Simulations of the SPS kickers with CST Particle Studio
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Transcript of Simulations of the SPS kickers with CST Particle Studio
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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
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Overview• Objectives
• Simulations and comparison with theory
• Conclusions
• Future Plans
• Appendix (back up slides, if needed and time permitting)
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Objectives
• To simulate the simple model (Tsutsui): longitudinal and transverse wake separating dipolar and quadrupolar terms.
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Overview• Objectives
• Simulations and comparison with theory
• Conclusions
• Future Plans
• Appendix (back up slides, if needed and time permitting)
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SPS MKE kickers analyzed
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Fit used for the ferrite'''* jrr 0
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Fit used for the ferrite'''* jrr 0
'
''
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Model used (Tsutsui)
L
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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
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Longitudinal Impedance
Theory from Tsutsui L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4
σ=10cmSimulated length=1m
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Longitudinal Impedance
Theory from Tsutsui L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4
σ=2cmSimulated length=1m
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Vertical driving ImpedanceL=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4
σ=10cmSimulated length=1.66m
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Horizontal driving ImpedanceL=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4
σ=10cmSimulated length=0.2m
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L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4
s(cm)
W[V/pC]
Wake Potential
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L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4
s(cm)
W[V/pC]
Wake Potential
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L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4
s(cm)
W[V/pC]
Wake Potential
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L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4
s(cm)
W[V/pC]
Wake Potential
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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
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L=1.66mb=0.016md=0.076ma=0.0675mFerrite 4A4
Horizontal driving and detuning impedance
Frequency(GHz)
Z[Ω/m]
σ=10cmSimulated length=1m
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Vertical Impedance
All terms are simulated
)()()( sZsZsZ detuningy
drivingy
generaly
Frequency(GHz)
Z[Ω/m]
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Horizontal Impedance
)()()( sZsZsZ detuningx
drivingx
generalx
All terms are simulated
Frequency(GHz)
Z[Ω/m]
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Courtesy M. Barnes
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Overview• Objectives
• Simulations and comparison with theory
• Conclusions
• Future Plans
• Appendix (back up slides, if needed and time permitting)
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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
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Overview• Objectives
• Simulations and comparison with theory
• Conclusions
• Future Plans
• Appendix (back up slides, if needed and time permitting)
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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.
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Comparison between simulations with different bunch lengths
Frequency(GHz)
Z[Ω/m]
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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 ?
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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
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• 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
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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]
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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?
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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?
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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?
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Appendix
Other models of simulation
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Model (Tsutsui and Zotter)
Model1Model1r
Model2
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Model1
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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
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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
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Form Factor between circular and rectangular model
• By the theory between a circular pipe and a rectangular pipe there is only a form factor.
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Comparing circular and rectangular model
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Comparing two different rectangular models
There is a good agreement for the vertical driving
Frequency(GHz)
Z[Ω/m]
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Frequency(GHz)
Z[Ω/m]
Comparing two different rectangular models
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The ration between the circular and rectangular structure is not simply the Yokoya factor, like for purely conductive walls.
Comparing circular and rectangular model