1. Follow up on SPS transverse impedance
G. Arduini, F. Caspers, E. Métral, G. Rumolo, B. Salvant
Acknowledgements: C. Boccard, T. Bohl, R. Calaga, H. Damerau, R. Jones, R. de Maria, N. Mounet, F. Roncarolo, E. Shaposhnikova, R. Steinhagen, C. Zannini, B. Zotter
SPS Upgrade Study Team – May 19th 2009

2. Agenda Objectives for the transverse impedance team
Obtaining the wake functions for single SPS elements
Analytical calculations for simple geometries (beam pipe, kickers)
Electromagnetic simulations for more complicated geometries (BPMs)
Bench RF measurements
“Total” wakes for the SPS and importing into Headtail
SPS Measurements of observables and comparison with simulations
Tune shift and instability thresholds
Localization of transverse impedance
Measurements with long bunches
Sum up and future work

3. Objectives for the transverse impedance team
SPS machine
measurements
Analytical Calculations
Electromagnetic Simulations
Bench Measurements
Impedance of a single SPS element
Wake potential of a
single SPS element
Impedance of a single SPS element
DFT
deconvolution
DFT
Wake function of a single SPS element
Wake function of a single SPS element
Wake function of a single SPS element
Sum for all available SPS elements
“Total” SPS Wake function
Headtail macroparticle simulations ?
Measured observables
(Tune shift, Instability threshold…)
Simulated observables
(tune shift, instability threshold…)
How much of the measured transverse impedance is accounted for in the model?
Which are the main transverse impedance contributors?

4. Agenda Objectives for the transverse impedance team
Obtaining the wake functions for single SPS elements
Analytical calculations for simple geometries (beam pipe, kickers)
Electromagnetic simulations for more complicated geometries (BPMs)
Bench RF measurements
“Total” wakes for the SPS and importing into Headtail
SPS Measurements of observables and comparison with simulations
Tune shift and instability thresholds
Localization of transverse impedance
Measurements with long bunches
Sum up and future work

5. Objectives for the transverse impedance team
SPS machine
measurements
Analytical Calculations
Electromagnetic Simulations
Bench Measurements
Impedance of a single SPS element
Wake potential of a
single SPS element
Impedance of a single SPS element
DFT
deconvolution
DFT
Wake function of a single SPS element
Wake function of a single SPS element
Wake function of a single SPS element
Sum for all available SPS elements
“Total” SPS Wake function
Headtail macroparticle simulations ?
Measured observables
(Tune shift, Instability threshold…)
Simulated observables
(tune shift, instability threshold…)
How much of the measured transverse impedance is accounted for in the model?
Which are the main transverse impedance contributors?

6. Analytical calculation for simple geometries
Long range wake (1 m)
Example: Transverse Wall impedance of a 2 cm stainless steel m round beam pipe for a  = 27.7 beam 
DFT  
Short range wake ( 5mm)
DFT on a large frequency range is an issue:
- sampling interval too small
 wrong long range wake value
fmax too small
wrong short range wake+oscillations   
Here, need for fmax  1 THz and fsampling 0.1 MHz
 107 points DFT
 CPU limit in windows
Possible solutions: - UNIX (up to points)
- and Nicolas’s new DFT algorithm

7. Agenda Objectives for the transverse impedance team
Obtaining the wake functions for single SPS elements
Analytical calculations for simple geometries (beam pipe, kickers)
Electromagnetic simulations for more complicated geometries (BPMs)
Obtaining wake potentials
RF measurements to confirm the simulations
Obtaining the wake function from the wake potential
Bench RF measurements
“Total” wakes for the SPS and importing into Headtail
SPS Measurements of observables and comparison with simulations
Tune shift and instability thresholds
Localization of transverse impedance
Measurements with long bunches
Sum up and future work

8. Objectives for the transverse impedance team
SPS machine
measurements
Analytical Calculations
Electromagnetic Simulations
Bench Measurements
Impedance of a single SPS element
Wake potential of a
single SPS element
Impedance of a single SPS element
DFT
deconvolution
DFT
Wake function of a single SPS element
Wake function of a single SPS element
Wake function of a single SPS element
Sum for all available SPS elements
“Total” SPS Wake function
Headtail macroparticle simulations ?
Measured observables
(Tune shift, Instability threshold…)
Simulated observables
(tune shift, instability threshold…)
How much of the measured transverse impedance is accounted for in the model?
Which are the main transverse impedance contributors?

