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
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 [10## ]
1.0
0.33
0.6
0.8
1.7
Horizontal emittance [nm]
Vertical emittance [pm]
0.2
1
0.09
1
0.26
1
0.61
1.2
1.3
2.5
Mom. Compaction[10$% ]
0.7
RF frequency [MHz]
400
RF voltage [GV]
0.4
0.2
0.8
3
10
Bunch length [mm]
- Synchrotron radiation
- Total
1.2
6.7
1.6
3.8
2.0
3.1
2.0
2.4
2.1
2.5
IR length [mm]
0.66
0.62
1.02
1.35
1.74
Outline
Ø The FCC-ee interaction region
Ø
Impedance studies
q Heat load due to resistive wall impedance
q Heat load due to geometric impedance
q Heat load due to trapped modes
Ø
Electron cloud studies
q Heat load in the final quadrupoles
v uniform distribution
v photoemission due to synchrotron radiations
q Single bunch head-tail instability
Ø
Conclusions
The Interaction Region
Trapped modes can escape
to the outside through the
larger beam pipes
Ø Symmetric layout (M.Sullivan)
q 20mm radius at IP
q 12mm radius for outgoing-ingoing pipes
Ø Asymmetric layout (K.Oide)
q 20mm at IP
q 13mm for ingoing pipes
q 20mm for outgoing pipes
Power loss model for impedance studies
Ø FCC-ee beam pipes at room temperature (KEKB, SuperKEKB,etc.)
v No cryogenic systems
Ø Heat load can still represent an issue
Ø For an uniformly filled machine (𝑀 = ℎ) with bunch spacing 𝜏* =
depends only on the real part of the longitudinal impedance
BC
𝑃1233 = 𝐼 + 5 Λ 𝑝𝑀𝜔9
+
𝑅𝑒[𝑍∥ (𝑝𝑀𝜔9 )]
DE$C
Ø
Possible heat load sources in the IR
q RW impedance
q geometric impedance
q HOMs
q Electron cloud
the power loss
𝑀 = number of bunches
ℎ =harmonic number
+,
𝑇9 =
= revolution period
𝐼
Bunch spectrum
+,
,
-./
./
HIJ
=
K/
= average beam current
Heat load due to RW impedance
Ø Wake fields induced by the finite resistivity of the beam vacuum chamber
Ø Analytic formula for a circular beam pipe with radius 𝑏
𝑃1233
1 𝑁 + 𝑒 + 𝑐 𝑍9
3
=
Γ
𝑀
T
𝐿
𝑇9
2𝜎V 4
+
+
4𝜋 𝑏𝜎S
3 layers:
v 2mm Cu or Al
v 2mm insulator
v stainless steel
ImpedanceWake2D
Energy [GeV]
45.6
175
Bunch spacing [ns]
7.5
2.5
4000
Bunch pop. [10## ]
1.0
0.33
1.7
30180
91500
81
6.7
3.8
2.5
𝑷𝒍𝒐𝒔𝒔 [W/m] (Al)
74.11
57.25
2.52
𝑷𝒍𝒐𝒔𝒔 [W/m] (Cu)
59
45.58
2
Bunches/beam
Bunch length [mm]
Heat load due to geometric impedance
Ø Masks after each quadrupole to shield the magnets from SR
Ø Wake fields induced by variations in the geometry of the beam pipe
Ø step-in + step-out
Ø Peak at cutoff of the larger pipe
Ø Above cutoff:
c
*
𝑅𝑒[𝑍2ab ] ≈ / 𝑙𝑛
𝑅𝑒[𝑍^_ ] ≈ 0
,
Ø At low frequencies:
f
𝑍9 + 𝑙ℎ
8𝜋𝑙
𝑍 𝜔 = 2𝑗𝜔
ℎ +
2𝑙𝑛
−3
4𝑏𝑐
𝜋
ℎ
Energy [GeV]
175
Bunch spacing [ns]
7.5
2.5
4000
Bunch population [10## ]
1.0
0.33
1.7
30180
91500
81
6.7
3.8
2.5
8.077 10-3
6.38 10-2
1.93 10-1
189.1
493.2
35
Bunches/beam
Bunch length [mm]
𝒌 [V/pC]*
𝑷𝒍𝒐𝒔𝒔 [W]
*
45.6
from ABCI
𝑃1233 =
𝐸1233
1
=
𝑘𝑁 + 𝑞 +
𝑇mJn
𝑇mJn
≈ 5.39𝑚𝑊
Trapped modes in the IR
Ø Small variations in the beam pipe geometry can produce trapped modes
Ø These modes cannot propagate into the pipe and therefore they remain localized near
the discontinuity, producing narrow resonance peaks of the impedance.
