1. Electron Cloud & IBS Update
T. Demma, INFN-LNF
SuperB General Meeting October , SLAC

2. Plan of Talk Electron Cloud Effects
Electron Cloud Single Bunch Instability
Simulations
Electron Cloud Build-Up
Dipole
Quadrupole
Mitigation Techniques
e-cloud summary
IBS

3. SuperB Configuration Options
LER/HER
Unit
June 2008
Jan. 2009
March 2009
Sep. 2009
E+/E-
GeV
4/7
4.18/6.7 L
cm-2 s-1
1x1036
I+/I-
Amp
1.85 /1.85
2.00/2.00
2.80/2.80
2.12/2.12
Npart
x1010
5.55 /5.55
6/6
4.37/4.37
6.33/4.06
Nbun
1250
2400
1011
q/2
mrad 25 30
bx* mm
35/20
20/20
by*
0.22 /0.39
0.21 /0.37
0.2 /0.32 ex nm
2.8/1.6
2.6/1.6 ey pm
7/4 sx
9.9/5.7
5.7/9.05 sy
39/39
38/38
36/36 sz
5/5 xx
X tune shift
0.007/0.002
0.005/0.0017
0.004/0.0013 xy
Y tune shift
0.14 /0.14
0.125/0.126
0.091/0.092
RF stations
5/6
5/8
RF wall plug power MW
16.2 18
25.5
Circumference m
1800

4. Simulation of single-bunch instability
Simulations were performed using CMAD (M.Pivi):
Parallel bunch-slices based decomposition to achieve perfect load balance
Beam and cloud represented by macroparticles
Particle in cell PIC code 9-point charge deposition scheme
Define at input a cloud density level [0<r<1] for each magnetic element type
Tracking the beam (x,x’,y,y’,z,d) in a MAD lattice by 1st order and 2nd (2nd order switch on/off) transport maps
MAD8 or X “sectormap” and “optics” files as input
Apply beam-cloud interaction point (IP) at each ring element
Input parameters (Sep.09 conf.) for CMAD
Beam energy E[GeV]
6.7
circumference L[m]
1370
bunch population Nb
5.74x1010
bunch length σz [mm] 5
horizontal emittance εx [nm]
1.6
vertical emittance εy [pm] 4
hor./vert. betatron tune Qx/Qy
40.57/17.59
synchrotron tune Qz
0.01
hor./vert. av. beta function
20/20
momentum compaction 
4.04e-4

5. Emittance growth due to fast head-tail instability (LNF conf.)
=7x1011e-/m-3
<5x1011e-/m-3
The interaction between the beam and the cloud is evaluated at 40 different positions around the SuperB HER (LNF option) for different values of the electoron cloud density.
The threshold density is determined by the density at which the growth starts:

6. Bunch shape at last turn
Above instability threshold
Below instability threshold

7. Beam losses =3x1011e-/m-3; =7x1011e-/m-3
Hor. Bunch centroid oscillations
Particles per bunch vs. time
Ver. Bunch centroid oscillations
=3x1011e-/m-3; =7x1011e-/m-3

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:
where: dn/ds is the average number of emitted photons per meter per e+, Y is the quantum efficiency, and  is the percentage of photons absorbed by the antechambers.

9. Build Up Input Parameters for ECLOUD
Bunch population Nb
4.2x1010
Number of bunches nb
500
Bunch spacing
Lsep[m]
1.2
Bunch length
σz [mm] 5
Bunch horizontal size
σx [mm]
0.3
Bunch vertical size
σy [mm]
0.012
Photoelectron Yield Y
0.2
Photon rate (e-/e+/m)
dn /ds
0.72
Photon Reflectivity R
100%
Max. Secondary Emission Yeld
δmax
Energy at Max. SEY
Εm [eV]
250
SEY model
Cimino-Collins ((0)=0.5)

10. Buildup in the SuperB arcs: Dipoles
By=0.3 T; =95%
SEY=1.1 SEY=1.2 SEY=1.3 SEY=1.4
Snapshot of the electron (x,y) distribution “just before” the passage of the last bunch

11. Electron Cloud Density at Center of Beam Pipe
Center e-cloud density for =95%
SEY=1.1 SEY=1.2 SEY=1.3
Center e-cloud density for = 99%
SEY=1.1 SEY=1.2 SEY=1.3

12. Buildup in the SuperB arcs: Quadrupoles
LER Arc quadrupole vacuum chamber (CDR)
dBy/dx=2.5T/m, =99%
max=1.2
average
center
Snapshot of the electron (x,y) distribution “just before” the passage of the last bunch

13. Head-Tail Instability Threshold
June 2008
January 2009
March 2009
int [1015m-2] solenoids
int [1015m-2] no solenoids
SEY=1.1
95%
0.06
2.1
0.09
2.5
0.22
2.7
99%
0.02
0.25
0.04
0.3
0.7
SEY=1.2
2.8
0.27
3.2
0.45
6.5
0.045
0.71
0.82
0.07
2.4
SEY=1.3
20.2
2.9
25.7
5.4 25
0.94
1.3
4.1
4.5 13
Sep.2009
int [1015m-2] solenoids
0.1
0.07
0.3
2.0
0.7
Instability occurs if:
where cent. ande,th are obtained from simulations.
LNF conf.