9. Electromagnetic simulations for more complicated geometries
SPS BPH
SPS BPH model geometry

10. Comparing time domain and frequency domain simulations
Time domain (CST Particle Studio)
Frequency domain (CST Microwave Studio)
1.90GHz
2.58GHz
1.08GHz
fres (GHz)
Rs (y=0mm) [Ω] Q
1.08
3270
1.69
167
2100
1.88
3630
longitudinal
1.68GHz
Very high R/Q! (~150 Ω)
Similar to Fritz’s slotline pickup
0.97GHz
fres (GHz)
Rs (y=5mm) [Ω] Q
0.55
3.6
2100
1.20
6480
8000
1.30
130
2680
1.64
4060
1.80
1280
13700
1.92
230
6580
1.69GHz
1.29GHz
vertical
2.14GHz
1.92GHz
0.55GHz

11. Electrode coaxial port
Effect of matching the impedance at electrodes coaxial ports in Particle Studio simulations (BPH)
Modes are damped by the “perfect matching layer” at the coaxial port
Short bunch (1 cm rms)
SPS bunch (20 cm rms)
Electrode coaxial port
Importance to match the BPM electrodes!

12. Remark on BPM matching for higher order modes
From discussions with Rhodri and Ralph, the BPM matching is currently performed up to 500 or 600 MHz.
Besides they mention that an activity around 1.8 GHz can be observed on the HeadTail monitor (sum and longitudinal).
Should be damped by the termination
If not damped, this mode could be the most critical
This may be just a coincidence and will be investigated together with RF and BI.

13. Agenda Objectives for the transverse impedance team
Obtaining the wake functions for single SPS elements
Analytical calculations for simple geometries (beam pipe, kickers)
Electromagnetic simulations for more complicated geometries (BPMs)
Obtaining wake potentials
RF measurements to confirm the simulations
Obtaining the wake function from the wake potential
Bench RF measurements
“Total” wakes for the SPS and importing into Headtail
SPS Measurements of observables and comparison with simulations
Tune shift and instability thresholds
Localization of transverse impedance
Measurements with long bunches
Sum up and future work

14. Benchmark with RF measurements
Transmission measurement between electrode ports (S21)
More convenient than wire measurement in this case (small signal expected, radioactive device, no need to recondition)

15. Adding the ceramic spacers
Ceramic insulator spacers designed to mechanically stabilize the thin electrodes
(homemade at CERN, cf BPH/BPV technical specs, 1973)
BPH
BPV
BPV
BPV

16. Agenda Objectives for the transverse impedance team
Obtaining the wake functions for single SPS elements
Analytical calculations for simple geometries (beam pipe, kickers)
Electromagnetic simulations for more complicated geometries (BPMs)
Obtaining wake potentials
RF measurements to confirm the simulations
Obtaining the wake function from the wake potential
Bench RF measurements
“Total” wakes for the SPS and importing into Headtail
SPS Measurements of observables and comparison with simulations
Tune shift and instability thresholds
Localization of transverse impedance
Measurements with long bunches
Sum up and future work

17. Objectives for the transverse impedance team
SPS machine
measurements
Analytical Calculations
Electromagnetic Simulations
Bench Measurements
Impedance of a single SPS element
Wake potential of a
single SPS element
Impedance of a single SPS element
DFT
deconvolution
DFT
Wake function of a single SPS element
Wake function of a single SPS element
Wake function of a single SPS element
Sum for all available SPS elements
“Total” SPS Wake function
Headtail macroparticle simulations ?
Measured observables
(Tune shift, Instability threshold…)
Simulated observables
(tune shift, instability threshold…)
How much of the measured transverse impedance is accounted for in the model?
Which are the main transverse impedance contributors?

