1. 11 Update of the SPS impedance model G. Arduini, O. Berrig, F. Caspers, A. Grudiev, E. Métral, G. Rumolo, B. Salvant, E. Shaposhnikova, B. Spataro (INFN), C. Zannini, B. Zotter. Acknowledgments: M. Barnes, C. Boccard, T. Bohl, R. Calaga, J. Evans, H. Damerau, E. Jensen, G. Papotti,R. Tomas, R. Steinhagen, OP teams, M. Balk (CST AG), L. Haenichen, W. Mueller (TU Darmstadt) Machine Studies Working Group - January 15 th, 2009

2. 2 Update of the SPS impedance model Context –LHC intensity upgrade scheme requires 4 or 5 10 11 protons per bunch (p/b) –For instance, fast transverse instability limits bunch intensity to less than 2 10 11 p/b (with nominal parameters)  SPS transverse impedance will be one of the bottlenecks to produce 4 10 11 p/b –Ongoing work to identify the major SPS impedance contributors  propose possible SPS hardware modifications (such as the large campaign to shield the vacuum pumping ports in 99/01 or the MKE kicker shielding campaign from 2006). Objectives of this talk (Focus has been mainly on transverse impedance) –Stress the importance of separating the dipolar and quadrupolar impedance contributions –Use new tools to obtain the impedance and wakes of SPS components (theory and simulations)  Example of the SPS kickers, BPMs and beam pipe –Status of the current transverse impedance model and comparison with measurements –Next steps

3. 3 Agenda Separating the dipolar and quadrupolar impedance contributions. Use new tools to obtain the impedance and wakes of SPS components Status of the current transverse impedance model and comparison with beam measurements Next steps

4. 4 Separating the dipolar and quadrupolar impedance contributions Dipolar and quadrupolar contributions (resp. driving and detuning contributions) linearization of the wake dependence with the source (1) and witness (2) transverse locations y s z 2 1 Accelerator element y2y2 y1y1 In general, we assume we can expand the wake anywhere in a transverse cross section with powers of x and y Total vertical wake: Then we classically:(1) assume top/down and bottom/left symmetries (2) linearize for small displacements (3) assume no coupling between the horizontal and vertical plane (1) with i,j,k,l odd numbers (2) (3) Dipolar wakeQuadrupolar wake Total wake

5. 5 Why is it important to separate the dipolar and quadrupolar impedance contributions? dipolar wake leads to coherent oscillations of all particles in the bunch  dipolar wake drives coherent instabilities quadrupolar wake leads to oscillations that depends on the individual particle’s amplitude  quadrupolar wakes leads to incoherent effects (damping and emittance growth) y s z 2 1 Accelerator element y2y2 y1y1 Dipolar wakeQuadrupolar wake Total wake Very different impact on beam dynamics! Vertical coherent motionVertical beam size Example: HEADTAIL simulation of a bunch interacting with - only dipolar - dip + quad Quadrupolar  Damping Quadrupolar  emittance growth

6. 6 Agenda Separating the dipolar and quadrupolar impedance contributions. Use new tools to obtain the impedance and wakes of SPS components –General framework to obtain an SPS impedance model –Example of the impedance of the SPS ferrite kickers Status of the current transverse impedance model and comparison with beam measurements Next steps

7. 77 General framework to obtain the impedance model of a machine Overview for the case of the SPS Measured observables (Tune shift, Instability threshold…) 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 Wake function of a single SPS element iDFT deconvolution “Total” SPS Wake function SPS machine measurements Sum for all available SPS elements Headtail macroparticle simulations 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? ? Accounting for the respective beta functions MADX HEADTAIL simulates the dynamics of a bunch of macroparticles interacting with an impedance model

8. 8 Agenda Separating the dipolar and quadrupolar impedance contributions. Use new tools to obtain the impedance and wakes of SPS components –General framework to obtain an SPS impedance model –Example of the impedance of the SPS ferrite kickers Status of the current transverse impedance model and comparison with beam measurements Next steps

