1. Eirini Koukovini-Platia EPFL, CERN
Effect of impedance and coatings in the CLIC damping rings
Eirini Koukovini-Platia EPFL, CERN
3rd Low Emittance Ring workshop - 8th-10th July Oxford

2. Introduction Damping Rings
CLIC DR parameters
Small emittance, short bunch length and high current
Rise to collective effects which can degrade the beam quality
Their study and control will be crucial
3rd Low Emittance Ring workshop - 8th-10th July Oxford

3. Impedance budget and coating
Focus on single bunch instabilities driven by impedance
Define an impedance budget
To suppress some of the collective effects, coating will be used
Positron Damping Ring (PDR): electron-cloud effects  amorphous carbon (aC)
Electron Damping Ring (EDR): fast ion instabilities  need for ultra-low vacuum pressure  Non-Evaporable Getter (NEG)
Techniques to fight electron cloud or have good vacuum do not come for free and can be serious impedance sources
Suppress the built up of e cloud  treating the vacuum chamber surface  coating with a low SEY (1.2 after conditioning) material  aC
Ion effects  residual gas can be ionized  good vacuum  NEG
3rd Low Emittance Ring workshop - 8th-10th July Oxford

4. Resistive Wall Impedance: Various options for the pipe
Vertical impedance in the wigglers (3 TeV option) for different materials
Resonance peak of ≈1MW/m at almost 1THz for C- coated Cu
Coating is “transparent” up to ~10 GHz
But at higher frequencies some narrow peaks appear
Above 10 GHz the impact of coating is quite significant
N. Mounet, LER Workshop, January 2010

5. Single bunch simulations without space charge to define the instability thresholds
HEADTAIL code
Simulates single/multi bunch collective phenomena associated with impedances
Computes the evolution of the bunch by bunch centroid as a function of time
ImpedanceWake2D
Computes the longitudinal and transverse wake functions of multilayer structures, cylindrical or flat
Goal
Estimate the available impedance budget for the various elements to be installed after known impedance sources such us the broad-band resonator, the resistive wall and the kickers are considered
3rd Low Emittance Ring workshop - 8th-10th July Oxford

6. Estimating the impedance budget with a 4-kick approximation
Straight section:
13 FODO
FODO cell
9mm radius round
6mm radius, flat
ARC (9mm round):
DS1- 47 TME cells - DS2
wiggler
wiggler QF QD
A uniform coating of NEG, 2μm thickness, on stainless steel pipe
The contributions from the resistive wall of the beam chamber were singled out for both the arc dipoles and the wigglers
52 wigglers per DR, 2m long each
1st kick broadband resonator
2nd kick  resistive wall from the arcs
3rd kick wigglers
4th kick  rest of the FODO
3rd Low Emittance Ring workshop - 8th-10th July Oxford

7. Estimating the machine impedance budget with a 4-kick approximation – single bunch simulations
Mode spectrum of the horizontal and vertical coherent motion as a function of impedance (applying an FFT to the HEADTAIL output)
TMCI 15 MΩ/m
TMCI 4 MΩ/m
For zero chromaticity, the (remaining) impedance budget is estimated at 4 MΩ/m
No mode coupling
Higher TMCI thresholds
Head-tail instability
<bx>=3.475m, <by>=9.233m
x y kick of 1e-5 m ξx
0.055 ξy
0.057
For positive chromaticity, the impedance budget is estimated now at 1 MΩ/m
3rd Low Emittance Ring workshop - 8th-10th July Oxford

8. 6-kick study- adding stripline kickers
2 kickers in the DR (injection&extraction)
Calculate the wake function, and add this wake as a kick in our impedance model
Idea: Use the shortest bunch length possible in the CST simulation so that the wake function (input for HEADTAIL) could be approximated with the wake potential (output of CST)
CST simulation
R=25mm, Aperture=12mm/20mm, h=20mm, Thickness=4mm
By Rob: length of the kicker=2.56 m for 12 mm aperture
L=3.58 m for 20 mm aperture
Bunch of 0.2 mm
3 lines per wavelength
~150 million meshcells
time consuming simulation
Untrustworthy results
Use at least 10 lines per wavelength
1 billion meshcells!
Limit for CST
Design from Carolina Belver-Aguilar, IFIC

