1. Simulations and RF Measurements of SPS Beam Position Monitors (BPV and BPH)
G. Arduini, C. Boccard, R. Calaga, F. Caspers, A. Grudiev, E. Metral, F. Roncarolo, G. Rumolo, B. Salvant, B. Spataro, C. Zannini
Acknowledgments: J. Albertone, M. Barnes, A. d’Elia, S. Federmann, F. Grespan, E. Jensen R. Jones, G. de Michele, Radiation Protection, AB-BT workshop
GSI/CERN collaboration meeting – Darmstadt, Feb 19th 2009

2. Agenda Context Simulations RF Measurements Open questions Perspectives
Creating the model
Time domain (Particle Studio)
Frequency Domain (Microwave Studio)
Consistency between Frequency and time domain
RF Measurements
Setup and strategy
Without wire
With wire
Open questions
Perspectives

3. Context
High intensity in the CERN SPS for nominal LHC operation, and foreseen LHC upgrade
Need for a good knowledge of the machine beam impedance and its main contributors
To obtain the total machine impedance, one can:
Measure the quadrupolar oscillation frequency shift (longitudinal) or the tune shift (transverse) with the SPS beam
obtain the impedance of each equipment separately and sum their contributions:
Analytical calculation (Burov/Lebedev, Zotter/Metral or Tsutsui formulae) for simple geometries
Simulations for more complicated geometries
RF Measurements on the equipment
 available impedance and wake data compiled in the impedance database ZBASE
In this talk, we focus on the simulations and RF measurements of the SPS BPMs

4. Objective Obtain the wake field and impedance of the SPS BPH and BPV
Notes:
Impedance of these SPS BPMs is expected to be small, but ~200 BPMs are installed in the machine.  Summed effect?
2 mm gaps seen by the beam are small  would affect only high frequencies? Is that really correct?

5. Broader objectives for the “impedance team”:
1) Which code should we trust to obtain the wake?
2) Assess the reliability of bench measurements with wire

6. Agenda Context Simulations RF Measurements Open questions Perspectives
Creating the model
Time domain (Particle Studio)
Frequency Domain (Microwave Studio)
Consistency between Frequency and time domain
RF Measurements
Setup and strategy
Without wire
With wire
Open questions
Perspectives

7. Creating the Model
SPS BPV
SPS BPH

8. Creating the BPH model Input for simulations: Technical drawings
Available prototype

9. Structure of the BPH Perfect conductor (PEC) vacuum Output coax Casing
Electrodes
Beam
Cut along y=0
Cut along x=0

10. Agenda Context Simulations RF Measurements Open questions Perspectives
Creating the model
Time domain (Particle Studio)
Frequency Domain (Microwave Studio)
Consistency between Frequency and time domain
RF Measurements
Setup and strategy
Without wire
With wire
Open questions
Perspectives

11. SPS BPH – time domain simulations
Wakefield solver
Boundary conditions: perfect conductor except for beam pipe aperture (open)
Indirect testbeam wake calculation
106 mesh cells
Simulated wake length=15 m
Frequency resolution ~ 0.02 GHz
Material modelled as perfect conductor
1 cm rms Bunch length (=1)
FFT calculated by particle studio

12. BPH - Time domain simulations
Wake is calculated at the location of the beam  “Total” impedance (dipolar + quadrupolar+…)
Longitudinal
Horizontal
Vertical y y y x x x
s (mm)
s (mm)
s (mm)
1.90GHz
1.29GHz
1.08GHz
2.58GHz
Same resonance frequencies as longitudinal
1.69GHz
0.97GHz
2.14GHz
1.68GHz
1.92GHz
0.55GHz
 Negative imaginary part of the vertical impedance.

