Simulations of the SPS kickers with CST Particle Studio

1. 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

2. Overview • Objectives • Simulations and comparison with theory • Conclusions • Future Plans • Appendix (back up slides, if needed and time permitting)

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

4. Overview • Objectives • Simulations and comparison with theory • Conclusions • Future Plans • Appendix (back up slides, if needed and time permitting)

5. SPS MKE kickers analyzed

6. Fit used for the ferrite

7. Fit used for the ferrite

8. Model used (Tsutsui) L

9. Longitudinal Impedance Theory from Tsutsui L=1m b=0.016m d=0.076m a=0.0675m Ferrite 4A4 s σ=8cm Simulated length=0.2m Gaussian bunch used for the excitation

10. Longitudinal Impedance Theory from Tsutsui L=1.66m b=0.016m d=0.076m a=0.0675m Ferrite 4A4 σ=10cm Simulated length=1m

11. Longitudinal Impedance L=1.66m b=0.016m d=0.076m a=0.0675m Ferrite 4A4 Theory from Tsutsui σ=2cm Simulated length=1m

12. Vertical driving Impedance • L=1.66m • b=0.016m • d=0.076m • a=0.0675m • Ferrite 4A4 σ=10cm Simulated length=1.66m

13. Horizontal driving Impedance • L=1.66m • b=0.016m • d=0.076m • a=0.0675m • Ferrite 4A4 σ=10cm Simulated length=0.2m

14. L=1.66m • b=0.016m • d=0.076m • a=0.0675m • Ferrite 4A4 Wake Potential W[V/pC] s(cm)

15. L=1.66m • b=0.016m • d=0.076m • a=0.0675m • Ferrite 4A4 Wake Potential W[V/pC] s(cm)

16. L=1.66m • b=0.016m • d=0.076m • a=0.0675m • Ferrite 4A4 Wake Potential W[V/pC] s(cm)

17. L=1.66m • b=0.016m • d=0.076m • a=0.0675m • Ferrite 4A4 Wake Potential W[V/pC] s(cm)

18. L=1.66m • b=0.016m • d=0.076m • a=0.0675m • Ferrite 4A4 Vertical driving and detuning impedance σ=10cm Simulated length=1.66m Z[Ω/m] Frequency(GHz)

19. Horizontal driving and detuning impedance • L=1.66m • b=0.016m • d=0.076m • a=0.0675m • Ferrite 4A4 σ=10cm Simulated length=1m Z[Ω/m] Frequency(GHz)

20. Vertical Impedance Z[Ω/m] Frequency(GHz) All terms are simulated

21. Horizontal Impedance Z[Ω/m] Frequency(GHz) All terms are simulated

22. Courtesy M. Barnes

23. Overview • Objectives • Simulations and comparison with theory • Conclusions • Future Plans • Appendix (back up slides, if needed and time permitting)

24. 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

25. Overview • Objectives • Simulations and comparison with theory • Conclusions • Future Plans • Appendix (back up slides, if needed and time permitting)

26. 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.

27. Comparison between simulations with different bunch lengths Z[Ω/m] Frequency(GHz)

28. Vertical Impedance: comparison with the theory for short bunches • L=1.66m • b=0.016m • d=0.076m • a=0.0675m • Ferrite 4A4 σ=1.5cm Simulated length=1m Due to the mesh, which is not dense enough, maybe issue with the imaginary part ?

29. Vertical Impedance: comparison with the theory with an even shorter bunch (pushing the performance of Particle Studio with our present hardware resources) • L=1.66m • b=0.016m • d=0.076m • a=0.0675m • Ferrite 4A4 σ=1.1cm Simulated length=0.8m

30. Effect of finite length of the kicker • 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.

31. Simulations with different kicker lengths: differences are due to an effect of finite length or numerical error? • L=1.66m • b=0.016m • d=0.076m • a=0.0675m • Ferrite 4A4 Vertical Impedance Z[Ω/m] Frequency(GHz)

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

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

34. Simulations with different kicker lengths: differences are due to an effect of finite length or numerical error? • L=1.66m • b=0.016m • d=0.076m • a=0.0675m • Ferrite 4A4 σ=10cm Simulated length=0.2m Is the simulation wrong or the theory is not valid?

35. Appendix Other models of simulation

36. Model (Tsutsui and Zotter) Model2 Model1r Model1

37. Model1

38. Transverse impedance using Tsutsui model 1: comparison with the theory Theory: Elias&Benoit • L=1.66m • b=0.016m • d=0.076m • a=0.0675m • Ferrite 4A4 σ=10cm Simulated length=0.2m

39. Transverse impedance using Tsutsui model 1: comparison with the theory • L=1.66m • b=0.016m • d=0.076m • a=0.0675m • Ferrite 4A4 Theory: Elias&Benoit σ=10cm Simulated length=1.0m

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

41. Comparing circular and rectangular model

42. Comparing two different rectangular models Z[Ω/m] Frequency(GHz) There is a good agreement for the vertical driving

43. Comparing two different rectangular models Z[Ω/m] Frequency(GHz)

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