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Follow up on SPS transverse impedance

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					               Follow up on
        SPS transverse impedance

           G. Arduini, F. Caspers, E. Métral, G. Rumolo, B. Salvant

                             Acknowledgements:
C. Boccard, T. Bohl, R. Calaga, H. Damerau, R. Jones, R. de Maria, N. Mounet,
    F. Roncarolo, E. Shaposhnikova, R. Steinhagen, C. Zannini, B. Zotter



                SPS Upgrade Study Team – May 19th 2009


                                                                                1
                              Agenda
• Objectives for the transverse impedance team

• Obtaining the wake functions for single SPS elements
   – Analytical calculations for simple geometries (beam pipe, kickers)
   – Electromagnetic simulations for more complicated geometries (BPMs)
   – Bench RF measurements


• “Total” wakes for the SPS and importing into Headtail

• SPS Measurements of observables and comparison with simulations
   – Tune shift and instability thresholds
   – Localization of transverse impedance
   – Measurements with long bunches


• Sum up and future work
                                                                          2
                    Objectives for the transverse impedance team

       SPS machine                          Analytical             Electromagnetic                         Bench
       measurements                        Calculations              Simulations                        Measurements



                                           Impedance of          Wake potential of a                     Impedance of
                                       a single SPS element      single SPS element                  a single SPS element

                                              DFT                     deconvolution                         DFT


                                         Wake function of        Wake function of                      Wake function of
                                       a single SPS element    a single SPS element                  a single SPS element

                                                           Sum for all available SPS elements


                                                              “Total” SPS Wake function


                                                          Headtail macroparticle simulations

                                          ?
 Measured observables                                          Simulated observables
(Tune shift, Instability threshold…)                          (tune shift, instability threshold…)


                  How much of the measured transverse impedance is accounted for in the model?
                  Which are the main transverse impedance contributors?
                                                                                                                            3
                              Agenda
• Objectives for the transverse impedance team

• Obtaining the wake functions for single SPS elements
   – Analytical calculations for simple geometries (beam pipe, kickers)
   – Electromagnetic simulations for more complicated geometries (BPMs)
   – Bench RF measurements


• “Total” wakes for the SPS and importing into Headtail

• SPS Measurements of observables and comparison with simulations
   – Tune shift and instability thresholds
   – Localization of transverse impedance
   – Measurements with long bunches


• Sum up and future work
                                                                          4
                     Objectives for the transverse impedance team

       SPS machine                          Analytical             Electromagnetic                         Bench
       measurements                        Calculations              Simulations                        Measurements



                                           Impedance of          Wake potential of a                     Impedance of
                                       a single SPS element      single SPS element                  a single SPS element

                                              DFT                     deconvolution                         DFT


                                         Wake function of        Wake function of                      Wake function of
                                       a single SPS element    a single SPS element                  a single SPS element

                                                           Sum for all available SPS elements


                                                              “Total” SPS Wake function


                                                          Headtail macroparticle simulations

                                          ?
 Measured observables                                          Simulated observables
(Tune shift, Instability threshold…)                          (tune shift, instability threshold…)


                  How much of the measured transverse impedance is accounted for in the model?
                  Which are the main transverse impedance contributors?
                                                                                                                            5
                          Analytical calculation for simple geometries

Example: Transverse Wall impedance of a 2 cm stainless steel                                                Long range wake (1 m)
         6911 m round beam pipe for a  = 27.7 beam                                            15



          10 1 0

           10 8                                                                                                                                     




                                                                  Dipolar wake (in V/pCmm)
                                                                                               10
                                                                                                                      fmax=1THz - fsamp l=0.1M Hz
m




                                                                                                                      fmax=1THz - fsamp l=1M Hz
           10 6                                             DFT                                                       fmax=0.1THz - fsamp l=0.1M Hz    
                                                                                                                      fmax=0.01THz - fsamp l=0.01M Hz   
           10 4                                                                                 5
Z trans




                                                                                                                      fmax=10THz - fsamp l=10M Hz


           100

              1                                                                                 0
                                     6        9        12                                           0         0.2     0.4        0.6      0.8             1
                   1   1000     10       10       10
                                                                                                                    Wake Length (in m)

                              F requency Hz
                                                                                                            Short range wake ( 5mm)
          DFT on a large frequency range is an issue:                                          250
           - sampling interval too small                                                                                         
                                                                                                                       fmax=1THz - fsamp l=0.1M Hz

                       wrong long range wake value                                            200
                                                                                                                                 
                                                                                                                       fmax=1THz - fsamp l=1M Hz
                                                                                                                       fmax=0.1THz - fsamp l=0.1M Hz
          - fmax too small