18. Obtaining the transverse wake functions from time domain simulations
Time domain simulations to obtain dipolar and quadrupolar wake potentials (horizontal and vertical)
Deconvolution of the gaussian bunch distribution (DFT, division by gaussian distribution in frequency domain and windowing, DFT) y y
Beam
Wake integration x x
Wy dipolar
Wy quadrupolar
Note : This method assumes x and y symmetry.
How to deal with non symmetric geometries? Non linear terms? Coupled terms?

19. BPH and BPV transverse wake functions
Note: quadrupolar wakes are not related by Wx,quad= - Wy,quad
both BPMs only have one symmetry plane

20. Agenda Objectives for the transverse impedance team
Obtaining the wake functions for single SPS elements
Analytical calculations for simple geometries (beam pipe, kickers)
Electromagnetic simulations for more complicated geometries (BPMs)
Bench RF measurements
“Total” wakes for the SPS and importing into Headtail
SPS Measurements of observables and comparison with simulations
Tune shift and instability thresholds
Localization of transverse impedance
Measurements with long bunches
Sum up and future work

21. Objectives for the transverse impedance team
SPS machine
measurements
Analytical Calculations
Electromagnetic Simulations
Bench Measurements
Impedance of a single SPS element
Wake potential of a
single SPS element
Impedance of a single SPS element
DFT
deconvolution
DFT
Wake function of a single SPS element
Wake function of a single SPS element
Wake function of a single SPS element
Sum for all available SPS elements
“Total” SPS Wake function
Headtail macroparticle simulations ?
Measured observables
(Tune shift, Instability threshold…)
Simulated observables
(tune shift, instability threshold…)
How much of the measured transverse impedance is accounted for in the model?
Which are the main transverse impedance contributors?

22. Bench RF measurement of the transverse impedance
Cf for instance “Longitudinal and Transverse Wire Measurements for the Evaluation of Impedance Reduction Measures on the MKE Extraction Kickers”, T. Kroyer, F. Caspers, E. Gaxiola
Two wire measurement  dipolar impedance
Moving single wire measurement  total impedance (dipolar + quadrupolar+…)

23. Agenda Objectives for the transverse impedance team
Obtaining the wake functions for single SPS elements
Analytical calculations for simple geometries (beam pipe, kickers)
Electromagnetic simulations for more complicated geometries (BPMs)
Bench RF measurements
“Total” wakes for the SPS and importing into Headtail
SPS Measurements of observables and comparison with simulations
Tune shift and instability thresholds
Localization of transverse impedance
Measurements with long bunches
Sum up and future work

24. Objectives for the transverse impedance team
SPS machine
measurements
Analytical Calculations
Electromagnetic Simulations
Bench Measurements
Impedance of a single SPS element
Wake potential of a
single SPS element
Impedance of a single SPS element
DFT
deconvolution
DFT
Wake function of a single SPS element
Wake function of a single SPS element
Wake function of a single SPS element
Sum for all available SPS elements
“Total” SPS Wake function
Headtail macroparticle simulations ?
Measured observables
(Tune shift, Instability threshold…)
Simulated observables
(tune shift, instability threshold…)
How much of the measured transverse impedance is accounted for in the model?
Which are the main transverse impedance contributors?

25. Total wake for importing into Headtail
Kickers (ferrite model + BPHs + BPVs + Beam pipe)
Needs interpolation
Need to take into account the correct beta functions at each element location
The ferrite kicker model should be refined.