13. A few remarks…

14. Remark 1/4 : Wake length and particle studio fft
3 meters wake
20 meters wake
 Need for long wakes to obtain a sufficient frequency resolution
 Particle Studio FFT seems to introduce more ripple

15. Remark 2/4: How about “low” frequencies?
Z/n=Z/(f/f0)
Imaginary part of the longitudinal Impedance (in Ohm)
 = 20 cm
Low frequency imaginary longitudinal impedance is Z/n ~ 1 mΩ

16. Remark 3/4 : Comparing the full BPH with the simple structure with slits

17. longitudinal electric field Ez on plane x=0 at f=1.06 GHz
Simple Structure
Simple Structure with slits
Full BPH structure
 The gaps are small, but the electrode are so thin that the cavities behind the electrodes perturb the beam down to low frequencies (~1GHz)

18. Modes are damped by the “perfect matching layer” at the coaxial port
Effect of matching the impedance at electrodes coaxial ports in Particle Studio simulations (BPH)
Electrode coaxial port
In particle studio, ports can be defined and terminated
Modes are damped by the “perfect matching layer” at the coaxial port

19. Modes are damped by the “perfect matching layer” at the coaxial port
Effect of matching the impedance at electrodes coaxial ports in Particle Studio simulations (BPV)
Modes are damped by the “perfect matching layer” at the coaxial port

20. And for the real long SPS bunch ?(BPH)

21. SPS BPV – time domain simulations
Wakefield solver
Boundary conditions: perfect conductor except for beam pipe aperture (open)
Indirect testbeam wake calculation
106 mesh cells
Simulated wake length=15 m
Frequency resolution ~ 0.02 GHz
Material modelled as perfect conductor
1 cm rms Bunch length (=1)
FFT calculated by particle studio

22. BPV - Time domain Longitudinal Horizontal Vertical y y y x x x
Wake is calculated at the location of the beam  “Total” impedance (dipolar + quadrupolar+…)
Longitudinal
Horizontal
Vertical y y y x x x
s (mm)
s (mm)
s (mm)
2.22GHz
0.73GHz
1.13GHz
2.22GHz
1.97GHz
1.58GHz
1.14GHz
~ same resonance frequencies longitudinal
1.97GHz
 Negative imaginary part of the vertical impedance, again.

23. Agenda Context Simulations RF Measurements Open questions Perspectives
Creating the model
Time domain (Particle Studio)
Frequency Domain (Microwave Studio)
Consistency between Frequency and time domain
RF Measurements
Setup and strategy
Without wire
With wire
Open questions
Perspectives

24. SPS BPH – Frequency domain simulations
Eigenmode AKS solver
2 106 mesh cells
Material modelled as perfect conductor
Shunt impedance, frequencies and quality factor obtained from MWS Template postprocessing
Longitudinal shunt impedance: Rs=Vz2/W along z at (x,y)=(0,0)
Transverse shunt impedance: Rs=Vz2/W along z at (x,y)=(x,0) or (0,y)
Boundary conditions : perfect conductor.

25. BPH simulation : 30 first modes obtained with the eigenmode solver
longitudinal mode
horizontal mode
vertical mode
Mode
frequency (GHz)
Shunt impedance (center)
Shunt impedance (x=5mm)
Shunt impedance (y=5mm)
Quality factor 1
0.282
7.05E-02
6.95E-02
7.20E-02
1399 2
0.287
1.93E-25
1.00E-05
2.09E-25
1417 3
0.549
9.78E-28
1.33E-07
1.52E-26
1985 4
0.553
3.25E-06
3.10E-06
3.58E+00
2098 5
0.932
1.67E+00
1.64E+00
1.69E+00
2101 6
0.938
1.51E-28
2.86E-02
3.56E-28
2192 7
1.030
3.07E-23
4.62E-09
1.28E-27
7842 8
1.082
9.43E+04
9.48E+04
9.26E+04
3274 9
1.093
6.71E-28
1.27E+03
4.31E-28
3304 10
1.196
5.03E-06
4.65E-06
6.48E+03
7998 11
1.301
3.24E-05
3.19E-05
1.30E+02
2678 12
1.318
3.56E-25
1.84E-06
2.35E-27
2910 13
1.402
1.59E-23
1.78E-06
3.30E-27
6359 14
1.640
1.54E-03
1.50E-03
9.58E+03
4058 15
1.663
1.38E-29
3.12E-06
5.15E-28
5018 16
1.676
2.09E-27
2.87E-03
5.34E-27
2691 17
1.692
2.55E+02
2.51E+02
2.50E+02
2817 18
1.800
2.42E-06
2.06E-06
1.28E+03
13777 19
1.875
5.79E+05
5.68E+05
5.67E+05
3632 20
1.899
2.66E-26
4.63E+01
4.96E-26
3521 21
1.923
5.12E-02
5.03E-02
2.30E+02
6582 22
2.019
1.07E-26
1.66E-05
6.27E-29
5169 23
2.075
8.11E-22
8.84E-06
3.58E-26
5813 24
2.127
9.27E-25
8.75E-06
5.02E-25
8698 25
2.132
3.73E-03
3.71E-03
2.16E+00
4758 26
2.188
5.01E-03
5.00E-03
1.33E+04
6949 27
2.248
6.32E+02
6.18E+02
6.10E+02
4780 28
2.255
2.06E-25
7.59E+01
1.18E-25
4876 29
2.363
1.37E-03
1.38E-03
1.40E+04
6056 30
2.370
2.51E-12
5.56E-05
9.67E-14
4938
Transverse modes should show a strong transverse gradient of the longitudinal shunt impedance