                                                                    Dipolar wake (in V/pCmm)
                                                                                                                       fmax=0.01THz - fsamp l=0.01M Hz
                      wrong short range wake+oscillations                                     150
                                                                                                                                  
                                                                                                                       fmax=10THz - fsamp l=10M Hz



    Here, need for fmax  1 THz and fsampling 0.1 MHz                                         100

       107 points DFT
       CPU limit in windows                                                                    50



Possible solutions: - UNIX (up to 50 107 points)                                                    0
                                                                                                        0      1        2         3        4               5
                    - and Nicolas’s new DFT algorithm                                                               Wake Length (in m)
                                                                                                                                                   x 10
                                                                                                                                                          -3
                                                                                                                                                               6
                                      Agenda
•   Objectives for the transverse impedance team

•   Obtaining the wake functions for single SPS elements
     – Analytical calculations for simple geometries (beam pipe, kickers)
     – Electromagnetic simulations for more complicated geometries (BPMs)
         • Obtaining wake potentials
         • RF measurements to confirm the simulations
         • Obtaining the wake function from the wake potential
     – Bench RF measurements

•   “Total” wakes for the SPS and importing into Headtail

•   SPS Measurements of observables and comparison with simulations
     – Tune shift and instability thresholds
     – Localization of transverse impedance
     – Measurements with long bunches

•   Sum up and future work

                                                                            7
                    Objectives for the transverse impedance team

       SPS machine                          Analytical             Electromagnetic                         Bench
       measurements                        Calculations              Simulations                        Measurements



                                           Impedance of          Wake potential of a                     Impedance of
                                       a single SPS element      single SPS element                  a single SPS element

                                              DFT                     deconvolution                         DFT


                                         Wake function of        Wake function of                      Wake function of
                                       a single SPS element    a single SPS element                  a single SPS element

                                                           Sum for all available SPS elements


                                                              “Total” SPS Wake function


                                                          Headtail macroparticle simulations

                                          ?
 Measured observables                                          Simulated observables
(Tune shift, Instability threshold…)                          (tune shift, instability threshold…)


                  How much of the measured transverse impedance is accounted for in the model?
                  Which are the main transverse impedance contributors?
                                                                                                                            8
         Electromagnetic simulations
      for more complicated geometries
SPS BPH                      SPS BPH model geometry




                                                      9
     Comparing time domain and frequency domain simulations
                  Time domain                   Frequency domain
               (CST Particle Studio)          (CST Microwave Studio)

                          1.90GHz

                                   2.58GHz
                1.08GHz                      fres (GHz)    Rs (y=0mm) [Ω]      Q

longitudinal                                   1.08           9.43 104        3270
                         1.68GHz
                                               1.69             167           2100
                                               1.88           5.79 105        3630




                                                  Very high R/Q! (~150 Ω)
                                               Similar to Fritz’s slotline pickup
                  0.97GHz
                                              fres (GHz)     Rs (y=5mm) [Ω]          Q
                       1.69GHz
                                                 0.55              3.6             2100
                    1.29GHz
                                                 1.20             6480             8000
  vertical                     2.14GHz
                                                 1.30              130             2680
                          1.92GHz                1.64            9.58 103          4060
                                                 1.80             1280             13700
               0.55GHz
                                                 1.92              230             6580


                                                                                           10
Effect of matching the impedance at electrodes coaxial ports in Particle Studio simulations (BPH)

                                            Modes are damped
                                      by the “perfect matching layer”
                                             at the coaxial port
   Short bunch (1 cm rms)




                                                                        SPS bunch (20 cm rms)



                                  Electrode
                                  coaxial port


                                Importance to match the BPM
                                         electrodes!
                                                                                                11
    Remark on BPM matching for higher order modes
•    From discussions with Rhodri and Ralph, the BPM matching is currently performed
     up to 500 or 600 MHz.
•    Besides they mention that an activity around 1.8 GHz can be observed on the
     HeadTail monitor (sum and longitudinal).


