1. Finemet cavity impedance studies
Serena Persichelli
PS-LIU meeting
Acknowledgements
Simone Gilardoni
Mauro Migliorati
Mauro Paoluzzi
Benoit Salvant

2. Aim of the study
The aim of the study is to evaluate the impedance excited in the Finemet cavity by a bunch with the same length of the PS bunches (26 cm - 12m)
Time domain simulations with CST Particle Studio have been performed in order to get the longitudinal impedance of the cavity and make a comparison with the measured longitudinal impedance
The study has been performed on simplified 3D geometries imported from a mechanical CATIA drawing, assuming small impact on the final results.
The Finemet cavity has been simulated starting with the one cell model (the one that has also been measured) but also the cavity complete model with six cells has been studied
The dispersive material has been defined in CST with a dispersion model starting from the measurements of the μ’ and μ’’ parameters performed for Finemet by Mauro Paoluzzi .

3. Agenda Finemet cavity: one-cell model Finemet cavity: six-cells model
Design for simulation
1-cell cavity without Finemet
CST Finemet fitting (1st order): version 2012
CST Finemet fitting (nth order): version 2013
Wakefield CST Particle Studio analysis
Longitudinal wake potential
Comparison between measurements and simulations
Finemet cavity: six-cells model
Design for simulations

4. Agenda Finemet cavity: one-cell model Finemet cavity: six-cells model
Design for simulation
1-cell cavity without Finemet
CST Finemet fitting (1st order): version 2012
CST Finemet fitting (nth order): version 2013
Wakefield CST Particle Studio analysis
Longitudinal wake potential
Comparison between measurements and simulations
Finemet cavity: six-cells model
Design for simulations

5. Finemet 1-cell cavity design for CST simulations
Perfectly conducting walls
Finemet
Copper
Alumina
NB. The design considered for CST simulations has been simplify from the original mechanical model!

6. Agenda Finemet cavity: one-cell model Finemet cavity: six-cells model
Design for simulation
1-cell cavity without Finemet
CST Finemet fitting (1st order): version 2012
CST Finemet fitting (nth order): version 2013
Wakefield CST Particle Studio analysis
Longitudinal wake potential
Comparison between measurements and simulations
Finemet cavity: six-cells model
Design for simulations

7. 1-cell cavity without Finemet
Longitudinal impedance
Bunch length
260 mm
Wake length
800 m
fMAX
700 MHz
# of mesh
356,000
Method
Indirect test beam
In the longitudinal and transverse impedance one can identify a mode trapped around 208 MHz.
This mode will be dump by the insertion of the Finemet rings!

8. Agenda Finemet cavity: one-cell model Finemet cavity: six-cells model
Design for simulation
1-cell cavity without Finemet
CST Finemet fitting (1st order): version 2012
CST Finemet fitting (nth order): version 2013
Wakefield CST Particle Studio analysis
Longitudinal wake potential
Comparison between measurements and simulations
Finemet cavity: six-cells model
Design for simulations

9. CST Finemet fitting (1st order): version 2012
Fitting of μ’ used for simulations

10. CST Finemet fitting (1st order): version 2012
Fitting of μ’' used for simulations

11. Comparison between measurement and simulation
Longitudinal impedance
Bunch length
90 cm
Wake length
600 m
fMAX
200 MHz
# of mesh
Method
Direct
Because of the imprecise fitting of the dispersion parameters in CST 2012, the impedance obtained few month ago was not in perfect agreement with measurements
The differences between the two curves are due to the poor resolution at low frequencies and to the Direct integration method that has been used

12. Agenda Finemet cavity: one-cell model Finemet cavity: six-cells model
Design for simulation
1-cell cavity without Finemet
CST Finemet fitting (1st order): version 2012
CST Finemet fitting (nth order): version 2013
Wakefield CST Particle Studio analysis
Longitudinal wake potential
Comparison between measurements and simulations
Finemet cavity: six-cells model
Design for simulations

13. CST Finemet fitting (nth order): version 2013
Fitting of μ’ used for simulations

14. CST Finemet fitting (nth order): version 2013
Fitting of μ’' used for simulations
εr=25

15. Agenda Finemet cavity: one-cell model Finemet cavity: six-cells model
Design for simulation
1-cell cavity without Finemet
CST Finemet fitting (1st order): version 2012
CST Finemet fitting (nth order): version 2013
Wakefield CST Particle Studio analysis
Longitudinal wake potential
Comparison between measurements and simulations
Finemet cavity: six-cells model
Design for simulations

