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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. JensenR. Jones, G. de Michele, Radiation Protection, AB-BT workshop

GSI/CERN collaboration meeting – Darmstadt, Feb 19th 2009

- 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

- 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

- 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

- 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

SPS BPV

SPS BPH

- Input for simulations:
- Technical drawings
- Available prototype

Casing

Perfect conductor (PEC)

vacuum

Output coax

Electrodes

Cut along y=0

Beam

Cut along x=0

- 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

- 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

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…

3 meters wake

20 meters wake

Need for long wakes to obtain a sufficient frequency resolution

Particle Studio FFT seems to introduce more ripple

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

longitudinal electric field Ezon 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)

Electrodecoaxial 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

- 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

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.

- 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

- 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.

longitudinal mode

horizontal mode

vertical mode

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

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

- 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

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?

1.90GHz

1.08GHz

1.68GHz

1.29GHz

1.69GHz

0.97GHz

2.14GHz

1.92GHz

0.55GHz

- 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

SPS BPH

SPS BPV

- 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

- 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

- 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

S11

S22

Not much difference between S11 and S22

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

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!

Similar conclusions as for the BPH

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

To be understood

- 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

CST model

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

Port 2

Port 1

Measurement with wire behaves like the measurement without wire

Measurement without wire behaves like both simulations

Port 4

Port 3

Still a frequency-dependant frequency shift between measurements and simulations

- 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

- 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

- 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?

Ceramic insulator spacers designed to mechanically stabilize the thin electrodes

(homemade at CERN, cf BPH/BPV technical specs, 1973)

BPH

BPV

BPV

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.