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

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. JensenR. Jones, G. de Michele, Radiation Protection, AB-BT workshop GSI/CERN collaboration meeting – Darmstadt, Feb 19th 2009

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

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

Creating the Model SPS BPV SPS BPH

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

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

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+…) Vertical Longitudinal Horizontal 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 Ezon plane x=0 at f=1.06 GHz 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)

Effect of matching the impedance at electrodes coaxial ports in Particle Studio simulations (BPH) Electrodecoaxial port In particle studio, ports can be defined and terminated 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 Wake is calculated at the location of the beam  “Total” impedance (dipolar + quadrupolar+…) Vertical Longitudinal Horizontal 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.

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

Are frequency simulations and time domain simulations consistent? BPH case Vertical Longitudinal Horizontal 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 Vertical Longitudinal Horizontal 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) 1.90GHz 1.08GHz 1.68GHz

Comparison with Bruno (BPH vertical) 1.29GHz 1.69GHz 0.97GHz 2.14GHz 1.92GHz 0.55GHz

Comparison with Bruno

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

S parameters measurements for the BPH S11 S22 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 domainand frequency domain is not so good as with the BPH  To be understood

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 • 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

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