1. 1 Transverse single-bunch instabilities in the CERN SPS and LHC Benoit Salvant for the impedance team: Gianluigi Arduini, Theodoros Argyropoulos, Mike Barnes, Olav Berrig, Rama Calaga, Fritz Caspers, Hugo Day, Alexej Grudiev, Kevin Li, Elias Métral, Nicolas Mounet, Jean-Luc Nougaret, Diego Quatraro, Federico Roncarolo, Giovanni Rumolo, Elena Shaposhnikova, Bruno Spataro, Carlo Zannini, Bruno Zotter. http://impedance.web.cern.ch/impedance/ With many thanks to our colleagues from CERN, INFN, GSI and TU Darmstadt for their help and advice Beam physics for FAIR, July 5-6, Hotel Bastenhaus, Germany

2. 2 Main objectives of the talk Mention the importance of decomposing the transverse impedance into dipolar and quadrupolar components Describe the general framework used to: –obtain the impedance model of a machine –simulate its interaction with a single bunch Case of the CERN SPS –SPS transverse impedance model –TMCI threshold and coherent tune shifts for nominal emittance Case of the CERN LHC –LHC transverse impedance model –Compare simulations and measurements Opportunities for further collaborations?

3. 3 Agenda Context Separating the dipolar and quadrupolar impedance components Tools and methods for an impedance database Case of the SPS Case of the LHC Overview

4. 4 Context of the CERN LHC complex Luminosity Key parameter to assess the performance of a collider: luminosity N b (i) = number of protons per bunch in beam i f rev = revolution frequency N = number of bunches  x,y = transverse beam sizes High luminosity requires high intensity and low transverse beam sizes These dense bunches also need to be produced and accelerated in all the injectors. The performance of the injectors also affects the LHC luminosity

5. 5 Context of the CERN LHC complex for protons: Wakefields - Moving charged particles generate EM fields. - EM fields are reflected by the surroundings and act back on the trailing particles. - This perturbation can lead to beam size growth and beam losses. Electromagnetic wakefields are a limitation to circulating dense bunches: Wakefields in the LHC and its injectors can limit the LHC luminosity Denser bunch  larger EM fields  more beam losses and larger size  lower LHC luminosity Need for a good knowledge of the source of these wakefields in all machines  goal of the impedance team!

6. 6 Agenda Context Separating the dipolar and quadrupolar impedance components Tools and methods for an impedance database Case of the SPS Case of the LHC Overview

7. 7 Separating the dipolar and quadrupolar impedance contributions (1) Dipolar and quadrupolar contributions (resp. driving and detuning) 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

8. 8 Separating the dipolar and quadrupolar impedance contributions (2) dipolar wake leads to coherent oscillations of the bunch as a whole  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) Both dipolar and quadrupolar wakes contribute to the coherent tune shift y s z 2 1 Accelerator element y2y2 y1y1 Dipolar wakeQuadrupolar wake Total wake Coherent instabilities Incoherent effects Coherent tune shift as a function of bunch intensity

9. 9 Separating the dipolar and quadrupolar impedance contributions (3) y s z 2 1 Accelerator element y2y2 y1y1 Dipolar wakeQuadrupolar wake Total wake Vertical coherent motionVertical beam size Example: HEADTAIL macroparticle simulation of a bunch interacting with: - a dipolar impedance contribution - both dipolar and quadrupolar impedance contributions Quadrupolar  Damping Quadrupolar  emittance growth  Very different impact on beam dynamics!  We need to separate the dipolar and quadrupolar impedance contributions

10. 10 Methods to separate the dipolar and quadrupolar contributions Theoretical calculations –Calculate the impedance of a round structure and use Yokoya factors (only valid for  =1 and very good conductors) –Calculate the impedance with the beam and wake integration displaced (N. Mounet et al, Generalized Form Factors for the Beam Coupling Impedances in a Flat Chamber, proc. IPAC’10) Simulations –Displace the beam and wake integration positions (Heifets et al, Generalized impedances and wakes in asymmetric structures, SLAC-AP-110 1998) Bench measurements –1-wire measurement gives access to dipolar + quadrupolar –2-wire measurement gives access to dipolar (E. Metral et al, Kicker impedance measurements for the future multiturn extraction of the CERN Proton Synchrotron, EPAC’06) Machine measurements –Tune shift  dipolar + quadrupolar –Instability growth rate  dipolar y x W y dipolar Wake integration Beam y x W y quadrupolar Note: beware of asymmetric structures!!!