26. Agenda Objectives for the transverse impedance team
Obtaining the wake functions for single SPS elements
Analytical calculations for simple geometries (beam pipe, kickers)
Electromagnetic simulations for more complicated geometries (BPMs)
RF measurements to confirm the simulations (BPMs)
“Total” wakes for the SPS and importing into Headtail
SPS Measurements of observables and comparison with simulations
Tune shift and instability thresholds
Localization of transverse impedance
Measurements with long bunches
Sum up and future work

27. Objectives for the transverse impedance team
SPS machine
measurements
Analytical Calculations
Electromagnetic Simulations
Bench Measurements
Impedance of a single SPS element
Wake potential of a
single SPS element
Impedance of a single SPS element
DFT
deconvolution
DFT
Wake function of a single SPS element
Wake function of a single SPS element
Wake function of a single SPS element
Sum for all available SPS elements
“Total” SPS Wake function
Headtail macroparticle simulations ?
Measured observables
(Tune shift, Instability threshold…)
Simulated observables
(tune shift, instability threshold…)
How much of the measured transverse impedance is accounted for in the model?
Which are the main transverse impedance contributors?

28. Tune shift and instability threshold (vertical plane)
kickers only
kickers+BPMs
kickers+BPMs+pipe

29. Objectives for the transverse impedance team
SPS machine
measurements
Analytical Calculations
Electromagnetic Simulations
Bench Measurements
Impedance of a single SPS element
Wake potential of a
single SPS element
Impedance of a single SPS element
DFT
deconvolution
DFT
Wake function of a single SPS element
Wake function of a single SPS element
Wake function of a single SPS element
Sum for all available SPS elements
“Total” SPS Wake function
Headtail macroparticle simulations ?
Measured observables
(Tune shift, Instability threshold…)
Simulated observables
(tune shift, instability threshold…)
How much of the measured transverse impedance is accounted for in the model?
Which are the main transverse impedance contributors?

30. Simulations and measurements: tune Shift and instability threshold
Absolute tune shift slope with intensity is 40% smaller in the simulations than in the measurements
Transverse instability threshold is very similar (~ protons)
Impedance contributors are missing (RF cavities, pumping ports…) or are not correctly modelled (kickers)
absolute tune slope should increase and instability threshold should decrease
Direct space charge is missing
no effect expected on tune slope, but instability threshold should decrease

31. Localization of impedance
From R. Calaga et al, PAC’09

32. Simulations and measurements of long bunches
Headtail simulation with a
broadband impedance model Q=1, fres=1.3 GHz, Rs=7.6 MΩ/m
Headtail simulations with SPS kickers
Can be fitted by a broadband impedance Q=0.6, fres=2.3 GHz, Rs=3.5 MΩ/m
SPS Measurements
vertical
Time signals
vertical
DFT
As in the simulations with kickers model, no clear activity in the transverse plane. This is not a proof though.
Work ongoing.
Longitudinal
DFT

33. Agenda Objectives for the transverse impedance team
Obtaining the wake functions for single SPS elements
Analytical calculations for simple geometries (beam pipe, kickers)
Electromagnetic simulations for more complicated geometries (BPMs)
RF measurements to confirm the simulations (BPMs)
“Total” wakes for the SPS and importing into Headtail
SPS Measurements of observables and comparison with simulations
Tune shift and instability thresholds
Localization of transverse impedance
Measurements with long bunches
Sum up and future work

34. Sum up and future work
General framework designed to obtain a more accurate transverse impedance model of the SPS from analytical, simulated and measured estimates.
First try with the kickers, BPHs, BPVs and Wall impedance of the vacuum chamber. With the current results, the BPMs have a small impact on the single bunch dynamics, but strong higher order modes may affect the coupled bunch dynamics.
40% of the measured tune shift with intensity is not accounted for. Simulated and measured thresholds are very close.
Other means to access observables of the impedance are being investigated (localization, longer bunches), and are still a work-in-progress.