Update on the impedance of the SPS kickers by ewghwehws

VIEWS: 3 PAGES: 89

									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
                                                                                 1
                           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
                                                 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
                                                                                                                 3
                                             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
                     Definition of geometrical models


                    Geometric models for impedance calculations

Round chamber                     Flat chamber                     Tsutsui’s model



    y                                  y                      b          y
        x                                  x                                 x




                                                                             a
                   Vacuum
                   Ferrite
                   Perfect conductor

                                                                  Model studied

            Theory by Tsutsui valid for ultrarelativistic beams
                                                                                     5
          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)


EM fields for a source beam at (x,y)=(0,0))
                                                         At transverse coordinate (x,y)=(,0)




                                                  Detuning horizontal impedance




              For arbitrarily small 

            Same method
for vertical quadrupolar impedance
                                                                                                           6
    Dipolar and quadrupolar terms from Tsutsui’s theory

 Impedance for 1 MKE kicker (Tsutsui)




                               Yokoya factors ???
                                                          7
      Dipolar and quadrupolar terms from Tsutsui’s theory

Impedance for all MKE kickers (Tsutsui)          Wake function for all MKE kickers (Tsutsui)




                                          iDFT               Yokoya factors ???
                                                                                               8
    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
                                                                                                  9
                           Theory: form factors




 All form factors seem to converge to 2/24, even the vertical dipolar term!   10
                              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…
                                                                                            11
                            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
                                                                                            12
                                             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
Geometrical model used (Tsutsui)


                L




                                   14
CST simulations for 1 MKE kicker (ferrite 4A4) :
           Model used for the ferrite 4A4




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

          0 * r           r   ' j ' '




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

             0 *r           r   ' j ' '




                                   '



     ''



                                                   17
           CST simulations for 1 MKE kicker (ferrite 4A4) :
Vertical driving impedance: comparison between simulations with different bunch lengths
  Z[Ω/m]




                                      Frequency(GHz)



                                                                                          18
CST simulations for 1 MKE kicker (ferrite 4A4) :
     Vertical driving impedance: comparison with theory
         L=1.66m
         b=0.016m
         d=0.076m                σ=1.5cm
         a=0.0675                Simulated length=1m
         Ferrite 4A4


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




                                                                        19
CST simulations for 1 MKE kicker (ferrite 4A4) :
   Horizontal driving impedance: comparison with theory
          L=1.66m
          b=0.016m
          d=0.076m                σ=1.5cm
          a=0.0675                Simulated length=1m
          Ferrite 4A4




                                                          20
CST simulations for 1 MKE kicker (ferrite 4A4) :
  Horizontal detuning impedance: comparison with theory

        L=1.66m
        b=0.016m
        d=0.076m               σ=1.5cm
        a=0.0675               Simulated length=1m
        Ferrite 4A4




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




                                                          22
CST simulations for 1 MKE kicker (ferrite 4A4) :
  Vertical detuning impedance: comparison with the theory

            L=1.66m
            b=0.016m
            d=0.076m               σ=1.5cm
            a=0.0675               Simulated length=1m
            Ferrite 4A4




                                                            23
CST simulations for 1 MKE kicker (ferrite 4A4) :
   Comparing simulated horizontal and vertical detuning




           At high frequency   Z det   Z x
                                 y
                                           det



                                                          24
    CST simulations for 1 MKE kicker (ferrite 4A4) :
Vertical general impedance: comparison with the theory for short bunches




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




                                                                             26
      CST simulations for 1 MKE kicker (ferrite 8C11) :
Model used for the ferrite 8C11 from measurements mentioned in L. Vos, 2000




                                                                              27
CST simulations for 1 MKE kicker (ferrite 8C11) :
             Fit used for the ferrite 8C11


            0 * r            r   ' j ' '




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


            0 * r           r   ' j ' '




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

              0 * r           r   ' j ' '




                                                     30
Comparing Tsutsui theories for 4A4, 8C11fit and 8C11measure

                     Longitudinal Impedance




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


                  Horizontal driving Impedance




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

                   Vertical driving Impedance




            Again similar…                                    33
Comparing theory 4A4,8C11fit and 8C11measure

              Detuning vertical impedance




      Again similar…                           34
                 Comparing simulations for 4A4 and 8C11fit

                            Longitudinal Impedance
Impedance[Ohm]




                                                             35
Comparing simulations for 4A4 and 8C11fit


             Horizontal impedance

      Comparing 4A4 and 8C11 transverse Impedance




                                                    36
Comparing simulations for 4A4 and 8C11fit


            Vertical impedance




                                            37
All kickers




              38
CST time domain simulations
        Rms Bunch length 2 cm




              DFT
                                39
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)                    40
           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
                                                                                                 41
        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…




                                                          42
                                             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
               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.
HEADTAIL simulations with the wake of the
           SPS kickers only

          (Zotter/Métral and Tsutsui models)




                                               45
Mode spectra for Zotter/Métral model of the SPS kickers




                                                          46
Mode spectra for Tsutsui model of the SPS kickers




                                                    47
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 and Tsutsui models)                     (Zotter/Métral models)

                                     CST simulations




                                                                                50
Wake functions             Wxdip
    for SPS
  impedance
    models
accounting for:            Wydip

     - kickers
     - BPMs
     - Beam pipe

                       Wxquad




                       Wyquad


importing into HEADTAIL…
                                   51
     Mode spectra for SPS model:
BPMs + beam pipe+ kickers (Zotter/Métral)




