1. Electron Cloud in Positron Rings and Intra-beam Scattering
Mauro Pivi, MedAustron - work made while at SLAC -
in collaboration with: T. Demma (Frascati & LAL), the ILC / CLIC and SuperB Working Groups, colleagues at LBNL, Cornell University and SLAC.

2. Intra-beam scattering
Intra-beam scattering (IBS) is associated with multiple small angle scattering events leading to emittance growth.
In most storage rings, typical radiation damping times are shorter than IBS growth times and IBS effect is not observed.
However, for high population and ultra-low emittance bunches, IBS may lead to emittance increase  IBS important for future colliders.

3. IBS Formalisms, models and simulation tools
Piwinski, Bjorken and Mtingwa formalisms
First formalisms ‘70/’80 for calculating IBS growth rates in storage rings based for Gaussian bunch distributions
K. Bane model
High energy approximation for Gaussian beams
A. Chao model
Novel analytical model, coupled differential eqs. valid for Gaussian beams
Semi-analitical model
Using fit parameters from simulations iteratively, estimate emittance
Monte Carlo macroparticle tracking code (T. Demma et al.)
6-D Monte Carlo, realistic studies for non-Gaussian beam distributions
‘IBS-Track’ based on Zenkevich-Bolshakov Algorithm
aims at exploring final equilibrium for non-Gaussian beams. Tails.
ex, ey and ez evolution in time
Methods are in good agreement
M. Boscolo, USR Workshop, Oct.30th 2012

4. IBS – Monte Carlo code based on Zenkevich-Bolshakov Algorithm
During the two particles small angle collision, the momentum change for 1 particle can be expressed as:
with the equivalent polar angle eff and the azimuthal angle  distributing uniformly in [0; 2], the invariant changes caused by the equivalent random process are the same as that of the IBS in the time interval ts
M. Pivi, December 2015

5. Intrabeam Scattering in SuperB LER
Parameter
Unit
Value
Energy
GeV
4.18
Bunch population
1010
6.5
Circumference m
1257
Emittances (H/V)
nm/pm
1.8/4.5
Bunch Length mm
3.99
Momentum spread %
0.0667
Damping times (H/V/L) ms
40/40/20
N. of macroparticles -
105
N. of grid cells
64x64x64
Bane
Piwinski
IBS-Track
Bane
Piwinski
IBS-Track
T.Demma, INFN
December 2011

6. Emittance Evolution in SuperB LER
SuperB V12 LER
Nb= 2x x1010
F=10
tx = 10-1 x 40 ms
ty = 10-1x 40 ms
ts = 10 -1x 20 ms
T.Demma, INFN
December 2011

7. Simulations for SuperB
Equilibrium horizontal emittance vs bunch current
Equilibrium longitudinal emittance vs bunch current
The easy computable semi-analytical approach allows a quick scan of some key design parameters, such as the bunch population
M. Boscolo, USR Workshop, Oct.30th 2012

8. Intra-Beam Scattering (IBS) Simulation Algorithm: CMAD
The Monte Carlo IBS routine was imported in the CMAD (M.P.) code by Theo Demma.
CMAD parallel code: Collective effects & MAD
Accelerator lattice uploaded from MADX files
Bunch particles are 6D tracked along the ring.
The IBS scattering routine is called, at each element in the ring. IBS method:
All beam particles are grouped in cells.
Each 2 particles within a cell are coupled.
Momentum of 2 particles is changed due to scattering.
Radiation damping and excitation effects are evaluated at each turn.
Code physics: Electron Cloud + IBS + Radiation Damping & Quantum Excitation
IBS applied at each element of the Ring
M.Pivi, A.Chao, C.Rivetta, T.Demma, M.Boscolo, F. Antoniou, K.Li, Y.Papaphilippou, K.Sonnad, IPAC2012
T. Demma, M. Pivi
May 9-11, 2012
Mauro Pivi, CERN, CLIC

9. IBS modeling: animation

10. IBS - SuperB LER Bane IBS-Track Piwinski C-MAD IBS-Track
Parameter
Unit
Value
Energy
GeV
4.18
Bunch population
1010
6.5
Circumference m
1257
Emittances (H/V)
nm/pm
1.8/4.5
Bunch Length mm
3.99
Momentum spread %
0.0667
Damping times (H/V/L) ms
40/40/20
N. of macroparticles -
105
N. of grid cells
64x64x64
Bane
Piwinski
IBS-Track
IBS-Track
C-MAD
T. Demma (INFN), M. Pivi (SLAC)
December 2011