9. 9 Context: –SPS beam based measurements over the years  SPS ferrite kickers suspected to be major contributors to the transverse SPS impedance. –Method to obtain the impedance of the SPS kickers: 1. Compute impedance for a cylindrical ferrite beam pipe with Zotter/Métral model 2. Multiply it by constant form factors to obtain the dipolar and quadrupolar impedance contributions for a flat chamber beam pipe. –Analytical dipolar impedance agrees with bench measurements of SPS kickers… –…However, 1.Form factors can only be applied if the field penetration in the material is smaller than the aperture, which is not the case for the dielectrics and ferrites. 2.negative total horizontal impedance measured on PS kickers on a bench negative total horizontal impedance measured with beam in the SPS  Quadrupolar impedance of the kickers suspected to be underestimated –Tsutsui formalism also exists, but only dipolar impedance is available New tools: –new theoretical formulae for the quadrupolar impedance in the frame of Tsutsui formalism –New 3D simulations of the dipolar and quadrupolar impedance of kickers Transverse impedance of simple models of kickers Context and objectives Transverse dipolar impedance: theory (Zotter/Metral) and 2 wire-measurement (Caspers, Gaxiola, Kroyer) SPS impedance, Metral et al., BEAM 07

10. 10 Transverse impedance of simple models of kickers New quadrupolar contribution New quadrupolar impedance was derived from the electromagnetic fields derived by Tsutsui for the longitudinal impedance (same source charge distribution)  Analytical impedance for 1 MKE kicker  not possible to apply constant factors to relate the dipolar and quadrupolar contributions  Which theory is valid?  benchmark with 3D bench measurements Re(Z) is thick Im(Z) is dashed

11. 11 Transverse impedance of simple models of kickers CST Particle Studio 3D simulations Strategy to obtain dipolar and quadrupolar wake potentials from time domain CST simulations y x W y dipolar Wake integration Beam y x W y quadrupolar CST Particle Studio is a commercial code that simulates the wake potentials from 3D models 3D kicker modelKicker structure Dipolar wakeQuadrupolar wake Total wake

12. 12 Transverse impedance of simple models of kickers CST Particle Studio 3D simulations 1.7 million mesh cells Simulated Rms Bunch length 2 cm Vertical electric field

13. 13 Transverse impedance of simple models of kickers CST Particle Studio 3D simulations DFT 1.7 million mesh cells Simulated Rms Bunch length 2 cm Let’s compare with the theory…

14. 14 Transverse impedance of simple models of kickers Comparison between theory (with new quadrupolar) and new simulations (1) Good agreement between Tsutsui’s dipolar and the new quadrupolar impedance theories with impedance obtained from 3D simulations (2) This confirms that we should not use the constant form factors for kickers (3) Gives more confidence in the new theory and in the CST simulations (4) |Im(Zx quad)| > Im(Zx dip) as predicted by previous measurements

15. 15 Comparison between Tsutsui, Zotter/Metral and 2 wire measurements Tsutsui Tsutsui formula much lower than both 2 wire measurements and Zotter/Metral formula  we still need to understand this difference  refine the simple kicker model (cells, external circuits, gaps)  redo experiments with a focus on getting both the dip and quad impedance

16. 16 Agenda Separating the dipolar and quadrupolar impedance contributions. Use new tools to obtain the impedance and wakes of SPS components Status of the current transverse impedance model and comparison with beam measurements Next steps

17. 17 Wake function for the updated impedance model horizontal Vertical dipolarquadrupolar  Kickers is the largest single bunch contribution  BPMs leads to significant oscillations  beam pipe mostly affects the very short range and the multibunch SPS bunch length (4  )  into HEADTAIL

18. 18 Simulated growth rate Vs bunch population for all kickers Horizontal Vertical Coherent position Exponential fit Vertical coherent motion for selected bunch populations HEADTAIL simulations with all the kickers (2006 situation) Nb=74 10 9 p/b Nb=14 10 9 p/b Nb=158 10 9 p/b Nb=178 10 9 p/b Nb=184 10 9 p/b

19. 19 HEADTAIL simulation with the current SPS impedance model  positive horizontal tune shift, as observed in SPS beam measurements since many years!  observed vertical tune is carried by several coherent modes until the instability All SPS kickers in 2006 (Tsutsui model) Simulated growth rate Vs bunch population for all kickers Horizontal Vertical small coupling between modes 0 and -1 medium coupling? between modes -2 and ? large coupling? between modes -3 and ?

