1. Electron cloud and collective effects in the FCC-ee Interaction Region
E.Belli
M.Migliorati, G.Rumolo
58th ICFA Advanced Beam Dynamics Workshop
on High Luminosity Circular e+e-Colliders
October 25, 2016

2. FCC-ee beam parameter list
Circumference [km]
100
Beam energy [GeV]
45.6 80
120
175
Beam current [mA]
1450
152 30
6.6
Bunches/ beam
30180
91500
5260
780 81
Bunch spacing [ns]
7.5
2.5 50
400
4000
Bunch population [ ]
1.0
0.33
0.6
0.8
1.7
Horizontal emittance [nm]
Vertical emittance [pm]
0.2 1
0.09
0.26
0.61
1.2
1.3
Mom. Compaction[1 0 −5 ]
0.7
RF frequency [MHz]
RF voltage [GV]
0.4 3 10
Bunch length [mm]
- Synchrotron radiation
- Total
6.7
1.6
3.8
2.0
3.1
2.4
2.1
IR length [mm]
0.66
0.62
1.02
1.35
1.74

3. Outline The FCC-ee interaction region Impedance studies
Heat load due to resistive wall impedance
Heat load due to geometric impedance
Heat load due to trapped modes
Electron cloud studies
Heat load in the final quadrupoles
uniform distribution
photoemission due to synchrotron radiations
Single bunch head-tail instability
Conclusions

4. The Interaction Region
Trapped modes can escape to the outside through the larger beam pipes
Symmetric layout (M.Sullivan)
20mm radius at IP
12mm radius for outgoing-ingoing pipes
Asymmetric layout (K.Oide)
20mm at IP
13mm for ingoing pipes
20mm for outgoing pipes

5. Power loss model for impedance studies
FCC-ee beam pipes at room temperature (KEKB, SuperKEKB,etc.)
No cryogenic systems
Heat load can still represent an issue
For an uniformly filled machine (𝑀=ℎ) with bunch spacing 𝜏 𝑏 = 2𝜋 ℎ 𝜔 0 , the power loss depends only on the real part of the longitudinal impedance
Possible heat load sources in the IR
RW impedance
geometric impedance
HOMs
Electron cloud
𝑃 𝑙𝑜𝑠𝑠 = 𝐼 2 𝑝=−∞ +∞ Λ 𝑝𝑀 𝜔 𝑅𝑒[ 𝑍 ∥ (𝑝𝑀 𝜔 0 )]
𝑀= number of bunches
ℎ= harmonic number
𝑇 0 = 2𝜋 𝜔 0 = revolution period
𝐼= 𝑀𝑁𝑒 𝑇 0 = average beam current
Bunch spectrum

6. Heat load due to RW impedance
Wake fields induced by the finite resistivity of the beam vacuum chamber
Analytic formula for a circular beam pipe with radius 𝑏
𝑃 𝑙𝑜𝑠𝑠 𝐿 = 1 𝑇 0 𝑁 2 𝑒 2 𝑐 4 𝜋 2 𝑏 𝜎 𝑧 𝑍 0 2 𝜎 𝑐 Γ 𝑀
ImpedanceWake2D
3 layers:
2mm Cu or Al
2mm insulator
stainless steel
Energy [GeV]
45.6
175
Bunch spacing [ns]
7.5
2.5
4000
Bunch pop. [ ]
1.0
0.33
1.7
Bunches/beam
30180
91500 81
Bunch length [mm]
6.7
3.8
𝑷 𝒍𝒐𝒔𝒔 [W/m] (Al)
74.11
57.25
2.52
𝑷 𝒍𝒐𝒔𝒔 [W/m] (Cu) 59
45.58 2

7. Heat load due to geometric impedance
Masks after each quadrupole to shield the magnets from SR
Wake fields induced by variations in the geometry of the beam pipe
step-in + step-out
Peak at cutoff of the larger pipe
Above cutoff:
At low frequencies:
𝑅𝑒[𝑍 𝑜𝑢𝑡 ]≈ 𝑍 0 𝜋 𝑙𝑛 𝑏 𝑎
𝑅𝑒[𝑍 𝑖𝑛 ]≈0
𝑍 𝜔 =2𝑗𝜔 𝑍 0 4𝑏𝑐 ℎ 2 + 𝑙ℎ 𝜋 2𝑙𝑛 8𝜋𝑙 ℎ −3
Energy [GeV]
45.6
175
Bunch spacing [ns]
7.5
2.5
4000
Bunch population [ ]
1.0
0.33
1.7
Bunches/beam
30180
91500 81
Bunch length [mm]
6.7
3.8
𝒌 [V/pC]*
𝑷 𝒍𝒐𝒔𝒔 [W]
189.1
493.2 35
𝑃 𝑙𝑜𝑠𝑠 = 𝐸 𝑙𝑜𝑠𝑠 𝑇 𝑟𝑒𝑣 = 1 𝑇 𝑟𝑒𝑣 𝑘𝑁 2 𝑞 2
≈5.39𝑚𝑊
* from ABCI