11. Emittance Evolution in SuperB LER
M. Pivi (SLAC), T. Demma (INFN)

12. IBS Distribution study: tails
Parameter
c2799
Confidence Z
<1e-6 X Y
0.6920
T. Demma (INFN), M. Pivi (SLAC)

13. SIRE: IBS Distribution study in CLIC DR: tails
Parameter
c2999
Confidence
Dp/p
3048.7
<1e-15 X
1441.7 Y
1466.9
Parameter
Value
Eq. ex (m rad)
2.001e-10
Eq. ey (m rad)
2.064e-12
Eq. sd
1.992e-3
Eq. sz (m)
1.687e-3
A. Vivoli (CERN)

14. IBS - Swiss Light Source (SLS)
-- 6×109 ppb
-- 60 ×109 ppb
×109 ppb
Evolution of the emittances obtained by tracking with IBS for different bunch populations. Horizontal lines: Piwinski (full) and Bane (dashed) models for the considered bunch populations.
Comparison with experimental data at SLS: F. Antoniou et al. IPAC 2012
IBS_Track, T. Demma (INFN)

15. Summary IBS
Both tracking codes (INFN/CERN), that implement the Zenkevich-Bolshakov algorithm, successfully benchmarked with conventional theories (i.e. K. Bane) and with the novel semi-analytical model.
Monte Carlo code was implemented in the parallelized CMAD code
Comparison between theoretical models and multi-particle algorithms, give good agreement for IBS dominated regimes.
IBS features that cannot be studied by analytical models such as the impact on the damping process and the generation of non- Gaussian tails can be investigated with multi-particles tracking codes.
Code benchmarked with SLS real data [F. Antoniou et al., IPAC2012], planned also with CESR-TA data.
Multi-particle codes are suited for studies of ultra-low emittance beams for future colliders.

16. Electron cloud effect in proton and positron storage rings
In a positron or proton storage ring, electrons are generated by a variety of processes, and can be accelerated by the beam to hit the vacuum chamber with sufficient energy to generate multiple “secondary” electrons (multipacting).
Under certain conditions, the “electron cloud” density can reach high levels and can drive the beam unstable, increase the beam emittance, vacuum etc. decreasing the collider performances.
Electron cloud in the LHC
25 ns
25 ns

17. The Secondary Electron Yield (SEY) on a surface: Key Parameter for Electron Multiplication
Surface measurements at SLAC. F. Le Pimpec et al.
The secondary electron yield (SEY) is the number of electrons emitted per primary incident electron. It depends on:
the energy of the incident electron
Surface treatment and history
For convenience the SEY maximum value is often quoted.

18. Observations of Electron Cloud
J. Flanagan et al.
H. Fukuma et al.
KEK-B accelerator, Japan: the vertical bunch size increases along the train due to the build-up of the electron cloud density.
Electron cloud has been observed in several accelerators including: PEP-II, DAFNE, CESRTA, CERN SPS and at LHC.

19. Electron cloud assessment Linear Colliders working group: Worldwide Laboratory Effort
Development of mitigation techniques: e- conditioning, surface coatings, clearing electrodes, grooves, solenoids
SEY measured on samples placed in accelerator environments: SLAC, CERN, KEK, CesrTA, Dafne
Instability simulations: to determine instability threshold
Build-up & evolution simulations: fed with measured SEY to evaluate level of electron cloud in the accelerator
Converge to recommendation for adoption of mitigations
Jan 18, ILC BAW-2
Global Design Effort

20. Electron Cloud Effect Mitigations
Electron “scrubbing” or “conditioning”: electrons impinging on the surface.  decrease of SEY linked to surface “graphitization”
Secondary electron Yield (dmax) vs electron dose for different electron energies on LHC beam screen colaminated Cu.
R. Cimino, T. Demma, M. Commisso, D. R. Grosso, V. Baglin, R. Flammini and R. Larciprete Phys. Rev. Lett. 109, – 2012

21. Electron Cloud Technical Mitigations
Surface coating with low Secondary Electron Yield material
Surface with grooves confine electrons
Coating and grooves e-
Solenoid magnetic field modifies electron dynamics
“Clearing” electrodes capture electrons in the time between bunches.

