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

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

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 (a)the beam is ultrarelativistic, (b)the beam pipe is longitudinally uniform, (c)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

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

6 Dipolar and quadrupolar terms from Tsutsui’s theory EM fields for a source beam at (x,y)=(0,0)) At transverse coordinate (x,y)=( ,0) Detuning horizontal impedance 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) Same method for vertical quadrupolar impedance For arbitrarily small 

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) Main differences: Short range Wydip Medium range quadrupolar wakes It is not possible to relate the curves using simply Yokoya factors!

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

37 Comparing simulations for 4A4 and 8C11fit Vertical impedance

38 All kickers

39 CST time domain simulations DFT Rms Bunch length 2 cm

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

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

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

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)

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

47 Mode spectra for Tsutsui model of the SPS kickers

48

49 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)

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

51 Wake functions for SPS impedance models accounting for: importing into HEADTAIL… Wxdip Wydip Wxquad Wyquad - kickers - BPMs - Beam pipe

52 Mode spectra for SPS model: BPMs + beam pipe+ kickers (Zotter/Métral)

53 Mode spectra for SPS model: BPMs + beam pipe+ kickers(Tsutsui)

54 Comparison between the tune shifts obtained from the two SPS impedance models

55 Comparison between the growth rates obtained from the two SPS impedance models

56 Comparing simulated observables with measurements (SPS kickers + beam pipe + BPMs)  Current SPS model accounts for 60% of the measured vertical SPS impedance  Horizontal tune shift is very close to measurements for the Tsutsui model  Instability threshold in measurements is of the same order than the instability thresholds in simulations (Tsutsui), but most likely it is the 3 rd instability threshold that matters. In this case, the current SPS model again accounts for 60% of the impedance.

57 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

58 Comparing Measure and theoretical results in a PS kickers (KFA13) x y x y Using the coaxial wire method, we measure the longitudinal impedance at different positions and then following the approach shown above we obtain the transverse generalized terms

59 MEASURED LONGITUDINAL IMPEDANCE (Re) VS. HORIZONTAL OFFSET 100 pictures (every 10 MHz until 1 GHz) Elias Métral, APC meeting, 08/12/05

60 MEASURED LONGITUDINAL IMPEDANCE (Im) VS. HORIZONTAL OFFSET 100 pictures (every 10 MHz until 1 GHz) Elias Métral, APC meeting, 08/12/05

61 MEASURED LONGITUDINAL IMPEDANCE (Re) VS. VERTICAL OFFSET 100 pictures (every 10 MHz until 1 GHz) Elias Métral, APC meeting, 08/12/05

62 Elias Métral, APC meeting, 08/12/05 MEASURED LONGITUDINAL IMPEDANCE (Im) VS. VERTICAL OFFSET 100 pictures (every 10 MHz until 1 GHz)

pictures (every 10 MHz until 1 GHz) THE NEXT 4 SLIDES ARE THE SAME AS THE PREVIOUS 4 ONES, BUT WITHOUT A FIXED VERTICAL SCALE Elias Métral, APC meeting, 08/12/05

pictures (every 10 MHz until 1 GHz) Elias Métral, APC meeting, 08/12/05

pictures (every 10 MHz until 1 GHz) Elias Métral, APC meeting, 08/12/05

pictures (every 10 MHz until 1 GHz) Elias Métral, APC meeting, 08/12/05

67 Comparing Measure and theoretical results in a PS kickers (KFA13) Generalized horizontal Impedance Measurements: courtesy E. Métral, F. Caspers, M. Giovannozzi, A. Grudiev, T. Kroyer, L. Sermeus, EPAC’06

68 Comparing Measure and theoretical results in a PS kickers (KFA13) Generalized vertical Impedance Measurements: courtesy E. Métral, F. Caspers, M. Giovannozzi, A. Grudiev, T. Kroyer, L. Sermeus, EPAC’06

69 Comparing Measure and theoretical results in a PS kickers (KFA13) Longitudinal Impedance Measurements: courtesy E. Métral, F. Caspers, M. Giovannozzi, A. Grudiev, T. Kroyer, L. Sermeus, EPAC’06

70 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

71 Conclusions We used the Tsutsui formalism to calculate a new formula for the quadrupolar impedance We benchmarked CST time domain simulations for the simple model of kicker proposed by Tsutsui with the dipolar and quadrupolar theory based on Tsutsui’s formalism. Comparing with the theories from Zotter/Métral, we can conclude that the Yokoya factors do not hold in this case, and are most likely frequency dependent, as investigated by Burov/Lebedev. Using ferrites 4A4 or 8C11 does not lead to significant differences in the frequency range of interest, as already mentioned by Elias. We performed HEADTAIL simulations and assessed the beam dynamics impact of using the Tsutsui formalism: –The horizontal tune shift is positive, as in the measurements with beam in the SPS –Current SPS model accounts for 60% of the measured vertical SPS impedance We compared the theory and EM simulations with RF impedance measurements with wire for a PS kicker. We can only compute the general contributions, and not disentangle the dipolar and quadrupolar contributions. The behaviour is somewhat similar, but it seems many effects are not accounted for in the simple model of kicker used for theory and simulations.

72 Future plans Characterization of the EM parameters of ferrite (collaboration with Tatiana Pieloni)  main assumption in the calculations and simulations Theory for flat chamber without Yokoya factors (by Nicolas Mounet). Transverse dipolar and quadrupolar impedance measurements of a single cell of an MKE kicker, and a full MKE kicker. Include more impedance sources in the model (RF cavities as mentioned by Bruno, pumping ports, other instrumentation). Refine the current models (MKQH in laminated steel) and see the effect of not matching 1 or more BPMs on HEADTAIL simulations See the changes in CST 2010 beta version provided by CST this week.

73 Thank you for your attention!

74

75 Geometrical model for time domain simulations Ferrite 4A4 Beam path Wake integration path Rms Bunch length 2 cm

76 Longitudinal Impedance Theory from Tsutsui L=1.66m b=0.016m d=0.076m a= Ferrite 4A4 σ=10cm Simulated length=1m  Gaussian bunch used for the excitation

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

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

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

80 Horizontal Detuning Impedance L=1.66m b=0.016m d=0.076m a= Ferrite 4A4 σ=10cm Simulated length=1m

81 Vertical Detuning Impedance L=1.66m b=0.016m d=0.076m a= Ferrite 4A4 σ=10cm Simulated length=1.66m

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

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

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

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

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

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

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

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