1. Observations and Predictions for DAFNE and SuperB
Theo Demma - LAL

2. Plan of Talk Observation and prediction for DAFNE
Introduction
Analysis of the e-cloud induced DAFNE
Coupled bunch
Clearing electrodes for DAFNE dipoles and wigglers
Summary
Predictions for SuperB
Electron Cloud Single Bunch Instability
Simulations
Electron Cloud Build-Up
Dipole
Quadrupole

3. The DANE Collider BTF Energy per beam 510 [MeV] Machine length 97 [m]
Max. beam current
(KLOE run)
2.5(e-) 1.4(e+) [A]
N of colliding bunches
100
RF frequency
[MHz]
RF voltage
200[kV]
Harmonic number
120
Bunch spacing
2.7[ns]
Max ach. Luminosity
(SIDDHARTA run)
4.51032 [cm-2s-1]
BTF

4. E-Cloud effects @ DAFNE
e+ current limited by a 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
Instability sensitive to orbit in wiggler and bending magnets
Main change for the 2003 was wiggler field modification

5. Characterization of the Horizontal Instability
Solenoids installed in free field regions strongly reduce pressure but have poor effect on the instability
Most unstable mode -1

6. Solenoids Off 28/05/20122
VUGPS203
VUGPL201
VUGI2001

7. PEI-M Tracking simulation K. Ohmi, PRE55,7550 (1997),K
PEI-M Tracking simulation 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.

8. Input parameters for DAFNE simulations
Bunch population Nb
2.1; (4.2 x1010)
Number of bunches nb
120; (60)
Missing bunches
Ngap
Bunch spacing
Lsep[m]
0.8;(1.6)
Bunch length
σz [mm] 18
Bunch horizontal size
σx [mm]
1.4
Bunch vertical size
σy [mm]
0.05
Chamber Radius
R [mm] 40
Hor./vert. beta function
x[m]/y[m]
4.1/1.1
Hor./vert. betatron tune
x/y
5.1/5.2
Primary electron rate
dλ/ds
0.0088
Photon Reflectivity R
100% (uniform)
Max. Secondary Emission Yeld
Δmax
1.9
Energy at Max. SEY
Εm [eV]
250
Vert. magnetic field
Bz [T]
1.7

9. Mode spectrum and growth rate
60 equispaced bunches
Beam current 1.2 A
Growth time ~ 100 turn
-1 mode (60-5-1=54)

10. Mode spectrum and growth rate
Measurment
Simulation
I[A]/nb
/T0
1/105 73
1.2/120
100
0.75/105 56
900/120 95
0.5/105
600/120
130

11. Clearing Electrodes @ DAFNE
To mitigate the e-cloud instability copper electrodes have been inserted in all dipole and wiggler chambers of the machine and have been connected to external dc voltage generators.
The dipole electrodes have a length of 1.4 or 1.6 m depending on the considered arc, while the wiggler ones are 1.4 m long.

12. Test of e-cloud clearing electrodes at DAFNE
Very positive results: vertical beam dimension, tune shift and growth rates
clearly indicate the good behaviour of these devices,
which are complementary to solenoidal windings in field free regions
Beam loss above this current
if no feedbacks
See M. Zobov Talk

13. Summary
Coupled-bunch instability has been simulated using PEI-M for the DAFNE parameters. Results are in qualitative agreement with grow-damp measurements.
Clearing electrodes for DAFNE have been designed, installed, and tested (M. Zobov Talk)

14. Super B main parameters
HER (e+)
LER (e-)
Luminosity (cm-2s- 1)
1036
C (m)
1200
E (GeV)
6.7
4.18
Crossing angle (mrad) 60
Piwinski angle
20.8
16.9
I (mA)
1900
2440
ex/y (nm/pm) (IBS)
2/5
2.5/6.2
IP sx/y (mm/nm)
7.2/36
8.9/36
sl (mm) 5
N. bunches
978
Part/bunch (x1010)
5.1
6.6
sE/E (x10-4)
6.4
7.3
bb tune shift (x/y)
0.0026/0.107
0.004/0.107
Beam losses (MeV)
2.1
0.86
Total beam lifetime (s)
254
269
Polarization (%) 80
RF (MHz)
476

15. Single Bunch Instability in SuperB HER
Input parameters for CMAD
Vertical emittance growth induced by e-cloud
Beam energy E[GeV]
6.7
circumference L[m]
1200
bunch population Nb
5.06x1010
bunch length σz [mm] 5
horizontal emittance εx [nm rad]
1.6
vertical emittance εy [pm rad] 4
hor./vert. betatron tune Qx/Qy
40.57/17.59
synchrotron tune Qz
0.01
hor./vert. av. beta function
25/25
momentum compaction 
4.04e-4
The interaction between the beam and the cloud is evaluated at 40 locations around the SuperB HER tacking into account beam size variations.
The threshold density is determined by the density at which the growth starts:

16. Electron cloud buildup simulation
Cloud buildup was calculated by code “ECLOUD” developed at CERN.
Assumptions:
- Elliptical or round 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:
e-/e+/m=dn/ds Y (1-)
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.

17. Build Up Input Parameters for ECLOUD
Bunch population Nb
5.0x1010
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
Chamber hor. Aperture
hx [mm] 50
Chamber vert. aperture
hy [mm]
Photoelectron Yield Y
0.1
Photon rate (e-/e+/m)
dn /ds
0.66
Photon Reflectivity R
100%
Max. Secondary Emission Yeld
δmax
Energy at Max. SEY
Εm [eV]
250
SEY model
Cimino-Collins ((0)=0.5)

18. Buildup in Free Field Regions
Average electron cloud density =95%
Snapshot of the electron (x,y) distribution “just before” the passage of the last bunch
Density at center of the beam pipe is larger then the average value.

19. 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

20. Electron Cloud Buildup in a 50G Solenoid
Snapshot of the electron (x,y) distribution “just before” the passage of the last bunch
max=1.4
Solenoids reduce to 0 the e-cloud density at center of beam pipe

21. Buildup in the SuperB arcs: Dipoles
HER Arc quadrupole vacuum chamber (CDR)
By=0.3 T; =99%
SEY=1.0 SEY=1.1 SEY=1.2 SEY=1.3
Snapshot of the electron (x,y) distribution “just before” the passage of the last bunch

22. 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
Densities are computed, within a region of 10σx×10σy around the beam centre.

23. Buildup in the SuperB arcs: Quadrupoles
HER 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

24. Single Bunch Instability Threshold
SuperB V12
int [1015m-2] solenoids
int [1015m-2] no solenoids
SEY=1.1
95%
0.22
2.7
99%
0.04
0.7
SEY=1.2
6.5
0.45
2.4
SEY=1.3
5.4 25
4.5 13
Instability occurs if:
where cent. ande,th are obtained from simulations.
SuperB V12

25. Summary
Simulations indicate that a peak secondary electron yield of 1.1 and 99% antechamber protection result in a cloud density below 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:
Set up a working group to clearly assess the elctron cloud effects in Superb HER and individuate needed countermeasures….
estimate other effects: multi-bunch instability, incoherent emittance growth...