                    Should be damped by the termination




                           If not damped, this mode could be the most critical

This may be just a coincidence and will be investigated together with RF and BI.
                                                                                       12
                                      Agenda
•   Objectives for the transverse impedance team

•   Obtaining the wake functions for single SPS elements
     – Analytical calculations for simple geometries (beam pipe, kickers)
     – Electromagnetic simulations for more complicated geometries (BPMs)
         • Obtaining wake potentials
         • RF measurements to confirm the simulations
         • Obtaining the wake function from the wake potential
     – Bench RF measurements

•   “Total” wakes for the SPS and importing into Headtail

•   SPS Measurements of observables and comparison with simulations
     – Tune shift and instability thresholds
     – Localization of transverse impedance
     – Measurements with long bunches

•   Sum up and future work

                                                                            13
                           Benchmark with RF measurements

    •             Transmission measurement
                  between electrode ports (S21)

    •             More convenient than wire
                  measurement in this case
                  (small signal expected,
                  radioactive device, no need
                  to recondition)


                                     BPH                                                                        BPV
         0                                                                         0




         -2                                                                        -2
logMag




                                                                          logMag



         -4                                                                        -4
   21




                                                                             21
S




                                                                          S




         -6                                             measured S                 -6
                                                                   21                             measured S
                                                                                                              21
                                                        simulated S
                                                                     21                           simulated S
                                                                                                               21

         -8                                                                        -8
              0      0.5    1         1.5         2   2.5      3                        0   0.5      1          1.5        2   2.5   3
                                                                                                         Frequency in Hz
                                Frequency in Hz                                                                                          14
      Adding the ceramic spacers

                   Ceramic insulator    BPH
                   spacers designed
                   to mechanically
                   stabilize the thin
                   electrodes
                   (homemade at
         BPV       CERN, cf BPH/BPV
                   technical specs,
                   1973)


BPV                       BPV




                                              15
                                      Agenda
•   Objectives for the transverse impedance team

•   Obtaining the wake functions for single SPS elements
     – Analytical calculations for simple geometries (beam pipe, kickers)
     – Electromagnetic simulations for more complicated geometries (BPMs)
         • Obtaining wake potentials
         • RF measurements to confirm the simulations
         • Obtaining the wake function from the wake potential
     – Bench RF measurements

•   “Total” wakes for the SPS and importing into Headtail

•   SPS Measurements of observables and comparison with simulations
     – Tune shift and instability thresholds
     – Localization of transverse impedance
     – Measurements with long bunches

•   Sum up and future work

                                                                            16
                    Objectives for the transverse impedance team

       SPS machine                          Analytical             Electromagnetic                         Bench
       measurements                        Calculations              Simulations                        Measurements



                                           Impedance of          Wake potential of a                     Impedance of
                                       a single SPS element      single SPS element                  a single SPS element

                                              DFT                     deconvolution                         DFT


                                         Wake function of        Wake function of                      Wake function of
                                       a single SPS element    a single SPS element                  a single SPS element

                                                           Sum for all available SPS elements


                                                              “Total” SPS Wake function


                                                          Headtail macroparticle simulations

                                          ?
 Measured observables                                          Simulated observables
(Tune shift, Instability threshold…)                          (tune shift, instability threshold…)


                  How much of the measured transverse impedance is accounted for in the model?
                  Which are the main transverse impedance contributors?
                                                                                                                            17
   Obtaining the transverse wake functions from time
                   domain simulations
  1) Time domain simulations to obtain dipolar and quadrupolar wake
     potentials (horizontal and vertical)
                            y                  y
  Beam
  Wake integration                x                  x

                     Wy dipolar         Wy quadrupolar


  2) Deconvolution of the gaussian bunch distribution (DFT, division by
     gaussian distribution in frequency domain and windowing, DFT)



Note : This method assumes x and y symmetry.
       How to deal with non symmetric geometries? Non linear terms? Coupled terms?

                                                                               18
BPH and BPV transverse wake functions




Note: quadrupolar wakes are not related by Wx,quad= - Wy,quad
      both BPMs only have one symmetry plane
                                                                19
                              Agenda
• Objectives for the transverse impedance team

• Obtaining the wake functions for single SPS elements
   – Analytical calculations for simple geometries (beam pipe, kickers)
   – Electromagnetic simulations for more complicated geometries (BPMs)
   – Bench RF measurements


• “Total” wakes for the SPS and importing into Headtail

• SPS Measurements of observables and comparison with simulations
   – Tune shift and instability thresholds
   – Localization of transverse impedance
   – Measurements with long bunches


• Sum up and future work
                                                                          20
                    Objectives for the transverse impedance team

       SPS machine                          Analytical             Electromagnetic                         Bench
       measurements                        Calculations              Simulations                        Measurements



                                           Impedance of          Wake potential of a                     Impedance of
                                       a single SPS element      single SPS element                  a single SPS element

                                              DFT                     deconvolution                         DFT


                                         Wake function of        Wake function of                      Wake function of
                                       a single SPS element    a single SPS element                  a single SPS element

                                                           Sum for all available SPS elements


                                                              “Total” SPS Wake function


                                                          Headtail macroparticle simulations

                                          ?
 Measured observables                                          Simulated observables
(Tune shift, Instability threshold…)                          (tune shift, instability threshold…)