11. 11 Agenda Context Separating the dipolar and quadrupolar impedance components Tools and methods for an impedance database Case of the SPS Case of the LHC Overview

12. 12 ZBASE: General framework to obtain the impedance model of a machine 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

13. 13 Agenda Context Separating the dipolar and quadrupolar impedance components Tools and methods for an impedance database Case of the SPS –SPS transverse impedance model –TMCI threshold and coherent tune shifts for low emittance Case of the LHC Overview

14. 14 Why worry about the SPS impedance? SPS: Super Proton Synchrotron, built in 1976 (circumference 6.9 km). SPS recently refurbished to be used as the injector into the LHC (removal of LEP elements, new ejection kickers, impedance reduction campaign in 2001) SPS is able to produce the nominal intensity (1.2 10 11 p/b) and emittances for LHC Intensity upgrade is foreseen  multiply by three or four the nominal intensity With our knowledge, fast transverse instability (TMCI?) limits bunch intensity to less than 2 10 11 p/b  SPS transverse impedance will be one of the bottlenecks to produce large intensities We may increase chromaticity to push the instability threshold, but large chromaticities lead to slow losses and emittance growth Need for a good understanding of the SPS impedance to identify its major contributors and propose possible SPS hardware modifications.

15. 15 Status of the impedance model Elements included in the database: –6.911 km beam pipe (Zotter/Metral analytical calculations for a round pipe including indirect space charge, transformed with Yokoya factor) –20 kickers (situation during 2006 run, analytical calculations with Tsutsui model) –106 BPHs (CST 3D simulations) –96 BPVs (CST 3D simulations) –2 TW 200 MHz cavities (4 sections of 11 cells) without couplers (CST 3D simulations) –2 TW 200 MHz cavities (5 sections of 11 cells) without couplers (CST 3D simulations) –2 TW 800 MHz cavities (3 sections of 11 cells) with couplers (CST 3D simulations) Some of the assumptions we need to make: –Ideal electromagnetic material properties (copper, ferrite) –Transverse kick is linear with transverse displacement –Simplified geometries: kicker Beam pipe BPH BPV TW 800 MHz TW 200 MHz

16. 16 Wake functions for the current SPS model Horizontal wakes Vertical wakes Dipolar contributionQuadrupolar contribution

17. 17 Real impedance for the current SPS model (note: the simulated BPMs wake was optimized for HEADTAIL, and too short to get an accurate impedance) Real Horizontal impedance Real Vertical impedance Dipolar contributionQuadrupolar contribution

18. 18 Imaginary impedance for the current SPS model Imaginary Horizontal impedance Imaginary Vertical impedance Dipolar contributionQuadrupolar contribution

19. 19 - impedance and wakes have complicated shapes  complicated beam dynamics - negative horizontal impedance at low frequencies  positive tune shift in the horizontal plane - smaller bunch  wider bunch spectrum  smaller effective impedance Impedance model (without TW800 MHz) Sum of SPS impedance sources (imaginary dip+quad) 0.3 m  Zeff = 14.3 M  /m (Sacherer equation for mode 0) 0.15 m  Zeff = 13.4 M  /m (Sacherer equation for mode 0)

20. 20 Example of refining the kicker model: simulations and measurements of an SPS MKP kicker Courtesy Hugo Day and Carlo Zannini Many thanks to TE/ABT for technical support (Yves, Salim, Mike and Wim)

21. 21 HEADTAIL simulations with this SPS impedance model HEADTAIL can simulate the interaction of a single bunch of macroparticles with an impedance source lumped in a single location. Benchmark between HEADTAIL simulations and MOSES mode coupling calculations for a broadband impedance (see for instance our talk at HB2008). Previous studies were performed at injection energy in the SPS with low longitudinal emittance (to decrease the instability threshold) The aim now is to predict the limits with nominal longitudinal emittance in order to assess the need for design and installation of cures (feedback, shielding, etc) Note: these HEADTAIL simulations do not take space charge into account.