22. Recommendation of Electron Cloud Mitigations
amorphous-Carbon, CERN
Grooves on Cu
Grooves w/TiN coating, KEK/SLAC
Manufacturing Techniques & Quality
Reliable Feedthroughs
CESRTA
Clearing
Electrode
Stable Structures
Clearing Electrodes
KEK

23. Evaluation of Electron Cloud Effect
Used two categories of simulation codes:
The build-up codes: follow the evolution in time of the electron cloud interacting with a stable (fixed) beam.
Secondary electron yields as measured in accelerator environments and all technical mitigations are included in simulations.
The beam instability codes: assume already formed clouds with given density and track the beam particles.
used to define the cloud density that results in an instability threshold.

24. Beam Instability Code: CMAD
CMAD (M. Pivi, Theo Demma, Kiran Sonnad, Claudio Rivetta):
The code simulates:
electron cloud instability. (Mauro P., Kiran S.)
Intra-beam scattering (Theo D.)
Feedback system to mitigate electron cloud instability (Claudio R.)
The accelerator model is uploaded via MAD-X.
The code tracks the beam for several turns and computes the electromagnetic interaction between particles in the beam and the electrons in the cloud. Parallelized code.
CMAD has been used at a number of institutions including CesrTA Cornell University, Frascati Laboratory Italy and SLAC.
M. Pivi, in the Proceedings PAC07 Conference THPAS066 (2007)

25. Electron Cloud instability threshold
3.2 km ILC Damping Ring
Cloud density (e/m3)
4.4e11
3.9e11
3.5e11
Instability simulations for the International Linear Collider Positron Damping Ring. Instability threshold ~2×1011 e/m3

26. Build up simulations: Quadrupole in wiggler section
Electron cloud density (e/m3) Electron energies (eV)
J. Crittenden, Cornell U.

27. Sextupole in TME arc cell
Electron cloud density (e/m3) Electron energies (eV)
J. Crittenden, Cornell U.

28. Build-up simulations: Model of clearing electrode in wiggler magnets
Modeling of clearing electrode: round chamber is used
Clearing Field (left) & potential (right)
L. Wang, SLAC

29. Build-up simulations: Electrodes with negative (above) or positive (below) potential
detail 0v
-300V
-600V
+600V
+600V
+400V
+100V
L. Wang, SLAC

30. Mitigations: Wiggler Chamber with Clearing Electrode
Thermal spray tungsten electrode and Alumina insulator
0.2mm thick layers
20mm wide electrode in wiggler
Antechamber full height is 20mm
Joe Conway – Cornell U.

31. Mitigations: Dipole Chamber with Grooves
20 grooves (19 tips)
0.079in (2mm) deep with 0.003in tip radius
0.035in tip to tip spacing
Top and bottom of chamber
Joe Conway – Cornell U.

32. Electron Cloud Mitigation Recommendation
Dedicated ILC DR Workshop at Cornell University, NY, USA on Recommendation on electron cloud mitigations
Efficacy
Photoelectric yield (PEY)
Secondary emission yield (SEY)
Ability to keep the vertical emittance growth below 10%
Cost
Design and manufacturing of mitigation
Maintenance of mitigation
Ex: Replacement of clearing electrode PS
Operational
Ex: Time incurred for replacement of damaged clearing electrode PS
Risk
Mitigation manufacturing challenges:
Ex: ≤1mm or less in small aperture VC
Ex: Clearing electrode in limited space or in presence of BPM buttons
Technical uncertainty
Incomplete evidence of efficacy
Incomplete experimental studies
Reliability
Durability of mitigation
Ex: Damage of clearing electrode feed-through
Impact on Machine Performance
Impact on vacuum performance
Ex: NEG pumping can have a positive effect
Ex: Vacuum outgassing
Impact on machine impedance
Ex: Impedance of grooves and electrodes
Impact on optics
Ex: x-y coupling due to solenoids
Operational
Ex: NEG re-activation after saturation
Global Design Effort
Nov 3-4, CLIC coll. meeting

33. Structured Evaluation of EC Mitigations
Criteria for the evaluation of mitigations: Working Group rating
Efficacy of Mitigation
Costs
Risks
Impact on Machine
Rating 10 1 4
Normalized Weighting
0.53
0.05
0.21
Nov 3-4, CLIC coll. meeting
Global Design Effort

34. Summary of Electron Cloud Mitigation Plan
Mitigation Evaluation conducted at ILC DR Working Group Workshop meeting
ILC Working Group Baseline Mitigation Recommendation
Drift*
Dipole
Wiggler
Quadrupole*
Baseline Mitigation I
TiN Coating
Grooves with TiN coating
Clearing Electrodes
Baseline Mitigation II
Solenoid Windings
Antechamber
Alternate Mitigation
Carbon coating/ NEG Coating
Grooves with TiN Coating
Clearing Electrodes or Grooves
*Drift and Quadrupole chambers in arc and wiggler regions will incorporate antechambers
CESRTA results and simulations suggest the possible presence of sub-threshold emittance growth
Further investigation required
May require reduction in acceptable cloud density a reduction in safety margin
Aggressive mitigation plan is required to obtain optimum performance from the 3.2km positron damping ring and to pursue the high current option
M. Pivi, S. Guiducci, M. Palmer, J. Urakawa on behalf of the ILC DR Electron Cloud Working Group
Global Design Effort

