Simulations and RF Measurements of SPS Beam Position Monitors (BPV and BPH)

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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

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Agenda

• Context• Simulations

– 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

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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

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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?

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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

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Agenda





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Creating the Model

SPS BPVSPS BPH

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Creating the BPH model

Input for simulations:- Technical drawings- Available prototype

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Structure of the BPHvacuumPerfect conductor (PEC)

BeamElectrodes

Cut along x=0

Cut along y=0

Casing

Output coax

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Agenda





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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 mFrequency resolution ~ 0.02 GHz

Material modelled as perfect conductor

1 cm rms Bunch length (=1)

FFT calculated by particle studio

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BPH - Time domain simulations

y

x

y

x

y

x

Wake is calculated at the location of the beam “Total” impedance (dipolar + quadrupolar+…)

1.08GHz

1.68GHz

1.90GHz

2.58GHz Same resonance frequencies as longitudinal

0.55GHz

0.97GHz

1.29GHz

1.69GHz2.14GHz

Longitudinal Horizontal Vertical

Negative imaginary part of the vertical impedance.

1.92GHz

s (mm) s (mm) s (mm)

A few remarks…

Remark 1/4 : Wake length and particle studio fft

20 meters wake

3 meters wake

Need for long wakes to obtain a sufficient frequency resolution Particle Studio FFT seems to introduce more ripple

Remark 2/4: How about “low” frequencies?Im

ag

ina

ry p

art

of

the

lon

gitu

din

al I

mp

ed

an

ce (

in O

hm

)

Z/n=Z/(f/f0)

= 20 cm

Low frequency imaginary longitudinal impedance is Z/n ~ 1 mΩ

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

At f=1.06 GHzSimple Structure

longitudinal electric field Ez

on plane x=0 at f=1.06 GHz

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)

Effect of matching the impedance at electrodes coaxial ports in Particle Studio simulations (BPH)

Electrodecoaxial port

Modes are damped by the “perfect matching layer”

at the coaxial port

In particle studio, ports can be defined and terminated

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

And for the real long SPS bunch ?(BPH)

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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 mFrequency resolution ~ 0.02 GHz


1 cm rms Bunch length (=1)

FFT calculated by particle studio

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y

x

y

x

y

x

BPV - Time domain

1.13GHz

2.22GHz

1.97GHz

0.73GHz

1.58GHz

1.14GHz~ same resonance frequencies longitudinal

1.97GHz

2.22GHz


Negative imaginary part of the vertical impedance, again.

Wake is calculated at the location of the beam “Total” impedance (dipolar + quadrupolar+…)

s (mm) s (mm) s (mm)

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Agenda





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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=Vz

2/W along z at (x,y)=(0,0)

•Transverse shunt impedance: Rs=Vz

2/W along z at (x,y)=(x,0) or (0,y)

•Boundary conditions : perfect conductor.

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BPH simulation : 30 first modes obtained with the eigenmode solver

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 13992 0.287 1.93E-25 1.00E-05 2.09E-25 14173 0.549 9.78E-28 1.33E-07 1.52E-26 19854 0.553 3.25E-06 3.10E-06 3.58E+00 20985 0.932 1.67E+00 1.64E+00 1.69E+00 21016 0.938 1.51E-28 2.86E-02 3.56E-28 21927 1.030 3.07E-23 4.62E-09 1.28E-27 78428 1.082 9.43E+04 9.48E+04 9.26E+04 32749 1.093 6.71E-28 1.27E+03 4.31E-28 3304

10 1.196 5.03E-06 4.65E-06 6.48E+03 799811 1.301 3.24E-05 3.19E-05 1.30E+02 267812 1.318 3.56E-25 1.84E-06 2.35E-27 291013 1.402 1.59E-23 1.78E-06 3.30E-27 635914 1.640 1.54E-03 1.50E-03 9.58E+03 405815 1.663 1.38E-29 3.12E-06 5.15E-28 501816 1.676 2.09E-27 2.87E-03 5.34E-27 269117 1.692 2.55E+02 2.51E+02 2.50E+02 281718 1.800 2.42E-06 2.06E-06 1.28E+03 1377719 1.875 5.79E+05 5.68E+05 5.67E+05 363220 1.899 2.66E-26 4.63E+01 4.96E-26 352121 1.923 5.12E-02 5.03E-02 2.30E+02 658222 2.019 1.07E-26 1.66E-05 6.27E-29 516923 2.075 8.11E-22 8.84E-06 3.58E-26 581324 2.127 9.27E-25 8.75E-06 5.02E-25 869825 2.132 3.73E-03 3.71E-03 2.16E+00 475826 2.188 5.01E-03 5.00E-03 1.33E+04 694927 2.248 6.32E+02 6.18E+02 6.10E+02 478028 2.255 2.06E-25 7.59E+01 1.18E-25 487629 2.363 1.37E-03 1.38E-03 1.40E+04 605630 2.370 2.51E-12 5.56E-05 9.67E-14 4938

longitudinal mode horizontal mode vertical mode

Transverse modes should show a strong transverse gradient of the longitudinal shunt impedance

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SPS BPV – Frequency domain

Eigenmode AKS solver

2 106 mesh cells


Shunt impedance, frequencies and quality factor obtained from MWS template postprocessing

Boundary conditions perfect conductor.