8. Trapped modes can escape to the outside through the larger beam pipes
Trapped modes in the IR
Small variations in the beam pipe geometry can produce trapped modes
These modes cannot propagate into the pipe and therefore they remain localized near the discontinuity, producing narrow resonance peaks of the impedance.
Possible source of heating
A possible method to study HOMs:
Build CST model of the IR
Wakefield simulations (time domain)
Eigenmode simulations (frequency domain)
Extract parameters ( 𝜔 𝑟 , 𝑅 𝑠 , 𝑄) and compute
the impedance as
Compute power loss
Trapped modes can escape to the outside through the larger beam pipes
𝑍 𝜔 = 𝑅 𝑠 1+𝑗𝑄 𝜔 𝑟 𝜔 − 𝜔 𝜔 𝑟

9. HOMs – Symmetric layout
Large number of TE and TM modes
All the TM modes below cutoff ( 𝑓 𝑐𝑢𝑡𝑜𝑓𝑓 =9.57𝐺𝐻𝑧 for outgoing pipes with 12mm radius) have to be studied with particular care
≈7.6 GHz
Is there any trapped mode from eigenmode simulations corresponding to this frequency?
𝒇 𝒄𝒖𝒕𝒐𝒇𝒇 [𝑮𝑯𝒛]
𝑹 𝒔 [𝛀] 𝑸

10. Heat load due to HOMs – Symmetric layout
𝑃 𝑙𝑜𝑠𝑠 = 𝐼 2 𝑝=−∞ +∞ Λ 𝑝𝑀 𝜔 𝑅𝑒[ 𝑍 ∥ (𝑝𝑀 𝜔 0 )]
𝟏 𝝉 𝒃
Worst case when 𝜔 𝑟 ≃𝑝𝑀 𝜔 0 (resonant frequency close to an integer of a multiple of the the revolution frequency)
Realistic case (considering simulation results) gives 𝑷 𝒍𝒐𝒔𝒔 ≈𝟐.𝟕𝟒𝑾
Only longitudinal modes
Further studied are needed (statistical approach, other simulation codes, etc.)

11. HOMs – Asymmetric layout
The cutoff for outgoing pipes with 20mm radius is 𝑓 𝑐𝑢𝑡𝑜𝑓𝑓 =5.74𝐺𝐻𝑧 (same as IP)
No excited TM modes below cutoff
It seems that the are no dangerous trapped modes in the asymmetric layout case (as expected)

12. Electron cloud build up
Positively charged bunches passing through a section of an accelerator
Primary or Seed Electrons
Residual gas ionization
Molecules of the residual gas in the vacuum chamber can be ionized by the beam
Photoemission due to synchrotron radiation
Emitted photons hitting the wall can have enough energy to extract electrons from the pipe’s wall (photoelectrons)
~300𝑒𝑉
~10𝑒𝑉
Lost t
Bunch spacing
Beam pipe
Seed
Bunch

13. Electron cloud build up1 3
Primaries are attracted and accelerated by the beam to energies up to several hundreds of eV
Absorbed or reflected (no secondaries generation)
Property of the surface
𝑺𝑬𝒀(𝑬)= 𝑰 𝒆𝒎𝒊𝒕 𝑰 𝒊𝒎𝒑 (𝑬)
Scrubbing: SEY reduction through electron bombardment
𝒆 − emitter
𝒆 − absorber
~300𝑒𝑉
~10𝑒𝑉
Lost t
Bunch spacing
Beam pipe 2 4 5
Emission of secondary electrons (energies up to few tens of eV)
Accelerated by the following bunch (secondaries production)
Avalanche electron multiplication
(multipacting effect) 12

14. Electron cloud effects
The presence of the Electron Cloud in the vacuum chamber represents one of the major limitations in the accelerator performance
Heat load
Transverse beam instabilities
Emittance blow-up
Tune shift and spread
Particle losses
Degradation of the vacuum and of the beam diagnostics 16