35. Completing evaluation for ILC
With recommended mitigations the ring-average cloud density is 4×1010 e/m3, well below the instability threshold of 2×1011 e/m3.
ILC Technical Design Report 2012: implemented technical mitigations allowed reducing the size of the ILC damping rings to 3.2km (17km in 2004).
Mitigations adopted also at SuperKEKB and Daphne.

36. Electron cloud evolution with clearing electrodes (POSINST)
DAFNE: Clearing Electrodes D. Alesini, T. Demma et al. , in Proc. of IPAC 2010.
Electric Field as computed by POISSON
Clearing electrodes are installed in the vacuum chambers of wigglers and dipoles of DAFNE positron ring.
Electron cloud evolution with clearing electrodes (POSINST)
Time (ns)
Theo Demma, INFN

37. Clearing electrodes in DaFne
Simulated evolution of the cloud density for different electrode voltage.
Clearing electrodes ON/OFF: horizontal tune shift of
D. Alesini, A. Drago, A. Gallo, S. Guiducci, C. Milardi, A. Stella, M. Zobov, S. De Santis, T. Demma, P. Raimondi, Phys Rev. Letters 110, (2013)

38. Effect of clearing electrodes on beam in DaFne
Electrodes OFF
Electrodes ON
Beam dimension (um) at the Synchrotron light monitor turning all electrodes progressively off.
Horizontal fractional tune as a function of bunch number along train of bunches.
Growth rate of horizontal instability for different clearing electrode voltages.
D. Alesini, A. Drago, A. Gallo, S. Guiducci, C. Milardi, A. Stella, M. Zobov, S. De Santis, T. Demma, P. Raimondi, IPAC 2012

39. Electrod cloud mitigations in DaFne: clearing electrodes
Clearing electrodes installed in DaFne dipoles and wigglers
Experimental measurements have shown an impressive effectiveness of these devices in mitigating the e-cloud.
Electrodes ON indicate an evident reduction of the electron cloud density.
Electrodes allowed reducing the beam size, increase the instabilities growth rate, increase the beam current and luminosity.

40. T. Demma: Preliminary results for SuperB
Vertical emittance growth induced by e-cloud
Input parameters (LNF conf.) for CMAD
=5x1011
=4x1011
=3x1011
Beam energy E[GeV]
6.7
circumference L[m]
1200
bunch population Nb
5.7x1010
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 Interaction Points 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:

41. Buildup in Free Field Regions
Snapshot of the electron (x,y) distribution 50G solenoids on
Snapshot of the electron (x,y) distribution
Solenoids reduce to 0 the e-cloud density at center of beam pipe
Density at center of the beam pipe is larger then the average value.

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

43. Single Bunch 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
SuperB V12
center
1012 [e-/m3]
0.1
0.07
0.6
0.2
2.0
0.7
th= 1012 [e-/m3]

44. T.Demma: Summary of electron cloud evaluation for SuperB
Single bunch instability simulations for SuperB HER V12 taking into account the effect of solenoids have been performed using CMAD. They indicate a threshold density of ~1012 e-/m3 (roughly 2 times previous estimates).
Build-up simulations Indicate SEY<1.2, eta < 0.05 as safe region for the single-bunch instability..
But:
what is our confidence level in reaching these safe SEY values even including countermeasure such as antechambers, coatings, grooves, clearing electrodes…?
Do we have reliable estimates (from measurements) of parameters such as PEY, photon reflectivity…?
December 2011

45. Multi-particle code simulations
CODE DEVELOPMENT
SUMMARY
Evaluation of electron cloud build-up and instability in LHC, Super-B, ILC
Evaluation of IBS in ultra-low emittance rings: CLIC, Super-B
Validation of mitigations
T. Demma and M. Pivi, Collective effects in Super-B, IPAC 2010
C-MAD 0V
+100V
+1000V
Electron cloud: emittance growth with cloud density in Super-B
Electron cloud: clearing electrodes in Super-B
IBS in Super-B; Theory compared with C-MAD and IBS-Track codes.
Mauro Pivi