Ø Possible source of heating
Ø A possible method to study HOMs:
q
q
q
q
Build CST model of the IR
Wakefield simulations (time domain)
Eigenmode simulations (frequency domain)
Extract parameters (𝜔m , 𝑅3 , 𝑄) and compute
the impedance as
𝑍 𝜔 =
𝑅3
𝜔
𝜔
1 + 𝑗𝑄 m −
𝜔 𝜔m
q Compute power loss
Trapped modes
can escape to the
outside through the
larger beam pipes
HOMs – Symmetric layout
Ø Large number of TE and TM modes
Ø All the TM modes below cutoff (𝑓Vab2yy = 9.57𝐺𝐻𝑧 for outgoing pipes with 12mm radius) have to be
studied with particular care
≈7.6 GHz
Ø Is there any trapped mode from eigenmode simulations
corresponding to this frequency?
𝒇𝒄𝒖𝒕𝒐𝒇𝒇 [𝑮𝑯𝒛]
𝑹𝒔 [𝛀]
𝑸
7.618923
5883.42
19510.92
Heat load due to HOMs – Symmetric layout
BC
𝑃1233 = 𝐼 + 5 Λ 𝑝𝑀𝜔9
+
𝑅𝑒[𝑍∥ (𝑝𝑀𝜔9 )]
DE$C
𝟏
𝝉𝒃
Worst case when 𝜔m ≃ 𝑝𝑀𝜔9
(resonant frequency close to an
integer of a multiple of the the
revolution frequency)
Ø Realistic case (considering simulation results) gives 𝑷𝒍𝒐𝒔𝒔 ≈ 𝟐. 𝟕𝟒𝑾
q Only longitudinal modes
q Further studied are needed (statistical approach, other simulation codes, etc.)
HOMs – Asymmetric layout
Ø The cutoff for outgoing pipes with 20mm radius is 𝑓Vab2yy = 5.74𝐺𝐻𝑧(same as IP)
No excited TM modes
below cutoff
It seems that the are no dangerous
trapped modes in the asymmetric
layout case (as expected)
Electron cloud build up
Ø Positively charged bunches passing through a section of an accelerator
Ø Primary or Seed Electrons
o Residual gas ionization
Molecules of the residual gas in the vacuum chamber can be ionized by the beam
o Photoemission due to synchrotron radiation
Emitted photons hitting the wall can have enough energy to extract electrons from the pipe’s
wall (photoelectrons)
Beam pipe
Seed
Lost
Bunch
Bunch spacing
t
Electron cloud build up
1
Primaries are attracted and
accelerated by the beam to energies
up to several hundreds of eV
Property of the surface
Beam pipe
𝒆$ emitter
Lost
𝒆$ absorber
Bunch spacing
2
12
Emission of secondary
electrons (energies up to
few tens of eV)
𝑰𝒆𝒎𝒊𝒕
𝑺𝑬𝒀(𝑬) = 𝑰𝒊𝒎𝒑(𝑬)
t
Scrubbing: SEY reduction through electron
bombardment
Electron cloud build up
1
Primaries are attracted and
accelerated by the beam to energies
up to several hundreds of eV
3
Absorbed or reflected
(no secondaries
generation)
Beam pipe
Lost
Bunch spacing
2
12
Emission of secondary
electrons (energies up to
few tens of eV)
t
4
Accelerated by the
following bunch
(secondaries production)
5
Avalanche electron
multiplication
(multipacting effect)
Electron cloud effects
The presence of the Electron Cloud in the vacuum chamber represents one of the major
limitations in the accelerator performance
Ø Heat load
Ø Transverse beam instabilities
Ø Emittance blow-up
Ø Tune shift and spread
Ø Particle losses
Ø Degradation of the vacuum and of the beam diagnostics
16
Parameter list for EC studies
Energy [GeV]
45.6GeV
Bunch spacing
2.5
Bunch population [10## ]
0.33
Horizontal emittance [nm]
0.09
Vertical emittance [pm]
1
Bunch length [mm]
3.8
Filling pattern