                                            52
  Mode spectra for SPS model:
BPMs + beam pipe+ kickers(Tsutsui)




                                     53
Comparison between the tune shifts obtained
   from the two SPS impedance models




                                              54
Comparison between the growth rates obtained
   from the two SPS impedance models




                                               55
   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 3rd instability threshold
 that matters. In this case, the current SPS model again accounts for 60% of the
 impedance.                                                                             56
                                             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


                                                                 57
    Comparing Measure and theoretical results
            in a PS kickers (KFA13)



                                                                   y
y




                 x                                                                   x


     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

                                                                                     58
   MEASURED LONGITUDINAL IMPEDANCE (Re) VS. HORIZONTAL OFFSET

                                              100 pictures (every 10
                                              MHz until 1 GHz)




Elias Métral, APC meeting, 08/12/05                                59
   MEASURED LONGITUDINAL IMPEDANCE (Im) VS. HORIZONTAL OFFSET

                                              100 pictures (every 10
                                              MHz until 1 GHz)




Elias Métral, APC meeting, 08/12/05                                60
    MEASURED LONGITUDINAL IMPEDANCE (Re) VS. VERTICAL OFFSET

                                              100 pictures (every 10
                                              MHz until 1 GHz)




Elias Métral, APC meeting, 08/12/05                                61
    MEASURED LONGITUDINAL IMPEDANCE (Im) VS. VERTICAL OFFSET

                                              100 pictures (every 10
                                              MHz until 1 GHz)




Elias Métral, APC meeting, 08/12/05                                62
      THE NEXT 4 SLIDES ARE THE SAME AS THE PREVIOUS 4 ONES,
               BUT WITHOUT A FIXED VERTICAL SCALE
                                                100 pictures (every 10
                                                MHz until 1 GHz)




Elias Métral, APC meeting, 08/12/05                                  63
                                      100 pictures (every 10
                                      MHz until 1 GHz)




Elias Métral, APC meeting, 08/12/05                        64
                                      100 pictures (every 10
                                      MHz until 1 GHz)




Elias Métral, APC meeting, 08/12/05                        65
                                      100 pictures (every 10
                                      MHz until 1 GHz)




Elias Métral, APC meeting, 08/12/05                        66
         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   67
         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   68
         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   69
                                             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


                                                                 70
                                     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.                                                                         71
                               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.
                                                                                    72
Thank you for your attention!




                                73
74
   Geometrical model for time domain simulations
                          Ferrite 4A4




Beam
path




                                        Wake
                                        integration
                                        path

                         Rms Bunch length 2 cm
                                                      75
       Longitudinal Impedance

                                          Theory from Tsutsui
                                                                L=1.66m
                   s                                            b=0.016m
                                         σ=10cm                 d=0.076m
                                         Simulated length=1m    a=0.0675
Gaussian bunch used for the excitation
                                                                Ferrite 4A4




                                                                              76
Longitudinal Impedance

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




                                               77
Vertical driving Impedance
L=1.66m
b=0.016m
              σ=10cm
d=0.076m      Simulated length=1.66m
a=0.0675
Ferrite 4A4




                                       78
Horizontal driving Impedance
   L=1.66m
   b=0.016m
                 σ=10cm
   d=0.076m      Simulated length=0.2m
   a=0.0675
   Ferrite 4A4




                                         79
Horizontal Detuning Impedance
     L=1.66m
     b=0.016m
     d=0.076m
     a=0.0675      σ=10cm
     Ferrite 4A4   Simulated length=1m




                                         80
Vertical Detuning Impedance
   L=1.66m
   b=0.016m
   d=0.076m
                 σ=10cm
   a=0.0675
                 Simulated length=1.66m
   Ferrite 4A4




                                          81
                           L=1.66m
                           b=0.016m
          Wake Potential   d=0.076m
                           a=0.0675
                           Ferrite 4A4



W[V/pC]




                  s(cm)

                                         82
                           L=1.66m
          Wake Potential   b=0.016m
                           d=0.076m
                           a=0.0675
                           Ferrite 4A4



W[V/pC]




                  s(cm)

                                         83
                           L=1.66m
                           b=0.016m
          Wake Potential   d=0.076m
                           a=0.0675
                           Ferrite 4A4



W[V/pC]




                  s(cm)

                                         84
                             L=1.66m
          Wake Potential     b=0.016m
                             d=0.076m
                             a=0.0675
                             Ferrite 4A4



W[V/pC]




                     s(cm)

                                           85
Vertical driving and detuning impedance          L=1.66m
                                                 b=0.016m
                     σ=10cm                      d=0.076m
                     Simulated length=1.66m
                                                 a=0.0675
                                                 Ferrite 4A4



Z[Ω/m]




                                Frequency(GHz)

                                                               86
Horizontal driving and detuning impedance    L=1m
                                             b=0.016m
                       σ=10cm
                       Simulated length=1m
                                             d=0.076m
                                             a=0.0675
                                             Ferrite 4A4



 Z[Ω/m]




                            Frequency(GHz)

                                                           87
         Vertical Impedance


Z[Ω/m]




                           Frequency(GHz)

                  All terms are simulated

          Z ygeneral ( s )  Z driving ( s )  Z y
                                                     detuning
                               y                                ( s)

                                                                       88
         Horizontal Impedance


Z[Ω/m]




                         Frequency(GHz)

                     All terms are simulated

          Z xgeneral ( s )  Z x ( s )  Z x
                               driving         detuning
                                                          ( s)
                                                                 89

								
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