                  How much of the measured transverse impedance is accounted for in the model?
                  Which are the main transverse impedance contributors?
                                                                                                                            21
    Bench RF measurement of the transverse impedance
•   Cf for instance “Longitudinal and Transverse Wire Measurements for the Evaluation of Impedance
    Reduction Measures on the MKE Extraction Kickers”, T. Kroyer, F. Caspers, E. Gaxiola
     – Two wire measurement  dipolar impedance




     – Moving single wire measurement  total impedance (dipolar + quadrupolar+…)




                                                                                                     22
                              Agenda
• Objectives for the transverse impedance team

• Obtaining the wake functions for single SPS elements
   – Analytical calculations for simple geometries (beam pipe, kickers)
   – Electromagnetic simulations for more complicated geometries (BPMs)
   – Bench RF measurements


• “Total” wakes for the SPS and importing into Headtail

• SPS Measurements of observables and comparison with simulations
   – Tune shift and instability thresholds
   – Localization of transverse impedance
   – Measurements with long bunches


• Sum up and future work
                                                                          23
                    Objectives for the transverse impedance team

       SPS machine                          Analytical             Electromagnetic                         Bench
       measurements                        Calculations              Simulations                        Measurements



                                           Impedance of          Wake potential of a                     Impedance of
                                       a single SPS element      single SPS element                  a single SPS element

                                              DFT                     deconvolution                         DFT


                                         Wake function of        Wake function of                      Wake function of
                                       a single SPS element    a single SPS element                  a single SPS element

                                                           Sum for all available SPS elements


                                                              “Total” SPS Wake function


                                                          Headtail macroparticle simulations

                                          ?
 Measured observables                                          Simulated observables
(Tune shift, Instability threshold…)                          (tune shift, instability threshold…)


                  How much of the measured transverse impedance is accounted for in the model?
                  Which are the main transverse impedance contributors?
                                                                                                                            24
       Total wake for importing into Headtail
•   Kickers (ferrite model + BPHs + BPVs + Beam pipe)
•   Needs interpolation
•   Need to take into account the correct beta functions at each element location




      The ferrite kicker model should be refined.
                                                                                    25
                              Agenda
• Objectives for the transverse impedance team

• Obtaining the wake functions for single SPS elements
   – Analytical calculations for simple geometries (beam pipe, kickers)
   – Electromagnetic simulations for more complicated geometries (BPMs)
   – RF measurements to confirm the simulations (BPMs)


• “Total” wakes for the SPS and importing into Headtail

• SPS Measurements of observables and comparison with simulations
   – Tune shift and instability thresholds
   – Localization of transverse impedance
   – Measurements with long bunches


• Sum up and future work
                                                                          26
                    Objectives for the transverse impedance team

       SPS machine                          Analytical             Electromagnetic                         Bench
       measurements                        Calculations              Simulations                        Measurements



                                           Impedance of          Wake potential of a                     Impedance of
                                       a single SPS element      single SPS element                  a single SPS element

                                              DFT                     deconvolution                         DFT


                                         Wake function of        Wake function of                      Wake function of
                                       a single SPS element    a single SPS element                  a single SPS element

                                                           Sum for all available SPS elements


                                                              “Total” SPS Wake function


                                                          Headtail macroparticle simulations

                                          ?
 Measured observables                                          Simulated observables
(Tune shift, Instability threshold…)                          (tune shift, instability threshold…)


                  How much of the measured transverse impedance is accounted for in the model?
                  Which are the main transverse impedance contributors?
                                                                                                                            27
Tune shift and instability threshold (vertical plane)
                                                                    kickers only
                                                                    kickers+BPMs
                                                                    kickers+BPMs+pipe
    Growth rate in 1 turn

                                                                                   0.185
                            0.010                                                  0.180




                                                                         Tune Qy
                                                                                   0.175
                            0.005
                                                                                   0.170

                            0.000                                                  0.165

                                0   20 40 60 80 100 120 140                        0.160
                                                                                        0   20    40        60   80   100
                                      Nb in 109 protons                                                     9
                                                                                             Nb in 10 protons
                                                         0                                         0


                                                         1                                              1


                                                         2                                              2
                                           Re Q Q y Qs




                                                         3                                              3


                                                         4                                              4


                                                         5                                              5


                                                         6                                              6
                                                          0   20   40          60      80   100   120
                                                                                   9
                                                                        Nb 10 p b
                                                                                                                            28
                    Objectives for the transverse impedance team

       SPS machine                          Analytical             Electromagnetic                         Bench
       measurements                        Calculations              Simulations                        Measurements



