PEHTS, PEI, K.Ohmi; POSINST, M.Furman,M.Pivi).
benchmark codes using:
grow-damp and tune-shift measurements at DAFNE
pressure measurements vs solenoid field intensity at PEPII (S.Novokhatski)

23. Spare Slides

24. Electron cloud at DAFNE
e+ current limited to 1.2 A by strong horizontal instability
Large positive tune shift with current in e+ ring, not seen in e- ring
Instability depends on bunch current
Instability strongly increases along the train
Anomalous vacuum pressure rise has been oserved in e+ ring
Solenoids installed in free field regions strongly reduce pressure but have no effect on the instability
Instability sensitive to orbit in wiggler and bending magnets
Main change for the 2003 was wiggler field modification

25. Tracking simulation e+ bunches z y ~m x
K.Ohmi, PRE55,7550 (1997)
K.Ohmi, PAC97, pp1667.
Electron cloud
e+　bunches z y ~m x
Solve both equations of beam and electrons simultaneously, giving the transverse amplitude of each bunch as a function of time.
Fourier transformation of the amplitudes gives a spectrum of the unstable mode, identified by peaks of the betatron sidebands.

26. Bunch train evolution
x [m]
bunch
1.2 A in 120 equispaced bunches

27. Mode spectrum and growth rate
Measurment
Simulation
I[mA]/nb
/T0
1000/105 73
1200/120
100
750/105 56
900/120 95
500/105
600/120
130

28. e-cloud density evolution
1 turn
5 turn
10 turn
15 turn
20 turn
25 turn