22. 22 HEADTAIL simulations in the vertical plane Simulation parameters Initial 0.31 eVs – final 0.37 eVs V RF =2 MV Initial bunch length 1 sigma=0.27 m Final bunch length 1 sigma=0.22 m Simulated threshold = 1.5 10 11 p/b (mode -1 and -2) Real threshold in the SPS was not reached yet Vertical mode spectrum Vs bunch intensity Simulated effective impedance = 15 M  /m Measured effective impedance = 23 M  /m 35% is missing

23. 23 HEADTAIL simulations in the horizontal plane Simulated threshold > 3 10 11 p/b Real threshold in the SPS was not reached yet Simulated effective impedance = -2.2 M  /m Measured effective impedance = -2.6 M  /m Parameters Initial 0.31 eVs – final 0.37 eVs V RF =2 MV Initial bunch length 1 sigma=0.27 m Final bunch length 1 sigma=0.22 m Horizontal mode spectrum Vs bunch intensity

24. 24 HEADTAIL simulations in the vertical plane with slightly positive chromaticity Parameters Initial 0.31 eVs – final 0.37 eVs V RF =2 MV Initial bunch length 1 sigma=0.27 m Final bunch length 1 sigma=0.22 m  y = 2/26 ~ 0.0764 Simulated threshold = 2.2 10 11 p/b (mode -2 and -3) Real threshold in the SPS was not reached yet, measurements with very high intensity beam will be tried in the near future. Vertical mode spectrum Vs bunch intensity

25. 25 Summary for the SPS As for the low emittance case, the model accounts for 65 % of the measured vertical tune shift The model explains the positive horizontal tune shift observed in measurements With this model, TMCI threshold would occur at 1.5 10 11 p/b (more than 2 10 11 p/b with Q’y~2). HEADTAIL will be modified to import wake from the longitudinal impedance model and improve the feedback system model. Studies with double RF system under way Machine studies are under way to increase the beam intensity in the injector chain to assess their limits (both single bunch limits and nominal beam limits in the PSBooster, PS and SPS)

26. 26 Agenda Context Separating the dipolar and quadrupolar impedance components Tools and methods for an impedance database Case of the SPS Case of the LHC –Predicted and measured tune shifts with intensity –Measured transverse instability during the ramp Overview

27. 27 LHC impedance and collimators LHC transverse impedance is predicted to be one of the potential limitations to reach nominal beam parameters for collisions at top energy (14 TeV/c). LHC collimators are predicted to be the major contributors to the LHC transverse impedance at top energy. An upgrade of the collimation system is under study to reduce the impedance and improve the cleaning efficiency (Phase 2 collimation). Impedance theories, EM simulations, RF bench measurements and MDs in the SPS with a prototype collimator were all consistent and showed that we seem to understand the impedance of a single collimator (Roncarolo et al, PRSTAB, 2009). Now that beam is in the LHC, it is important to compare the LHC beam-based observations with predictions, in order to take decisions for the Phase 2.

28. 28 Methods LHC impedance model is calculated through ZBASE –Includes theoretical models of phase 1 collimators at desired settings, beam screens, warm pipe, MQW, MBW and a broadband impedance accounting for many other elelments (N. Mounet). –Significant contributors could be missing (kickers, PIMS, etc.). Tune shift predictions with LHC model –Impedance  Sacherer formulae for single bunch transverse tune shifts –Wake  Headtail macroparticle simulations  SUSSIX  transverse tune shifts MD –Record relevant beam parameters, in particular: intensity N b, transverse tune shifts  Q, bunch length L, as we expect

29. 29 LHC Beam 2: Moving IR7 collimators Many thanks to the operation, RF, collimation and beam instrumentations teams for the nice teamwork!

30. 30 Summary plot for beam 2 (moving all IR7 colimators) Collimator gap open at 15 sigma Collimator at 5 sig Bunchlength=1.4 ns  Qx<7 10 -4 Nb=9.3 10 10  Qy~-2.4 10 -4  The tune shift is correlated to the collimator position.   Qy (meas.) ~ -2.4 10 -4  Vertical tune shift prediction when moving IR7 from 15  to 5  (ZBASE model with measured collimator settings and Sacherer formula with measured beam settings):  Qy (theory) ~ -2.0 10 -4

31. 31 B2: Moving injection protection collimators

32. 32 B2: effect on horizontal tune shift of moving injection protection collimators (TDI+TCLIs) Tune shift due to injection protection collimators from B2 measurements:  Qy~ -3 10 -4 and  Qx~0 Coarse extrapolation from nominal model (only TDI):  Qy~ -1.2 10 -4 and  Qx~0  Correlation between the collimator gap and the vertical tune shift  The horizontal tune switches to another peak when collimators are in. To be investigated in more detail. TDI Collimator gap  Qx~0  Qy~-3 10 -4

33. 33 B2: Scraping the beam in IR3

34. 34 B2: effect of scraping in IR3 Bunch length Qx Qy Intensity Tune shift with intensity: –Scraping was performed with one collimator in IR3, resulting in a large bunch length decrease. –Accounting for this bunch length decrease and comparing with Sacherer tune shift from the nominal 450 GeV/c impedance model (collimators at nominal settings in the model instead of in the measurements): From 9.3 10 10 p to 1 10 10 p, tune shifts are less than 10 -3 and look similar in H and V

35. 35 B2: effect of scraping in IR3 Vertical tune shift (beam 2)Horizontal tune shift (beam 2) At Nb=9.3 10 10 p/b, nominal model predicts  Qy~-5.3 10 -4 (5.9) and  Qx~-5.7 10 -4 (6.3) measurements  Qy~-7.3 10 -4 and  Qx~-7.5 10 -4 Warning!!! Preliminary results obtained with nominal collimator settings!!! The model is being refined now to account for exact collimator positions during the MD.