                                           Impedance of          Wake potential of a                     Impedance of
                                       a single SPS element      single SPS element                  a single SPS element

                                              DFT                     deconvolution                         DFT


                                         Wake function of        Wake function of                      Wake function of
                                       a single SPS element    a single SPS element                  a single SPS element

                                                           Sum for all available SPS elements


                                                              “Total” SPS Wake function


                                                          Headtail macroparticle simulations

                                          ?
 Measured observables                                          Simulated observables
(Tune shift, Instability threshold…)                          (tune shift, instability threshold…)


                  How much of the measured transverse impedance is accounted for in the model?
                  Which are the main transverse impedance contributors?
                                                                                                                            29
                     Simulations and measurements:
                    tune Shift and instability threshold

                                       0.20


                                       0.19
                             Tune Qy
                                       0.18

                                                Simulations
                                       0.17
                                                Measurements
                                       0.16
                                           0   20      40       60     80     100
                                                            9
                                                    Nb in 10 protons



         - Absolute tune shift slope with intensity is 40% smaller in the simulations than in the measurements
         - Transverse instability threshold is very similar (~ 7.5 1010 protons)


 Impedance contributors are missing (RF cavities, pumping ports…) or are not correctly modelled (kickers)
      absolute tune slope should increase and instability threshold should decrease
 Direct space charge is missing
      no effect expected on tune slope, but instability threshold should decrease
                                                                                                             30
            Localization of impedance

From R. Calaga et al, PAC’09




                                        31
       Simulations and measurements of long bunches
         Headtail simulation with a  Headtail simulations with SPS kickers
       broadband impedance model Can be fitted by a broadband impedance                                                                                                                                                                             SPS Measurements
      Q=1, fres=1.3 GHz, Rs=7.6 MΩ/m Q=0.6, fres=2.3 GHz, Rs=3.5 MΩ/m

                                              600                                                                                                      600
           Simulated number of turns




                                                                                                                           Simulated number of turns
vertical                                      400                                                                                                      400

Time
                                              200                                                                                                      200
signals
                                                   0                                                                                                       0
                                                           -2       -1          0       1         2                                                            -2        -1          0        1       2
                                                                distance to bunch center (in m)                                                                     distance to bunch center (in m)

                                                                                                                                              800

                                                   600                                                                                                                                                                                    600
                       Simulated number of turns




                                                                                                          Simulated number of turns           600




                                                                                                                                                                                                              Measured number of turns
                                                   400
vertical                                                                                                                                      400                                                                                         400


DFT                                                200                                                                                        200
                                                                                                                                                                                                                                          200


                                                       0                                                                                               0
                                                           0         1              2         3       4                                                    0         1           2            3           4                                0
                                                                         Frequency (in GHz)                                                                              Frequency (in GHz)                                                     0    0.5      1        1.5      2    2.5
                                                                                                                                                                                                                                                           Frequency (in GHz)



                                                                                                                                                                                                                                          600




                                                                                                                                                                                                               Measured number of turns
  As in the simulations with kickers model,                                                                                                                                                                                               400

  no clear activity in the transverse plane.                                                                                                                              Longitudinal
  This is not a proof though.                                                                                                                                             DFT                                                             200


  Work ongoing.                                                                                                                                                                                                                             0
                                                                                                                                                                                                                                                0    0.5      1        1.5      2    2.5
                                                                                                                                                                                                                                                           Frequency (in GHz)       32
                              Agenda
• Objectives for the transverse impedance team

• Obtaining the wake functions for single SPS elements
   – Analytical calculations for simple geometries (beam pipe, kickers)
   – Electromagnetic simulations for more complicated geometries (BPMs)
   – RF measurements to confirm the simulations (BPMs)


• “Total” wakes for the SPS and importing into Headtail

• SPS Measurements of observables and comparison with simulations
   – Tune shift and instability thresholds
   – Localization of transverse impedance
   – Measurements with long bunches


• Sum up and future work
                                                                          33
                   Sum up and future work
•   General framework designed to obtain a more accurate transverse
    impedance model of the SPS from analytical, simulated and measured
    estimates.

•   First try with the kickers, BPHs, BPVs and Wall impedance of the vacuum
    chamber. With the current results, the BPMs have a small impact on the
    single bunch dynamics, but strong higher order modes may affect the
    coupled bunch dynamics.

•   40% of the measured tune shift with intensity is not accounted for.
    Simulated and measured thresholds are very close.

•   Other means to access observables of the impedance are being
    investigated (localization, longer bunches), and are still a work-in-progress.




                                                                                     34

				
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