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Update on the impedance of the SPS kickers

Update on the impedance of the SPS kickers. E. M étral, G. Rumolo, B. Salvant, C. Zannini. Acknowledgments: F. Caspers, A. Grudiev, R. Wegner, L. Haenichen, W. Mueller. SPS impedance meeting - Oct. 16 th 2009. Agenda. Context and objectives

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Update on the impedance of the SPS kickers

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  1. Update on the impedance of the SPS kickers E. Métral, G. Rumolo, B. Salvant, C. Zannini Acknowledgments: F. Caspers, A. Grudiev, R. Wegner, L. Haenichen, W. Mueller SPS impedance meeting - Oct. 16th 2009

  2. Agenda Context and objectives Dipolar and quadrupolar impedance from Tsutsui’s theory CST simulations and theory HEADTAIL simulations with updated impedance models Comparison with measurements for the PS kickers Conclusions Future plans 2

  3. Context • SPS kickers are major contributors to the SPS impedance. • Up to now, to obtain the impedance of the SPS kickers we have used • Zotter/Métral model for a cylindrical beam pipe made of ferrite • Applied the Yokoya form factors to transform into a flat chamber • However, the Yokoya factors were obtained providing • the beam is ultrarelativistic, • the beam pipe is longitudinally uniform, • the skin depth is much smaller than the dimensions of the beam pipe and the thickness of the material. Objectives • Use the Tsutsui formalism to obtain a new formula for the quadrupolar impedance • Perform CST time domain simulations and compare with theories of Zotter/Métral and Tsutsui • Perform HEADTAIL simulations to assess the beam dynamics impact of using the Tsutsui formalism and compare with measurements. • Compare the theory and EM simulations with RF impedance measurements with wire for a PS kicker

  4. Agenda Context and objectives Dipolar and quadrupolar impedance from Tsutsui’s theory Geometrical models Quadrupolar impedance formula using Tsutsui formalism Form factors CST simulations and theory for 1 MKE kicker (ferrite 4A4) for 1 MKE kicker (ferrite 8C11) for all SPS kickers (ferrite 4A4) HEADTAIL simulations with updated impedance models SPS kickers only Current SPS model from ZBASE (kickers+beam pipe+BPMs) Comparison with measurements for the PS kickers Conclusions Future plans 4

  5. Definition of geometrical models Geometric models for impedance calculations Round chamber Flat chamber Tsutsui’s model y b y y x x x a Vacuum Ferrite Perfect conductor Model studied Theory by Tsutsui valid for ultrarelativistic beams

  6. At transverse coordinate (x,y)=(,0) EM fields for a source beam at (x,y)=(0,0)) For arbitrarily small  Same methodfor vertical quadrupolar impedance Dipolar and quadrupolar terms from Tsutsui’s theory • Dipolar impedance is given by H. Tsutsui in his paper on transverse impedance (source beam displaced) • We computed the quadrupolar impedance from the E and H fields given by H. Tsutsui in his paper on longitudinal impedance (source beam on center) Detuning horizontal impedance

  7. Dipolar and quadrupolar terms from Tsutsui’s theory  Impedance for 1 MKE kicker (Tsutsui) Yokoya factors ???

  8. Dipolar and quadrupolar terms from Tsutsui’s theory Impedance for all MKE kickers (Tsutsui) Wake function for all MKE kickers (Tsutsui) Yokoya factors ??? iDFT

  9. Dipolar and quadrupolar terms from Tsutsui’s theory Wake function for all MKE kickers (Tsutsui) Wake function for all MKE kickers (Zotter/Métral) It is not possible to relate the curves using simply Yokoya factors! Main differences: • Short range Wydip • Medium range quadrupolar wakes

  10. Theory: form factors  All form factors seem to converge to 2/24, even the vertical dipolar term!

  11. Theory: form factors Comparing Tsutsui and Zotter theoretical results to Burov-Lebedev theoretical results accounting for frequency dependent form factors (EPAC’02) Horizontal driving Impedance Rather different… to be understood…

  12. Theory: form factors Comparing Tsutsui and Zotter theoretical results to Burov-Lebedev theoretical results accounting for frequency dependent form factors (EPAC’02) Vertical driving Impedance Tsutsui and Burov Lebedev with frequency dependent form factors are similar at high frequencies

  13. Agenda Context and objectives Dipolar and quadrupolar impedance from Tsutsui’s theory Geometrical models Quadrupolar impedance formula using Tsutsui formalism Form factors CST simulations and theory for 1 MKE kicker (ferrite 4A4) for 1 MKE kicker (ferrite 8C11) for all SPS kickers (ferrite 4A4) HEADTAIL simulations with updated impedance models SPS kickers only Current SPS model from ZBASE (kickers+beam pipe+BPMs) Comparison with measurements for the PS kickers Conclusions Future plans 13

  14. Geometrical model used (Tsutsui) L

  15. CST simulations for 1 MKE kicker (ferrite 4A4) :Model used for the ferrite 4A4

  16. CST simulations for 1 MKE kicker (ferrite 4A4) :Fit used for the ferrite 4A4

  17. CST simulations for 1 MKE kicker (ferrite 4A4) :Fit used for the ferrite 4A4

  18. CST simulations for 1 MKE kicker (ferrite 4A4) :Vertical driving impedance: comparison between simulations with different bunch lengths Z[Ω/m] Frequency(GHz)

  19. CST simulations for 1 MKE kicker (ferrite 4A4) :Vertical driving impedance: comparison with theory • L=1.66m • b=0.016m • d=0.076m • a=0.0675 • Ferrite 4A4 σ=1.5cm Simulated length=1m Due to the mesh, which is not dense enough, maybe issue with the imaginary part ?

