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

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

Objectives for the transverse impedance team SPS machine measurements Analytical Calculations Electromagnetic Simulations Bench Measurements Impedance of a single SPS element Wake potential of a single SPS element Impedance of a single SPS element DFT deconvolution DFT Wake function of a single SPS element Wake function of a single SPS element Wake function of a single SPS element Sum for all available SPS elements “Total” SPS Wake function Headtail macroparticle simulations ? Measured observables (Tune shift, Instability threshold…) Simulated observables (tune shift, instability threshold…) How much of the measured transverse impedance is accounted for in the model? Which are the main transverse impedance contributors?

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

Objectives for the transverse impedance team SPS machine measurements Analytical Calculations Electromagnetic Simulations Bench Measurements Impedance of a single SPS element Wake potential of a single SPS element Impedance of a single SPS element DFT deconvolution DFT Wake function of a single SPS element Wake function of a single SPS element Wake function of a single SPS element Sum for all available SPS elements “Total” SPS Wake function Headtail macroparticle simulations ? Measured observables (Tune shift, Instability threshold…) Simulated observables (tune shift, instability threshold…) How much of the measured transverse impedance is accounted for in the model? Which are the main transverse impedance contributors?

Analytical calculation for simple geometries Long range wake (1 m) Example: Transverse Wall impedance of a 2 cm stainless steel 6911 m round beam pipe for a  = 27.7 beam  DFT   Short range wake ( 5mm) DFT on a large frequency range is an issue: - sampling interval too small  wrong long range wake value fmax too small wrong short range wake+oscillations    Here, need for fmax  1 THz and fsampling 0.1 MHz  107 points DFT  CPU limit in windows Possible solutions: - UNIX (up to 50 107 points) - and Nicolas’s new DFT algorithm

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

Objectives for the transverse impedance team SPS machine measurements Analytical Calculations Electromagnetic Simulations Bench Measurements Impedance of a single SPS element Wake potential of a single SPS element Impedance of a single SPS element DFT deconvolution DFT Wake function of a single SPS element Wake function of a single SPS element Wake function of a single SPS element Sum for all available SPS elements “Total” SPS Wake function Headtail macroparticle simulations ? Measured observables (Tune shift, Instability threshold…) Simulated observables (tune shift, instability threshold…) How much of the measured transverse impedance is accounted for in the model? Which are the main transverse impedance contributors?

Electromagnetic simulations for more complicated geometries SPS BPH SPS BPH model geometry

Comparing time domain and frequency domain simulations Time domain (CST Particle Studio) Frequency domain (CST Microwave Studio) 1.90GHz 2.58GHz 1.08GHz fres (GHz) Rs (y=0mm) [Ω] Q 1.08 9.43 104 3270 1.69 167 2100 1.88 5.79 105 3630 longitudinal 1.68GHz Very high R/Q! (~150 Ω) Similar to Fritz’s slotline pickup 0.97GHz fres (GHz) Rs (y=5mm) [Ω] Q 0.55 3.6 2100 1.20 6480 8000 1.30 130 2680 1.64 9.58 103 4060 1.80 1280 13700 1.92 230 6580 1.69GHz 1.29GHz vertical 2.14GHz 1.92GHz 0.55GHz

Electrode coaxial port 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!

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.

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

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)

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

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

Objectives for the transverse impedance team SPS machine measurements Analytical Calculations Electromagnetic Simulations Bench Measurements Impedance of a single SPS element Wake potential of a single SPS element Impedance of a single SPS element DFT deconvolution DFT Wake function of a single SPS element Wake function of a single SPS element Wake function of a single SPS element Sum for all available SPS elements “Total” SPS Wake function Headtail macroparticle simulations ? Measured observables (Tune shift, Instability threshold…) Simulated observables (tune shift, instability threshold…) How much of the measured transverse impedance is accounted for in the model? Which are the main transverse impedance contributors?

Obtaining the transverse wake functions from time domain simulations Time domain simulations to obtain dipolar and quadrupolar wake potentials (horizontal and vertical) Deconvolution of the gaussian bunch distribution (DFT, division by gaussian distribution in frequency domain and windowing, DFT) y y Beam Wake integration x x Wy dipolar Wy quadrupolar Note : This method assumes x and y symmetry. How to deal with non symmetric geometries? Non linear terms? Coupled terms?

BPH and BPV transverse wake functions Note: quadrupolar wakes are not related by Wx,quad= - Wy,quad both BPMs only have one symmetry plane

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

Objectives for the transverse impedance team SPS machine measurements Analytical Calculations Electromagnetic Simulations Bench Measurements Impedance of a single SPS element Wake potential of a single SPS element Impedance of a single SPS element DFT deconvolution DFT Wake function of a single SPS element Wake function of a single SPS element Wake function of a single SPS element Sum for all available SPS elements “Total” SPS Wake function Headtail macroparticle simulations ? Measured observables (Tune shift, Instability threshold…) Simulated observables (tune shift, instability threshold…) How much of the measured transverse impedance is accounted for in the model? Which are the main transverse impedance contributors?

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+…)

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

Objectives for the transverse impedance team SPS machine measurements Analytical Calculations Electromagnetic Simulations Bench Measurements Impedance of a single SPS element Wake potential of a single SPS element Impedance of a single SPS element DFT deconvolution DFT Wake function of a single SPS element Wake function of a single SPS element Wake function of a single SPS element Sum for all available SPS elements “Total” SPS Wake function Headtail macroparticle simulations ? Measured observables (Tune shift, Instability threshold…) Simulated observables (tune shift, instability threshold…) How much of the measured transverse impedance is accounted for in the model? Which are the main transverse impedance contributors?

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.

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

Objectives for the transverse impedance team SPS machine measurements Analytical Calculations Electromagnetic Simulations Bench Measurements Impedance of a single SPS element Wake potential of a single SPS element Impedance of a single SPS element DFT deconvolution DFT Wake function of a single SPS element Wake function of a single SPS element Wake function of a single SPS element Sum for all available SPS elements “Total” SPS Wake function Headtail macroparticle simulations ? Measured observables (Tune shift, Instability threshold…) Simulated observables (tune shift, instability threshold…) How much of the measured transverse impedance is accounted for in the model? Which are the main transverse impedance contributors?

Tune shift and instability threshold (vertical plane) kickers only kickers+BPMs kickers+BPMs+pipe

Objectives for the transverse impedance team SPS machine measurements Analytical Calculations Electromagnetic Simulations Bench Measurements Impedance of a single SPS element Wake potential of a single SPS element Impedance of a single SPS element DFT deconvolution DFT Wake function of a single SPS element Wake function of a single SPS element Wake function of a single SPS element Sum for all available SPS elements “Total” SPS Wake function Headtail macroparticle simulations ? Measured observables (Tune shift, Instability threshold…) Simulated observables (tune shift, instability threshold…) How much of the measured transverse impedance is accounted for in the model? Which are the main transverse impedance contributors?

Simulations and measurements: tune Shift and instability threshold 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

Localization of impedance From R. Calaga et al, PAC’09

Simulations and measurements of long bunches Headtail simulation with a broadband impedance model Q=1, fres=1.3 GHz, Rs=7.6 MΩ/m Headtail simulations with SPS kickers Can be fitted by a broadband impedance Q=0.6, fres=2.3 GHz, Rs=3.5 MΩ/m SPS Measurements vertical Time signals vertical DFT As in the simulations with kickers model, no clear activity in the transverse plane. This is not a proof though. Work ongoing. Longitudinal DFT

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

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.