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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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