9. Next steps on the stripline kickers study
Convergence study with numerical parameters showed that the wake potential from CST in this frequency range (requires a very dense meshing and very long computational times) can not be just used as the wake function (for HEADTAIL simulations)
Further work needs to be done to understand and possibly overcome this problem. Benchmark of CST with other codes (such as the ImpedanceWake2D for resistive wall problems and GDfidl for geometric impedances) has also begun
Try ABCI (Azimuthal Beam Cavity Interaction)
Calculations of wake fields, wake potentials, loss factors and impedance
3rd Low Emittance Ring workshop - 8th-10th July Oxford

10. Motivation for the material EM properties characterization
Code calculating wake fields/ impedances
EM properties of NEG and aC
Instabilities studies for the CLIC DR
Need to characterize the properties of the coating materials at high frequencies (CLIC), i.e GHz
Wakes (time domain) of short bunches and impedances (frequency domain) at high frequencies
Characterize the electrical conductivity of NEG
Unknown values of the conductivity in this frequency range
3rd Low Emittance Ring workshop - 8th-10th July Oxford

11. Material EM properties characterization
Establishing and testing a method to measure the properties of NEG
Combine experimental results with CST simulations to characterize the electrical conductivity of NEG
Powerful tool for this kind of measurements
Experimental method
CST MWS simulation
Intersection
Study of instabilities with HEADTAIL
Material
properties
σ, ε, μ
Calculation of the wake fields
50 cm Cu wg
9-12 GHz
3rd Low Emittance Ring workshop - 8th-10th July Oxford

12. Experimental Method (I)
Waveguide Method
First tested at low frequencies, from 9-12 GHz
Use of a standard X-band waveguide, 50 cm length
Network analyzer
Measurement of the transmission coefficient S21
WR90 X band 8.20 — Cutoff Freq.of lowest mode f=6.557GHz, Cutoff freq. of next mode , Dimensions × (inches)
2x1, 50cm length
Experimental
setup
3rd Low Emittance Ring workshop - 8th-10th July Oxford

13. Experimental Method (II)
Copper waveguide
First test: a pure copper (Cu) X band waveguide
Measure the S21 from 9-12 GHz
|S21| for a Cu waveguide
Signals traveling in the waveguide experience loss due to the conductor resistance
S21 is related to the loss suffered in the transmission from one port to the other
Cu is a very good conductor and the losses are small
S21 is related to the material conductivity
3rd Low Emittance Ring workshop - 8th-10th July Oxford

14. Conductivity of Cu
Result from the intersection of measurements with CST MWS simulations
Cu conductivity was estimated within the same order of magnitude with the known value
Average is 5.91x107 S/m
Good agreement with the known value of 5.8x107 S/m
The attenuation is very sensitive to the errors because of the small losses (high conductivity of Cu)
Despite this, the results were encouraging to continue with a coated waveguide
3rd Low Emittance Ring workshop - 8th-10th July Oxford

15. NEG coating of the Cu waveguide
NEG coated Cu waveguide
Same Cu waveguide used before is now coated with NEG
Coating procedure
Elemental wires intertwisted together produce a thin Ti-Zr-V film by magnetron sputtering
Coating was targeted to be as thick as possible (9 µm from first x-rays results)
Stress limitation in the maximum achievable thickness. As thick as possible in order to measure the NEG (skin depth << thickness)
3rd Low Emittance Ring workshop - 8th-10th July Oxford

16. Comparison of Cu and NEG coated one
NEG coated Cu waveguide
Measure the S21 from 9-12 GHz
S21 results indicate that the skin depth is small enough compared to the coating thickness
Allows the EM interaction with the NEG
3rd Low Emittance Ring workshop - 8th-10th July Oxford

17. Conductivity of NEG Is this frequency dependent behavior physical?
Upper limit for the conductivity of NEG in this frequency range (assume 100 μm thickness)
Is this frequency dependent behavior physical?
Repeat measurements with a spare Cu waveguide to check reproducibility
Upper limit, 100um thickness assumed
The non uniformity of the coating might impose uncertainties in the characterization
X-Ray Fluorescence

18. Second Cu waveguide
Small difference observed in the S21 measurement between the 2 waveguides
How much does this affect the conductivity estimation?
20% difference
Observing the same frequency dependence behavior
Waiting to coat at max thickness this waveguide to check
3rd Low Emittance Ring workshop - 8th-10th July Oxford