16. Wakefield CST Particle Studio analysis
Longitudinal wake potential
Bunch length
260 cm
Wake length
700 m
fMAX
700 MHz
# of mesh
98,175
Method
Indirect test beam
NB. This model of longitudinal wake potential can be used for Headtail simulations

17. Wakefield CST Particle Studio analysis
Electric field monitor
All the modes of the pillbox cavity are strongly dumped by the Finemet rings: we predict to have no issues regarding trapped or parasitic modes in the cavity

18. Comparison between measurement and simulation
Longitudinal impedance: real part
Bunch length
90 cm
Wake length
600 m
fMAX
200 MHz
# of mesh
Method
Indirect test beam
Results obtained with CST 2013 show a good agreement with the measured impedance!
This improvement in resolution at low frequencies has been obtained thank to a better fitting of the dispersion parameters and to the use of the Indirect test beam integration method

19. Comparison between measurement and simulation
Longitudinal impedance: imaginary part
Bunch length
90 cm
Wake length
600 m
fMAX
200 MHz
# of mesh
Method
Indirect test beam
Results obtained with CST 2013 show a good agreement with the measured impedance!
This improvement in resolution at low frequencies has been obtained thank to a better fitting of the dispersion parameters and to the use of the Indirect test beam integration method

20. Agenda Finemet cavity: one-cell model Finemet cavity: six-cells model
Design for simulation
1-cell cavity without Finemet
CST Finemet fitting (1st order): version 2012
CST Finemet fitting (nth order): version 2013
Wakefield CST Particle Studio analysis
Longitudinal wake potential
Comparison between measurements and simulations
Finemet cavity: six-cells model
Design for simulations

21. Finemet 6-cell cavity design for CST simulations
Few moths ago we had several problem in the model because of the errors encountered during import from CATIA.
These problems were source of loss of resolution but they have been solved on the new model!

22. Agenda Finemet cavity: one-cell model Finemet cavity: six-cells model
Design for simulation
1-cell cavity without Finemet
CST Finemet fitting (1st order): version 2012
CST Finemet fitting (nth order): version 2013
Wakefield CST Particle Studio analysis
Longitudinal wake potential
Comparison between measurements and simulations
Finemet cavity: six-cells model
Design for simulations

23. Wakefield CST Particle Studio analysis
Longitudinal wake potential
Bunch length
50 cm
Wake length
800 m
fMAX
345 MHz
# of mesh
3,000,816
Method
Indirect test beam
NB. This model of longitudinal wake potential can be used for Headtail simulations

24. Wakefield CST Particle Studio analysis
Electric field monitor
All the modes of the pillbox cavity are strongly dumped by the Finemet rings: we predict to have no issues regarding trapped or parasitic modes in the cavity

25. Comparison between measurement and simulation
Longitudinal impedance: real part
Bunch length
50 cm
Wake length
800 m
fMAX
354 MHz
# of mesh
3,000,816
Method
Indirect test beam
Results obtained with CST 2013 show a good agreement with the measured impedance!
The blue curve was obtained multiplying by a factor 6 the data from measurement of the 1-cell cavity

26. Comparison between measurement and simulation
Longitudinal impedance: imaginary part
Bunch length
50 cm
Wake length
800 m
fMAX
354 MHz
# of mesh
3,000,816
Method
Indirect test beam
Results obtained with CST 2013 show a good agreement with the measured impedance!
The blue curve was obtained multiplying by a factor 6 the data from measurement of the 1-cell cavity

27. Conclusions
From simulations performed with two different versions of CST Particle Studio we can confirm that the impedance observed with measurements can be exited by bunches circulating in the PS.
In the six-cell cavity, a circulating bunch can excite a longitudinal impedance that has a maximum of 2 kΩ around 4 MHz on the real part, that also correspond to the zero crossing of the imaginary part curve.
The same mode seems to be produced also on the transverse plane: more investigations with the new SCT version are needed .
All the eigenmodes of the cavity are strongly dumped by the Finemet rings: we predict to have no issues regarding trapped or parasitic modes in the Finemet cavity.
Improvements of the quality of simulation have been obtained thanks to a better fitting of the dispersion parameters of CST version 2013 and thanks to the use of an indirect integration method that is more accurate that the direct method used few months ago. .