26. SPS BPV – Frequency domain
Eigenmode AKS solver
2 106 mesh cells
Material modelled as perfect conductor
Shunt impedance, frequencies and quality factor obtained from MWS
template postprocessing
Boundary conditions perfect conductor.

27. BPV simulation : 30 first modes obtained with the eigenmode solver
longitudinal mode
horizontal mode
vertical mode
Mode
frequency (GHz)
Shunt impedance (center)
Shunt impedance (x=5mm)
Shunt impedance (y=5mm)
Quality factor 1
0.305
2.37E-03
2.52E-03
2.16E-03
1207 2
0.310
7.39E-17
9.02E-17
7.88E-05
1218 3
0.719
6.93E-18
2.34E-16
2.51E-06
2013 4
0.730
3.31E-04
8.38E-01
3.28E-04
2135 5
1.104
1.40E+05
1.39E+05
2561 6
1.131
7.98E-29
1.98E-28
1.91E+03
2648 7
1.246
5.55E+01
5.52E+01
5.47E+01
2228 8
1.278
2.56E-18
2.34E-18
1.25E-01
2330 9
1.573
1.36E-17
6.61E-11
5.46E-08
2843 10
1.582
2.75E-04
3.30E+03
2.68E-04
2917 11
1.645
4.58E-16
1.85E-11
2.23E-05
2937 12
1.686
2.78E-04
5.29E+01
2.92E-04
2531 13
1.880
7.79E+02
8.30E+02
7.01E+02
13136 14
1.925
1.13E-11
7.48E-11
1.32E-04
8921 15
1.972
8.50E-14
2.28E-12
7.73E+02
7961 16
2.037
1.69E-03
1.13E+02
1.55E-03
15783 17
2.110
1.24E+05
1.25E+05
1.16E+05
4660 18
2.169
2.08E-11
1.29E-11
3.32E+02
3811 19
2.204
3.93E-12
3.27E-12
3.56E+02
3265 20
2.231
4.07E-07
4.91E-07
1.28E-04
19292 21
2.255
1.62E+05
1.61E+05
1.53E+05
4192 22
2.261
1.07E-10
1.64E-10
3.87E+00
4293 23
2.284
7.46E+04
7.37E+04
7.13E+04
3683 24
2.301
1.23E+05
1.20E+05
5548 25
2.347
1.39E+02
4.32E+03
2.31E+02
4601 26
2.438
7.75E-04
1.86E+02
7.31E-04
12187 27
2.482
3.17E-10
9.63E-10
3.80E+02
17597 28
2.572
3.07E+07
2.96E+07
13116 29
2.589
9.67E-08
4.94E-04
2.30E-05
3794 30
2.599
6.63E-02
1.52E+02
6.39E-02
4710
Transverse modes should show a strong transverse gradient of the longitudinal shunt impedance