19. Why all this trouble? Effect of NEG conductivity on the budget
Pipe material/ coating
Chromaticity
Impedance budget (MΩ/m)
ss and NEG 2μm
(σNEG = 106 S/m) 4
ξx = 0.055/ξy = 0.057 1
(σNEG = S/m) 5
ss/ Cu 10 μm / NEG 2 μm (σNEG = S/m) 2
Arcs: copper and NEG 2μm/ Rest of wiggler: ss/ Wigglers: ss+ Cu 10μm + NEG 2μm
Budget remaining after removing the resistive wall (kickers, rf cavities, belows, other discontinuities)
The characterization of NEG properties is important in the high frequency regime and affects the instability thresholds predictions
3rd Low Emittance Ring workshop - 8th-10th July Oxford

20. Define the accuracy of the experimental method
Measurements with the stainless steel waveguide- accuracy of the method
X band stainless steel (ss) waveguide of 50 cm length
Define the accuracy of the experimental method
3rd Low Emittance Ring workshop - 8th-10th July Oxford

21. Results with the stainless steel waveguide
Measurements and CST
Intersection with CST
Average σ= S/m while expected DC value is S/m (40% error)
Problem in the measurement or the model?
3rd Low Emittance Ring workshop - 8th-10th July Oxford

22. Further checks for errors during the measurements or the waveguide itself
Measurements output
Repeat 3 times
Results are in very good agreement, repeated the procedure 3 times
3rd Low Emittance Ring workshop - 8th-10th July Oxford

23. Problem of the waveguide?
Add aluminum foil along the connection to ensure good contact and any extra losses (the material is not welded there but two different pieces hold together with screws)  Results are in very good agreement
Seems the experimental results can be trusted
Need to work on the model (try another code? Analytical calculation of S21?)
Further checks on this method
Work on the model
Think of other possible methods?
Before going up to 700 GHz, should be fun… 
3rd Low Emittance Ring workshop - 8th-10th July Oxford

24. Summary Other tasks ongoing…
Coating and material properties characterization are important in this frequency regime
Stripline kickers and RF cavities to be added to complete further the impedance budget study
Properties at 750 GHz? (EPFL Network Analyzer)
Other tasks ongoing…
Longitudinal radiation damping being implemented. Tests to be done in the near future. Next step, transverse damping
Implementation of space charge in HEADTAIL. Modifying the code to give multiple kicks for space charge along the lattice of the ring. Tests to be done.
Study the effect of space charge with impedance in the TMCI threshold (moving to higher thresholds?)
Study the tolerable space charge tune spread in combination with the newly implemented radiation damping modules
Validate the models used- compare with sls
3rd Low Emittance Ring workshop - 8th-10th July Oxford

25. Acknowledgements C. Zannini N. Biancacci K. Li G. De Michele N. Mounet
P. Costa Pinto
G.Rumolo
M. Taborelli
Thank you for your attention!
3rd Low Emittance Ring workshop - 8th-10th July Oxford

26. Impedance threshold MΩ/m
Backup slides
BROADBAND MODEL
Chromaticity make the modes move less, therefore it helps to avoid coupling (move to a higher threshold)
Still some modes can get unstable due to impedance
As the chromaticity is increased, higher order modes are excited (less effect on the bunch)
Chromaticity
ξx/ ξy
Impedance threshold MΩ/m x y
0/ 0 18 7
0.018/ 0.019
6.5 6
0.055/ 0.057 4
0.093/ 0.096 5 3
-0.018/
-0.055/ 2
-0.093/
The goal is to operate at 0 chromaticity which allows for a larger impedance budget (7 MΩ/m)
But since chromaticity will be slightly positive, a lower impedance budget has to be considered, 4 ΜΩ/m
SPS, 7 km, 20 MΩ/m

27. 3D EM Simulations and measurements (I)
X band Cu waveguide, εr=µr=1, σ is the (unknown) scanned parameter
For each frequency from 9-12 GHz, the output result is the S21 coefficient as a function of conductivity
Combine with the measurement results  σ as a function of frequency
Example at 10 GHz
Intersection of the simulation results
with the measurement  point of
intersection defines the conductivity
Value of conductivity

28. The 2 integration methods in Gdfidl give different results between them
Not in agreement with CST either

29. Try a simple structure for resistive wall compare CST, Gdfidl, ImpedanceWake2D, analytical
Conductivity: 1.3e6 S/m
0.2mm bunch length

30. Analytical and ImpedanceWake2D are in very good agreement
CST: Indirect Testbeams, open-cond-open
Analytical and ImpedanceWake2D are in very good agreement
Factor of difference between CST and ImpedanceWake2D. Gdfidl is in even worse agreement.