20. 20 HEADTAIL simulation with the current SPS impedance model  positive horizontal tune shift, as observed in SPS beam measurements since many years!  observed vertical tune is carried by several coherent modes until the instability BPMs + beam pipe+ kickers (Tsutsui model for the kickers)

21. 21 Mode spectrum of the vertical coherent motion as a function of bunch current Measured with an SPS single bunch Measured spectral lines Max spectral line 2 nd max spectral line.. Fast transverse instability in the SPS Measurements (2007) and HEADTAIL simulations: mode spectra  Vertical tune shift with intensity  strong sidebands even at low currents (most likely non zero chromaticity)  complicated behaviour of the main mode and the second mode.  Indication that the mode that leads to the instability is not mode 0 Also see APC 24/10/2008

22. 22 History of the transverse impedance of kickers over the years: theory, simulations and measurements for the whole machine Im(Zeff) [M  /m] Tune shift Measurement Theory kickers (Sacherer) Simulation Kickers (Tsutsui) Simulation Kickers+BPMs +beam pipe (Tsutsui) 200119.13.53.67.2 200322.26.4 200623.68.79.012.8 200722 200822 +5MKE +4MKE  From HEADTAIL simulations, improved SPS impedance model accounts for: - 55% of the measured vertical SPS tune shift and main instability threshold - 90% of the measured horizontal SPS tune shift Need to include serigraphed kickers dipolar=2/3 totaldipolar<1/2 total  Tune shift is “proportional” to the total impedance, but proportion of dip and quad impedance? +4.5+5.2+5.4+5.6

23. 23 Agenda Separating the dipolar and quadrupolar impedance contributions. Use new tools to obtain the impedance and wakes of SPS components Status of the current transverse impedance model and comparison with beam measurements Conclusions and next steps

24. 24 Conclusions It is important to separate the dipolar and quadrupolar impedance contributions.  The dipolar impedance drives coherent instabilities  The quadrupolar impedance damps coherent motion and leads to emittance growth. New tools: example of kickers –New theoretical formulae for the quadrupolar impedance in the frame of Tsutsui formalism –New 3D simulations of the dipolar and quadrupolar impedance of simple models of kickers –Good agreement between theory and simulations! –Method with constant form factors is valid for good conductors but should not be applied for kickers From HEADTAIL simulations, improved SPS impedance model accounts for:  55% of the measured vertical SPS tune shift and main instability threshold  90% of the measured horizontal SPS tune shift Complicated wake function leads to complicated mode spectrum.  Monitoring the tune shift only gives information on the total impedance, when the main objective is reducing instabilities i.e. minimizing the dipolar impedance.

25. 25 Ongoing work and next steps Refine current impedance models for the kickers (cells, serigraphy, external circuits,etc.)  Carlo Zannini, Hugo Day et al Dipolar and quadrupolar simulations and/or measurements of other potential sources of impedance (pumping ports, RF cavities)  Olav Berrig, Bruno Spataro et al Include new theories and simulations to improve the longitudinal impedance model together with BE/RF-BR. Implement this framework to obtain the LHC impedance model  Nicolas Mounet et al Continue to follow the changes of hardware to trace the impedance sources Use localization of impedance technique to identify impedance contributors.  Rama Calaga et al Implement the effect of the wake in front of the bunch in HEADTAIL.

26. 26 Thank you very much for your attention!

27. 27 Tsutsui

28. 28 Wake functions from theory and wake potentials from simulations for all SPS kickers (2006 situation) Simulated rms bunch length: 2 cm  Important to use short bunch lengths!  Wake with bunch length of 2 cm is close enough to theory Simulated rms bunch length: 10 cm Theory gives an impedance, simulations gives a wake potential. For HEADTAIL simulations, we need the wake function….