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

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

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

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?

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

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

Creating the Model SPS BPV SPS BPH

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

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

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

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

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.

A few remarks…

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

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

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

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)

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

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

And for the real long SPS bunch ?(BPH)

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

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.

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

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.

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

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.

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

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

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

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?

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

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

Comparison with Bruno

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

Setup for the measurement SPS BPH SPS BPV

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

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

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

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

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

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

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!

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

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

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

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

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

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

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

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

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) BPH BPV BPV BPV

Taking into account the losses (BPV) The casing is not PEC. Stainless Steel 304L conductivity: 3 106 S/m Taking into account the losses does not fundamentally change the S21.

Thank you for your attention!