15. Parameter list for EC studies
Energy [GeV]
45.6GeV
Bunch spacing
2.5
Bunch population [ ]
0.33
Horizontal emittance [nm]
0.09
Vertical emittance [pm] 1
Bunch length [mm]
3.8
Filling pattern
300b
(8b + 4e)x30
IR elements
Quadrupole QC1R
Sym1
3.2
26.6
53.3
8934
Asym2
1.6
46.2
34.6
10265
Quadrupole QC2R
18.7
341
4488
16.3
297
4082
1 Pipe radius 𝑟= 12mm
2 Pipe radius 𝑟= 20mm

16. Heat load in the IR quadrupoles
Initial uniform distribution of electrons in the vacuum chamber
Gaps in the bunch train allow to mitigate the EC
Multipacting threshold in IR quadrupoles ≈ 1.1
In quad1, heat load up to 3x lower in the asymmetric layout case
In quad2, heat load up to 2x lower in the asymmetric layout case and even lower with gaps in bunch train

17. Photoemission due to SR
Photons emitted by particles can extract electrons from the pipe wall, depending on their energy
Photoelectrons are usually the main source of primaries in the EC build up
𝑁 𝑝ℎ = 𝑁 𝛾 ∙𝑌
Number of SR photons per particle per meter
𝑵 𝜸 = 𝟓𝜶 𝟐 𝟑 𝜸 𝝆
Photoelectron Yield
LHC
FCC-hh
FCC-ee
E [GeV]
7000
50000
45.6 𝛄
7400
53300
89236
𝛒 [km]
2.8
11.3
𝐍 𝛄 / 𝐩 + 𝐦
0.028
0.05
0.085
Photoelectrons also produced by scattered photons
Photon reflectivity 𝑅
No experimental data for photoelectron yield and photon reflectivity
Scan of 𝒀 and 𝑹 𝜸

18. Heat load in the IR quadrupoles
2.5ns beam in the symmetric layout case (300b)
𝑌=[0.05, 0.2, 0.3] and 𝑅=[2%, 50%, 80%]
Multipacting threshold in IR quadrupoles ≈ 1.1
Heat load ≈ W/m in both quadrupoles

19. Single bunch head-tail instability
Electron cloud acts as a short range wake field with frequency
Electron density threshold of the head-tail instability
𝜔 𝑒 = 2𝜆 𝑝 𝑟 𝑒 𝑐 2 𝜎 𝑦 ( 𝜎 𝑥 + 𝜎 𝑦 )
𝜌 e, th = 2𝛾 𝜐 𝑠 𝜔 𝑒 𝜎 𝑧 /𝑐 3 𝐾𝑄 𝑟 0 𝛽𝐶
𝐾= 𝜔 𝑒 𝜎 𝑧 /𝑐,
with
𝑄=min⁡( 𝜔 𝑒 𝜎 𝑧 /𝑐, 7)

20. Single bunch head-tail instabilityZ W H tt
Circumference [km]
100
Bending radius [km]
11.3
Energy [GeV]
45.6 80
120
175
Bunch spacing [ns]
7.5
2.5 50
400
4000
Bunch population [𝟏 𝟎 𝟏𝟏 ]
1.0
0.33
0.6
0.8
1.7
Horizontal emittance [nm]
0.2
0.09
0.26
0.61
1.3
Vertical emittance [pm] 1
1.2
Averaged 𝜷 [m]
Bunch length [mm]
6.7
3.8
3.1
2.4
Synchrotron tune
0.036
0.025
0.037
0.056
0.075
Electron frequency 𝝎 𝒆 /𝟐𝝅 [GHz]
177.81
163
190.4
194.5
191.4
Electron oscillation 𝝎 𝒆 𝝈 𝒛 /𝒄 25 13
12.3
9.8 10
Density threshold 𝝆 𝒕𝒉 [𝟏 𝟎 𝟏𝟎 / 𝒎 𝟑 ]
1.88
1.30
3.39
7.7 15

21. Conclusions
Beam heat load due to RW and geometric impedances has been estimated
Lower losses for all energies in case of copper (<60 W/m for the entire beam)
Power loss due to SR masks below 1W for all the energies
A large number of trapped TE and TM modes was found in the IR symmetric layout case
Asymmetric layout seems to be the best choice for the HOMs
Multipacting threshold in IR quadrupoles ≈ 1.1
SEY < 1.1 to avoid EC in the Interaction Region
Heat load in Quad1 3x lower in asymmetric layout
Heat load in Quad2 2x lower in the asymmetric layout and even lower with gaps
Gaps in the bunch train allow to mitigate EC
Electron density threshold was evaluated for all energies
Further studies are needed
TE modes, statistical approach for HOMs
EC beam dynamics studies
filling pattern studies based on both EC and HOMs considerations

22. Thanks for your attention