simulations of the sps kickers with cst particle studio

Simulations of the SPS kickers with CST Particle Studio

C. Zannini,E. Métral, G. Rumolo, B. Salvant

Thanks to:L. Haenichen, W. Mueller, TU Darmstadt

Overview• Objectives

• Simulations and comparison with theory

• Conclusions

• Future Plans

• Appendix (back up slides, if needed and time permitting)

2

Objectives

• To simulate the simple model (Tsutsui): longitudinal and transverse wake separating dipolar and quadrupolar terms.

Overview• Objectives

• Simulations and comparison with theory

• Conclusions

• Future Plans

• Appendix (back up slides, if needed and time permitting)

4

SPS MKE kickers analyzed

Fit used for the ferrite'''* jrr 0

Fit used for the ferrite'''* jrr 0

'

''

Model used (Tsutsui)

L

Longitudinal Impedance

Theory from Tsutsui L=1mb=0.016md=0.076ma=0.0675mFerrite 4A4

σ=8cmSimulated length=0.2m

s

Gaussian bunch used for the excitation

Longitudinal Impedance

Theory from Tsutsui L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4

σ=10cmSimulated length=1m

Longitudinal Impedance

Theory from Tsutsui L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4

σ=2cmSimulated length=1m

Vertical driving ImpedanceL=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4

σ=10cmSimulated length=1.66m

Horizontal driving ImpedanceL=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4

σ=10cmSimulated length=0.2m

L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4

s(cm)

W[V/pC]

Wake Potential

L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4

s(cm)

W[V/pC]

Wake Potential

L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4

s(cm)

W[V/pC]

Wake Potential

L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4

s(cm)

W[V/pC]

Wake Potential

L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4

Vertical driving and detuning impedance

Frequency(GHz)

Z[Ω/m]

σ=10cmSimulated length=1.66m

L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4

Horizontal driving and detuning impedance

Frequency(GHz)

Z[Ω/m]

σ=10cmSimulated length=1m

Vertical Impedance

All terms are simulated

)()()( sZsZsZ detuningy

drivingy

generaly

Frequency(GHz)

Z[Ω/m]

Horizontal Impedance

)()()( sZsZsZ detuningx

drivingx

generalx

All terms are simulated

Frequency(GHz)

Z[Ω/m]

Courtesy M. Barnes

Overview• Objectives

• Simulations and comparison with theory

• Conclusions

• Future Plans

• Appendix (back up slides, if needed and time permitting)

23

Conclusion

• The simulations exhibit very good agreement with theory for long bunches (8-10cm). However, to use the wake field data as an input for HEADTAIL, we need to investigate a larger frequency range. Therefore, we have to do simulations with decreased bunch length.

• When we decrease the bunch length, we need a very dense mesh, sometimes incompatible with our present memory resources. A compromise has to be found between the computing capacity and the requirements for HEADTAIL

• The dispersion model of the ferrite is less accurate, because we use always the same number of points to fit the model

Overview• Objectives

• Simulations and comparison with theory

• Conclusions

• Future Plans

• Appendix (back up slides, if needed and time permitting)

25

Future plans

• To simulate the kickers of SPS (driving and detuning terms) using a shorter bunch (1-2cm) and to feed the results into HEADTAIL.

Comparison between simulations with different bunch lengths

Frequency(GHz)

Z[Ω/m]

Vertical Impedance: comparison with the theory for short bunches

σ=1.5cmSimulated length=1m

L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4

Due to the mesh, which is not dense enough, maybe issue with the imaginary part ?

Vertical Impedance: comparison with the theory with an even shorter bunch (pushing the performance of Particle Studio

with our present hardware resources)

σ=1.1cmSimulated length=0.8m

L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4

• The theory is obtained using infinite length. Therefore the comparison between theory and simulations is meaningful if the results are linear with the length. The linearity with L (kicker length) should be true when the penetration depth is much smaller than the length (this is the case of conductive material). In the case of ferrite, the penetration depth δ is much larger and the linearity may not be verified.

Effect of finite length of the kicker

1L

fr

s 503

2

Simulations with different kicker lengths: differences are due to an effect of finite length or numerical error?

Vertical Impedance

L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4

Frequency(GHz)

Z[Ω/m]

20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0140000

150000

160000

170000

180000

190000

200000

210000

Real Vertical Impedance

f=800MHz

Z[/

m]

L(cm)

Simulations with different kicker lengths: differences are due to an effect of finite length or numerical error?

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0

300000

310000

320000

330000

340000

350000

360000

370000

Imaginary Vertical Impedance

f=500MHz

Z[/

m]

L(cm)

Simulations with different kicker lengths: differences are due to an effect of finite length or numerical error?

L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4

σ=10cmSimulated length=0.2m

Is the simulation wrong or the theory is not valid?

Simulations with different kicker lengths: differences are due to an effect of finite length or numerical error?

Appendix

Other models of simulation

Model (Tsutsui and Zotter)

Model1Model1r

Model2

Model1

Transverse impedance using Tsutsui model 1: comparison with the theory

Theory: Elias&Benoit L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4

σ=10cmSimulated length=0.2m

Transverse impedance using Tsutsui model 1: comparison with the theory

L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4

σ=10cmSimulated length=1.0m

Theory: Elias&Benoit

Form Factor between circular and rectangular model

• By the theory between a circular pipe and a rectangular pipe there is only a form factor.

Comparing circular and rectangular model

Comparing two different rectangular models

There is a good agreement for the vertical driving

Frequency(GHz)

Z[Ω/m]

Frequency(GHz)

Z[Ω/m]

Comparing two different rectangular models

The ration between the circular and rectangular structure is not simply the Yokoya factor, like for purely conductive walls.

Comparing circular and rectangular model