IR elements
300b
(8b + 4e)x30
Quadrupole QC1R
Quadrupole QC2R
1
2
Pipe radius 𝑟 = 12mm
Pipe radius 𝑟 = 20mm
Sym1
3.2 26.6
53.3
8934
Asym2
1.6 46.2
34.6
10265
Sym1
2.5 18.7
341
4488
Asym2
2.5 16.3
297
4082
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
Ø Multipacting threshold in IR quadrupoles ≈ 1.1
Ø In quad1, heat load up to 3x lower in the asymmetric layout case
Ø In quad2, heat load up to 2x lower in the asymmetric layout case and even lower with gaps in
bunch train
Photoemission due to SR
Ø Photons emitted by particles can extract electrons from the pipe wall, depending on their
energy
Ø Photoelectrons are usually the main source of primaries in the EC build up
𝑁D- = 𝑁 ¡ 𝑌
Number of SR photons per particle per meter
𝟓𝜶 𝜸
𝑵𝜸 =
𝟐 𝟑𝝆
LHC
FCC-hh
FCC-ee
E [GeV]
7000
50000
45.6
𝛄
7400
53300
89236
2.8
11.3
11.3
0.028
0.05
0.085
𝛒 [km]
𝐍𝛄 /𝐩B 𝐦
Photoelectron Yield
Ø Photoelectrons also produced by
scattered photons
q Photon reflectivity 𝑅
Ø No experimental data for photoelectron
yield and photon reflectivity
ü Scan of 𝒀 and 𝑹𝜸
Heat load in the IR quadrupoles
2.5ns beam in the symmetric layout case (300b)
Ø 𝑌 = [0.05, 0.2, 0.3] and 𝑅 = [2%, 50%, 80%]
Ø Multipacting threshold in IR quadrupoles ≈ 1.1
Ø Heat load ≈300-400 W/m in both quadrupoles
Single bunch head-tail instability
Ø Electron cloud acts as a short range wake field with frequency
𝜔J =
2𝜆D 𝑟J 𝑐 +
𝜎ª (𝜎« + 𝜎ª )
Ø Electron density threshold of the head-tail instability
𝜌-,®¯ =
2𝛾𝜐3 𝜔J 𝜎S /𝑐
3𝐾𝑄𝑟9 𝛽𝐶
with
𝐾 = 𝜔J 𝜎S /𝑐,
𝑄 = min(𝜔J 𝜎S /𝑐, 7)
Single bunch head-tail instability
Z
W
H
tt
80
120
175
Circumference [km]
100
Bending radius [km]
11.3
Energy [GeV]
45.6
Bunch spacing [ns]
7.5
2.5
50
400
4000
Bunch population [𝟏𝟎𝟏𝟏 ]
1.0
0.33
0.6
0.8
1.7
Horizontal emittance [nm]
0.2
0.09
0.26
0.61
1.3
1
1
1
1.2
2.5
Vertical emittance [pm]
Averaged 𝜷 [m]
Bunch length [mm]
100
6.7
3.8
3.1
2.4
2.5
Synchrotron tune
0.036
0.025
0.037
0.056
0.075
Electron frequency 𝝎𝒆 /𝟐𝝅 [GHz]
177.81
163
190.4
194.5
191.4
25
13
12.3
9.8
10
1.88
1.30
3.39
7.7
15
Electron oscillation 𝝎𝒆 𝝈𝒛 /𝒄
Density threshold 𝝆𝒕𝒉 [𝟏𝟎𝟏𝟎 /𝒎𝟑 ]
Conclusions
Ø Beam heat load due to RW and geometric impedances has been estimated
q Lower losses for all energies in case of copper (< 60 W/m for the entire beam)
q Power loss due to SR masks below 1W for all the energies
Ø A large number of trapped TE and TM modes was found in the IR symmetric layout case
q Asymmetric layout seems to be the best choice for the HOMs
Ø Multipacting threshold in IR quadrupoles ≈ 1.1
q SEY < 1.1 to avoid EC in the Interaction Region
Ø Heat load in Quad1 3x lower in asymmetric layout
Ø Heat load in Quad2 2x lower in the asymmetric layout and even lower with gaps
q Gaps in the bunch train allow to mitigate EC
Ø Electron density threshold was evaluated for all energies
Ø
Further studies are needed
q TE modes, statistical approach for HOMs
q EC beam dynamics studies
q filling pattern studies based on both EC and HOMs considerations
Thanks for your attention