14. Drift Mitigation Summary
Plots show average of all collectors for all drift RFAs
In general, the most cloud is seen in the bare Al chambers (blue)
Much less in copper chambers (black)
Less still in coated chambers
TiN: green
Carbon: red e- e+
J.Calvey (Cornell)
CesrTA Mitigation Studies: LCWA09
CesrTA Mitigation Studies: LCWA09

15. Drift Mitigation Summary II
Same plots as last slide, but not normalized to photon flux
Al is still by far the worst, but normalization makes some difference in the relative strength of the signal in the other chambers
Current calculation of photon flux assumes no reflections
A new synchrotron radiation program, which will include reflections, is under development e- e+
J.Calvey (Cornell)
CesrTA Mitigation Studies: LCWA09
CesrTA Mitigation Studies: LCWA09

16. Chicane Current Scan Current scan, 1x45 e+, 14ns, 5GeV
Both mitigation techniques show drastic improvement relative to Aluminum
Note that Al signal is divided by 20
Al shows significant
mutipacting
TiN actually seems to
saturate
Groove + TiN is even
better than just TiN
J.Calvey (Cornell)
CesrTA Mitigation Studies: LCWA09
CesrTA Mitigation Studies: LCWA09

17. Clearing Electrode Results
Y. Suetsugu (KEK)
Results
Drastic decrease in the electron density by applying Velec was observed.
The electron density decreased to less than 1/100 at Velec > ~+300 V
1585 bunches
(Bs ~ 6 ns)
6x10-7
6x10-9
2009/10/1
2009/10/1
LCWA09, Albuquerque
LCWA09, Albuquerque 17

18. Groove structure Result
Y. Suetsugu (KEK)
Result
The electron density decreased to 1/6~1/10 compared to the case of a flat surface.
[5 mm groove]
Flat
Groove
1585 bunches
(Bs ~ 6 ns)
Vr = 0 V
[Linear scale]
4x10-7
4x10-7
Center
2009/10/1
2009/10/1
LCWA09, Albuquerque
LCWA09, Albuquerque 18

19. Clearing electrodes for DAFNE
D.Alesini, A.Battisti, R. Sorchetti, V. Lollo (LNF)

20. Clearing electrodes installation: Wigglers
D.Alesini, A.Battisti, R. Sorchetti, V. Lollo (LNF)

21. Electrodes Field and e-Cloud build-up
Simulation unsing POSINST code of electron cloud build-up and suppression with clearing electrodes.

22. e-cloud summary
Simulations indicate that a peak secondary electron yield of 1.2 and 99% antechamber protection result in a cloud density close to the instability threshold.
Planned use of coatings (TiN, ?) and solenoids in SuperB free field regions can help.
Ongoing studies on mitigation techniques (grooves in the chamber walls, clearing electrodes) 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).
Needs:
more cpu power to track single bunch instability through a real lattice.
“stable” set of ring parameters.

23. Bane's approximation
K. Bane, “A Simplified Model of Intrabeam Scattering,” Proceedings of EPAC 2002, Paris (Fr.).

24. Calculations procedure
Evaluate equilibrium emittances ei and radiation damping times ti at low bunch charge
Evaluate the IBS growth rates 1/Ti(ei) for the given emittances, averaged around the lattice, using K. Bane approximation (EPAC02)
Calculate the "new equilibrium" emittance from:
For the vertical emittance use* :
where r varies from 0 (y generated from dispersion) to 1 (y generated from betatron coupling)
Iterate from step 2
* K. Kubo, S.K. Mtingwa, A. Wolski, "Intrabeam Scattering Formulas for High Energy Beams," Phys. Rev. ST Accel. Beams 8, (2005)

25. SuperB parameters Sep. 09 configuration
HER
LER IP
E[Gev]
h[nm]
v [pm]
s [mm]
p/p
h/ s [ms]
HER
6.7
1.6 4 5
6.15e-4
30/15
LER
4.12
2.6 7
6.57e-4
40/20

26. IBS in SuperB HER Sep.09 configuration
gr.~9%
gr.~9%
gr.~7%
gr.~4%
gr.~4%

27. IBS in SuperB LER Sep.09 configuration
gr.~19%
gr.~18%
gr.~16%
gr.~7%
gr.~7%

28. Recovering nominal emittance in LER
gr.~24%
same optics
smaller emittance

29. Parameters & IBS S. Siniatkin (BINP) Parameter Unit Value Input data
Energy
GeV
4.18
Number of particle
5.7*1010
Hor. Emmitance Em_x0
nm*rad
2.2
Coupling %
0.25
Energy spread dE_0
6.57*10-4
Damping time x / y / s
msec
44 / 44 / 22
Length Sigma_s0 mm 5
Voltage RF MV
4.1
fRF
MHz
475.8
Bucket RF
2.22
Result[1,2]
Ratio Em_x_IBS/Em_x0
1.23
Ratio dE_IBS/dE_0
1.11
S. Siniatkin (BINP)

30. IBS Summary
The effect of IBS on the transverse emittance is reasonably small for both rings in the Sep. 09 configuration
An interesting study: develop a MonteCarlo code to study the beam size distribution in the presence of IBS

31. Changing behavior of Twiss function
- increasing separation between horizontal and vertical beta functions. It is result to changing of compensation sextupole scheme;
Fig.8
S. Siniatkin (BINP)

32. 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.