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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 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 1.25E+05 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 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

BPV simulation : 30 first modes obtained with the eigenmode solverlongitudinal mode horizontal mode vertical mode

Transverse modes should show a strong transverse gradient of the longitudinal shunt impedance

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Agenda





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Modefrequency

(GHz)Shunt

impedance9 1.09 1.27E+03

20 1.90 4.63E+0128 2.25 7.59E+01

Are frequency simulations and time domain simulations consistent?BPH case

1.08GHz

1.68GHz

1.90GHz

Same resonance frequencies as longitudinal

0.55GHz

0.97GHz

1.29GHz

1.69GHz2.14GHz

Modefrequency

(GHz)Shunt

impedance5 0.93 1.67E+008 1.08 9.43E+04

17 1.69 2.55E+0219 1.88 5.79E+0527 2.25 6.32E+02

Modefrequency

(GHz)Shunt


10 1.19 6.48E+0311 1.30 1.30E+0214 1.64 9.58E+0318 1.80 1.28E+0321 1.92 2.30E+0226 2.18 1.33E+0429 2.36 1.40E+04


1.92GHz

Most of the modes are observed in both time and frequency domain.Reasonable agreement

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Are frequency and time domain simulations consistent?BPV case


More mixing between time and frequency domain modes than for the BPH. Coupling?

Modefrequency

(GHz)

Shunt impedance

(center)5 1.104 1.40E+057 1.246 5.55E+01

13 1.880 7.79E+0217 2.110 1.24E+0521 2.255 1.62E+0523 2.284 7.46E+0424 2.301 1.25E+0525 2.347 1.39E+0228 2.572 3.07E+07

Modefrequency

(GHz)

Shunt impedance

(center)4 0.730 8.38E-01

10 1.582 3.30E+0312 1.686 5.29E+0116 2.037 1.13E+0225 2.347 4.32E+0326 2.438 1.86E+0230 2.599 1.52E+02

Modefrequency

(GHz)

Shunt impedance

(center)6 1.131 1.91E+03

15 1.972 7.73E+0218 2.169 3.32E+0219 2.204 3.56E+0222 2.261 3.87E+0027 2.482 3.80E+02

1.13GHz

2.22GHz

1.97GHz

0.73GHz

1.58GHz

1.14GHz~ same resonance frequencies longitudinal

1.97GHz

2.22GHz

Comparison with Bruno (BPH longitudinal)

1.08GHz

1.68GHz

1.90GHz

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

Comparison with Bruno (BPH vertical)

0.55GHz

0.97GHz

1.29GHz

1.69GHz2.14GHz

Modefrequency

(GHz)Shunt


10 1.19 6.48E+0311 1.30 1.30E+0214 1.64 9.58E+0318 1.80 1.28E+0321 1.92 2.30E+0226 2.18 1.33E+0429 2.36 1.40E+04

1.92GHz

Comparison with Bruno

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Agenda





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Setup for the measurement

SPS BPV SPS BPH

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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 connectorsLinked to BPMElectrodes with a coax

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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

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Agenda





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S parameters measurements for the BPH

Not much difference between S11 and S22

S11

S22

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Simulations and measurements BPH

Measurement and simulations are shifted in frequency Frequency shift seems to increase with frequency

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Measurements, HFSS and Particle Studio simulations(BPH)

HFSS simulation: courtesy of F. Roncarolo

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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?

Apparently yes!!!

Observed S21 peaks are the longitudinal impedance frequency peaks

Useful for more than just the benchmark!

Let’s compare with the BPH time domain simulation!

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Comparison between measurements and simulations BPV

Similar conclusions as for the BPH

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And if we compare with time domain?

Again, agreement between time domainand frequency domain is not so good as with the BPH

To be understood

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Agenda





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Measurements with wire (only BPV)

Available BPV prototype equipped with a wire. However, nobody has looked inside for a long while

CST model

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BPV S21 Measurements and simulations with and without wire

Measurement with wire behaves like the measurement without wire Measurement without wire behaves

like both simulations

Port 1Port 2

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Powering the wire: Transmission should yield the longitudinal impedance

Port 3

Port 4

Still a frequency-dependant frequency shift between measurements and simulations

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Agenda




• Outlook• Open questions

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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

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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?

Adding the ceramic spacers

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

BPV

BPV BPV

BPH

Taking into account the losses (BPV)

Taking into account the losses does not fundamentally change the S21.

The casing is not PEC.

Stainless Steel 304L conductivity: 3 106 S/m

Thank you for your attention!

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Documents

Simulations and RF Measurements of SPS Beam Position Monitors (BPV and BPH)