28. Agenda Context Simulations RF Measurements Open questions Perspectives
Creating the model
Time domain (Particle Studio)
Frequency Domain (Microwave Studio)
Consistency between Frequency and time domain
RF Measurements
Setup and strategy
Without wire
With wire
Open questions
Perspectives

29. Are frequency simulations and time domain simulations consistent?
BPH case
Longitudinal
Horizontal
Vertical
Mode
frequency (GHz)
Shunt impedance 4
0.55
3.58E+00 10
1.19
6.48E+03 11
1.30
1.30E+02 14
1.64
9.58E+03 18
1.80
1.28E+03 21
1.92
2.30E+02 26
2.18
1.33E+04 29
2.36
1.40E+04
Mode
frequency (GHz)
Shunt impedance 5
0.93
1.67E+00 8
1.08
9.43E+04 17
1.69
2.55E+02 19
1.88
5.79E+05 27
2.25
6.32E+02
Mode
frequency (GHz)
Shunt impedance 9
1.09
1.27E+03 20
1.90
4.63E+01 28
2.25
7.59E+01
1.90GHz
1.29GHz
1.08GHz
Same resonance frequencies as longitudinal
1.69GHz
0.97GHz
2.14GHz
1.68GHz
1.92GHz
0.55GHz
 Most of the modes are observed in both time and frequency domain.
Reasonable agreement

30. Are frequency and time domain simulations consistent? BPV case
Longitudinal
Horizontal
Vertical
Mode
frequency (GHz)
Shunt impedance (center) 5
1.104
1.40E+05 7
1.246
5.55E+01 13
1.880
7.79E+02 17
2.110
1.24E+05 21
2.255
1.62E+05 23
2.284
7.46E+04 24
2.301
1.25E+05 25
2.347
1.39E+02 28
2.572
3.07E+07
Mode
frequency (GHz)
Shunt impedance (center) 4
0.730
8.38E-01 10
1.582
3.30E+03 12
1.686
5.29E+01 16
2.037
1.13E+02 25
2.347
4.32E+03 26
2.438
1.86E+02 30
2.599
1.52E+02
Mode
frequency (GHz)
Shunt impedance (center) 6
1.131
1.91E+03 15
1.972
7.73E+02 18
2.169
3.32E+02 19
2.204
3.56E+02 22
2.261
3.87E+00 27
2.482
3.80E+02
2.22GHz
0.73GHz
1.13GHz
2.22GHz
1.58GHz
1.97GHz
1.14GHz
~ same resonance frequencies longitudinal
1.97GHz
 More mixing between time and frequency domain modes than for the BPH. Coupling?

31. Comparison with Bruno (BPH longitudinal)
f [GHz]
R [Ω]
R/Q [Ω] Q
0.932
1.67
7.95E-04
2101
1.082
9.43E+04
2.88E+01
3274
1.692
255
9.05E-02
2817
1.875
5.79E+05
1.59E+02
3632
2.248
632
1.32E-01
4780
1.90GHz
1.08GHz
1.68GHz

32. Comparison with Bruno (BPH vertical)
Mode
frequency (GHz)
Shunt impedance 4
0.55
3.58E+00 10
1.19
6.48E+03 11
1.30
1.30E+02 14
1.64
9.58E+03 18
1.80
1.28E+03 21
1.92
2.30E+02 26
2.18
1.33E+04 29
2.36
1.40E+04
1.29GHz
1.69GHz
0.97GHz
2.14GHz
1.92GHz
0.55GHz

33. Comparison with Bruno

34. Agenda Context Simulations RF Measurements Open questions Perspectives
Creating the model
Time domain (Particle Studio)
Frequency Domain (Microwave Studio)
Consistency between Frequency and time domain
RF Measurements
Setup and strategy
Without wire
With wire
Open questions
Perspectives