36. 36 Agenda Context Separating the dipolar and quadrupolar impedance components Tools and methods for an impedance database Case of the SPS Case of the LHC –Predicted and measured tune shifts with intensity –Measured transverse instability during the ramp Overview

37. 37 Observed transverse instability in LHC A horizontal instability was observed during the ramp from injection energy to 3.5 TeV/c. This instability is cured by switching octupoles on.

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41. 41 Can we understand this instability with theory or simulations?

42. 42 HEADTAIL simulations with the LHC impedance model Detailed analysis in Elias Metral’s talk at the LCU meeting http://impedance.web.cern.ch/impedance/documents/SBInstabilityStudiesInTheLHCAt3500GeV_LCU.pdf http://impedance.web.cern.ch/impedance/documents/SBInstabilityStudiesInTheLHCAt3500GeV_LCU.pdf For zero chromaticity, TMCI threshold with current impedance model expected to be a factor 3 to 10 higher than nominal bunch intensity. Theoretical calculations and HEADTAIL simulations predict a Headtail instability for non zero chromaticity

43. 43 Horizontal rise time – 7 TeV nominal settings Vertical chromaticity in Q’ units Vertical rise time – 7 TeV nominal settings

44. 44 HEADTAIL simulations for LHC at 450 GeV/c Q’=3Q’=11 Q’=13 Mode 1 Mixed modes Mode 2 Transverse bunch profiles Q’=6 was measured During the MD Actually the most critical!!!

45. 45 HEADTAIL simulations for LHC at 3.5 TeV/c with octupoles As in measurements and theoretical calculations, HEADTAIL simulations predicts that the instability would be damped with an octupole current between 50A and 100A. 100 A 0 A 50 A

46. 46 LHC « status » Chromaticity was decreased (still positive) Octupoles function is now used along the ramp and on flat top to stabilize the bunches Now collisions of 7 bunches on 7 bunches with nominal intensity at 3.5 TeV/c. Many other issues to be overcome!

47. 47 Conclusions for the LHC and next steps The predictions with the impedance model from ZBASE and the measurements seem reasonably consistent. More detailed simulations with the HEADTAIL code should be performed. We need to work on getting a cleaner tune measurement The injection protection collimators may have a slightly larger impedance than expected, and this has to be investigated in more details. The ZBASE impedance model should improved  e.g. adding new kickers, other suspected sources of impedance and study shielding opportunities (Hugo Day). HEADTAIL will be modified to be able to simulate multi bunch effects (Nicolas Mounet).

48. 48 Agenda Context Separating the dipolar and quadrupolar impedance components Tools and methods for an impedance database Case of the SPS Case of the LHC Overview

49. 49 Overview Dipolar and quadrupolar impedance Tools and database to build an impedance model Simulated data and measurements for both LHC and SPS are reasonably consistent but both impedance models should be refined. In particular current work focuses on: –impedance calculations (Elias Metral, Nicolas Mounet, Frank Zimmermann) –Impedance simulations and measurements (Olav Berrig, Hugo Day, Bruno Spataro, Carlo Zannini) –Beam dynamics simulations and measurements (Gianluigi Arduini, Nicolo Biancacci, Rama Calaga, Kevin Li, Diego Quatraro, Giovanni Rumolo) –Impedance database (Jean Luc Nougaret) Further opportunities for collaborations?

50. 50 Thank you very much for your attention!

51. 51 Conclusions: - impedance and wakes have complicated shapes  complicated beam dynamics - negative horizontal impedance at low frequencies  positive tune shift in the horizontal plane - smaller bunch  wider bunch spectrum  smaller effective impedance 0.3 m  Zeff = 14.3 M  /m (Sacherer equation for mode 0) 0.15 m  Zeff = 13.4 M  /m (Sacherer equation for mode 0) Impedance model (without TW800 MHz) Sum of SPS impedance sources (imaginary) Sum of SPS impedance sources (real)