  20. CST simulations for 1 MKE kicker (ferrite 4A4) :Horizontal driving impedance: comparison with theory • L=1.66m • b=0.016m • d=0.076m • a=0.0675 • Ferrite 4A4 σ=1.5cm Simulated length=1m

  21. CST simulations for 1 MKE kicker (ferrite 4A4) :Horizontal detuning impedance: comparison with theory • L=1.66m • b=0.016m • d=0.076m • a=0.0675 • Ferrite 4A4 σ=1.5cm Simulated length=1m

  22. CST simulations for 1 MKE kicker (ferrite 4A4) :Vertical driving impedance: comparison with theory • L=1.66m • b=0.016m • d=0.076m • a=0.0675 • Ferrite 4A4 σ=1.5cm Simulated length=1m

  23. CST simulations for 1 MKE kicker (ferrite 4A4) :Vertical detuning impedance: comparison with the theory • L=1.66m • b=0.016m • d=0.076m • a=0.0675 • Ferrite 4A4 σ=1.5cm Simulated length=1m

  24. CST simulations for 1 MKE kicker (ferrite 4A4) :Comparing simulated horizontal and vertical detuning At high frequency

  25. CST simulations for 1 MKE kicker (ferrite 4A4) :Vertical general impedance: comparison with the theory for short bunches

  26. CST simulations for 1 MKE kicker (ferrite 4A4) :Horizontal general impedance: comparison with the theory for short bunches

  27. CST simulations for 1 MKE kicker (ferrite 8C11) :Model used for the ferrite 8C11 from measurements mentioned in L. Vos, 2000

  28. CST simulations for 1 MKE kicker (ferrite 8C11) :Fit used for the ferrite 8C11

  29. CST simulations for 1 MKE kicker (ferrite 8C11) :Fit used for the ferrite 8C11 and measurements

  30. CST simulations for 1 MKE kicker (ferrite 8C11) :Fit used for the ferrite 8C11 and measurements

  31. Comparing Tsutsui theories for 4A4, 8C11fit and 8C11measure Longitudinal Impedance Rather similar, as found out by Elias

  32. Comparing Tsutsui theories for 4A4, 8C11fit and 8C11measure Horizontal driving Impedance Again similar…

  33. Comparing Tsutsui theories for 4A4, 8C11fit and 8C11measure Vertical driving Impedance Again similar…

  34. Comparing theory 4A4,8C11fit and 8C11measure Detuning vertical impedance Again similar…

  35. Comparing simulations for 4A4 and 8C11fit Longitudinal Impedance Impedance[Ohm]

  36. Comparing simulations for 4A4 and 8C11fit Horizontal impedance Comparing 4A4 and 8C11 transverse Impedance

  37. Comparing simulations for 4A4 and 8C11fit Vertical impedance

  38. All kickers

  39. CST time domain simulations Rms Bunch length 2 cm DFT

  40. CST simulations and theory: 1 MKE kicker (ferrite 4A4) Impedance from theory and simulation for 1 MKE kicker Rms simulated bunch length 2 cm  Good agreement between dip and quad theories and 3D simulations!!!  Discrepancies occur for high frequencies (Zy dip)

  41. Wake functions from theory and wake potentials from simulations for all SPS kickers Theory gives an impedance, simulations gives a wake potential.For HEADTAIL simulations, we need the wake function…. Simulated rms bunch length: 2 cm Simulated rms bunch length: 10 cm  Important to use short bunch lengths!  Wake with bunch length of 2 cm is close enough to theory

  42. Summary for EM simulations • EM simulations in good agreement with the dipolar and quadrupolar contributions obtained from the Tsutsui theory • EM simulations for ferrites 4A4 and 8C11 are very similar • Importance of short bunch length in simulations • Now let us use the wake functions in Headtail…

  43. Agenda Context and objectives Dipolar and quadrupolar impedance from Tsutsui’s theory Geometrical models Quadrupolar impedance formula using Tsutsui formalism Form factors CST simulations and theory for 1 MKE kicker (ferrite 4A4) for 1 MKE kicker (ferrite 8C11) for all SPS kickers (ferrite 4A4) HEADTAIL simulations with updated impedance models SPS kickers only Current SPS model from ZBASE (kickers+beam pipe+BPMs) Comparison with measurements for the PS kickers Conclusions Future plans 43

  44. HEADTAIL simulations • Simulations of a bunch made of macroparticles interacting with one localized impedance source. • SPS parameters at injection • We show results with the more precise theoretical wakes. Results with simulated wake potentials are very similar to the Tsutsui model.

  45. HEADTAIL simulations with the wake of the SPS kickers only (Zotter/Métral and Tsutsui models) 45

  46. Mode spectra for Zotter/Métral model of the SPS kickers

  47. Mode spectra for Tsutsui model of the SPS kickers

  48. Comparing simulated observables with measurements(SPS kickers) • Modelled SPS kickers account for 45% of the measured vertical SPS impedance • Horizontal tune shift is very close to measurements for the Tsutsui model • Instability threshold in measurements represents 40 % of the first simulated threshold (Tsutsui)

  49. HEADTAIL simulations with the wake of the current SPS model (SPS kickers + BPHs +BPVs + beam pipe) (Zotter/Métral models) (Zotter/Métral and Tsutsui models) CST simulations 50

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