35. Setup for the measurement
SPS BPH
SPS BPV

36. Measurement strategy
Not ideal to measure the impedance with a wire (small signal expected, radioactive device, tampering with the device would mean reconditioning before being able to put it back in the machine).
Idea: first, try to measure S-parameters from the available N-ports at the BPM electrodes, to benchmark the simulations and the measurements
N connectors
Linked to BPM
Electrodes
with a coax

37. Measurement setup VNA parameters Number of point: 20001 (max)
IF bandwidth: 1 kHz
Linear frequency sweep between 1 MHz and 3 GHz
2-port calibration (short, open load for each port + transmission)
Port 1 is next to the beam pipe
Port 2 is next to the flange

38. Agenda Context Simulations RF Measurements Open questions Perspectives
Creating the model
Time domain (Particle Studio)
Frequency Domain (Microwave Studio)
Consistency between Frequency and time domain
RF Measurements
Setup and strategy
Without wire
With wire
Open questions
Perspectives

39. S parameters measurements for the BPH
Not much difference between S11 and S22

40. Simulations and measurements BPH
Measurement and simulations are shifted in frequency
Frequency shift seems to increase with frequency

41. Measurements, HFSS and Particle Studio simulations(BPH)
HFSS simulation: courtesy of F. Roncarolo

42. This benchmark with measurements without wire indicate that the model is not completely wrong. But do they give information on impedance peaks, by any chance?
Let’s compare with the BPH time domain simulation!
Apparently yes!!!
Observed S21 peaks are the longitudinal impedance frequency peaks
 Useful for more than just the benchmark!

43. Comparison between measurements and simulations BPV
Similar conclusions as for the BPH

44. And if we compare with time domain?
Again, agreement between time domain and frequency domain is not so good as with the BPH
 To be understood

45. Agenda Context Simulations RF Measurements Open questions Perspectives
Creating the model
Time domain (Particle Studio)
Frequency Domain (Microwave Studio)
Consistency between Frequency and time domain
RF Measurements
Setup and strategy
Without wire
With wire
Open questions
Perspectives

46. Measurements with wire (only BPV)
CST model
Available BPV prototype equipped with a wire. However, nobody has looked inside for a long while

47. BPV S21 Measurements and simulations with and without wire
Port 2
Port 1
Measurement with wire behaves like the measurement without wire
Measurement without wire behaves like both simulations

48. Powering the wire: Transmission should yield the longitudinal impedance
Port 4
Port 3
Still a frequency-dependant frequency shift between measurements and simulations

49. Agenda Context Simulations RF Measurements Outlook Open questions
Creating the model
Time domain (Particle Studio)
Frequency Domain (Microwave Studio)
Consistency between Frequency and time domain
RF Measurements
Setup and strategy
Without wire
With wire
Outlook
Open questions

50. Outlook and future plans
Reasonable agreement between time domain, frequency domain, eigenmode, and bench RF measurements.
The agreement seems better for the BPH than for the BPV
Powering the electrode without the wire gives information on the impedance related resonances.
From simulations, putting a wire in the BPV affects moderately the impedance spectrum.
Not discussed here: Time Domain Simulations of both BPH and BPV indicate that the ouput signals (corrected by the time delay) at both electrodes are not equal when the bunch is centered. This could explain difficulties to calibrate these specific BPMs.
Future plans:
Check dipolar, quadrupolar, coupled and higher order terms of the wake, and ways to obtain these terms in frequency domain.
Use the same approach to simulate the SPS kickers (much larger impedance contribution is expected)
Explore more in detail the effect of finite resistivity.
Effect of these wakes on the SPS beam

51. Some open questions…
Negative impedance for both BPV and BPH. Convention?
Linux version of CST?
How to decouple dipolar and quadrupolar terms in frequency domain for structures with no symmetry?
Are there limitations to calculating the transverse wake from the longitudinal?
Open boundary condition for low energy beams? (important for the PS Booster and the PS)
FFT in particle studio?
Which windowing should we use?

52. 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

53. Taking into account the losses (BPV)
The casing is not PEC.
Stainless Steel 304L conductivity: S/m
Taking into account the losses does not fundamentally change the S21.

54. Thank you for your attention!