1. Pushing the space charge limit in the CERN LHC injectors H. Bartosik for the CERN space charge team with contributions from S. Gilardoni, A. Huschauer, S. Machida, G. Rumolo, R. Wasef TWIICE workshop, Oxford 2016

2. Outline Introduction Space charge in the LHC proton injectors Space charge induced resonance in the PS Studies of losses in LEIR Summary & conclusions

3. Outline Introduction Space charge in the LHC proton injectors Space charge induced resonance in the PS Studies of losses in LEIR Summary & conclusions

4. Introduction Maximum vertical incoherent space charge tune shift Single bunch effect Decreases with beam energy like 1/  2 for given normalized emittances  n Inversely proportional to vertical normalized emittance  n Maximum tune shift proportional to local line density Depends on variation of beam sizes  x,  y around the machine Proportional to the classical particle radius r 0

5. Incoherent space charge tune spread Transverse space charge for Gaussian distribution Nonlinear force resulting in betatron-amplitude dependent tune shift  tune spread Variation of the line density in bunched beams result in additional tune spread z y x QxQx QyQy Particles at peak line density have the largest tune spread bare working point

6. Incoherent space charge tune spread Transverse space charge for Gaussian distribution Nonlinear force resulting in betatron-amplitude dependent tune shift  tune spread Variation of the line density in bunched beams result in additional tune spread z y x QxQx QyQy Tune spread is reduced for particles further away from peak line density bare working point

7. Incoherent space charge tune spread Transverse space charge for Gaussian distribution Nonlinear force resulting in betatron-amplitude dependent tune shift  tune spread Variation of the line density in bunched beams result in additional tune spread z y x QxQx QyQy Tune spread is reduced for particles further away from peak line density bare working point

8. Incoherent space charge tune spread Transverse space charge for Gaussian distribution Nonlinear force resulting in betatron-amplitude dependent tune shift  tune spread Variation of the line density in bunched beams result in additional tune spread z y x QxQx QyQy Tune spread is reduced for particles further away from peak line density bare working point

9. Incoherent space charge tune spread Transverse space charge for Gaussian distribution Nonlinear force resulting in betatron-amplitude dependent tune shift  tune spread Variation of the line density in bunched beams result in additional tune spread z y x QxQx QyQy v Tune spread is reduced for particles further away from peak line density bare working point

10. Incoherent space charge tune spread Transverse space charge for Gaussian distribution Nonlinear force resulting in betatron-amplitude dependent tune shift  tune spread Variation of the line density in bunched beams result in additional tune spread Tune spread until bare working point Tune of individual particles is modulated by twice the synchrotron period z y x QxQx QyQy For bunched beams the tune spread is as big as the maximum tune shift! bare working point Largest tune shift for particles in beam core

11. Incoherent space charge tune spread Transverse space charge for Gaussian distribution Nonlinear force resulting in betatron-amplitude dependent tune shift  tune spread Variation of the line density in bunched beams result in additional tune spread Tune spread until bare working point Tune of individual particles is modulated by twice the synchrotron period z y x QxQx QyQy For bunched beams the tune spread is as big as the maximum tune shift! bare working point Largest tune shift for particles in beam core The space charge detuning can push particles onto betatron resonances, which can result in emittance blow-up and losses Pushing the limits of low emittance rings, space charge can eventually become a limitation even for electron machines (e.g. vertical space charge tune spread in CLIC damping rings about 0.1-0.2) What can we learn from space charge effects in the LHC injectors?

12. Outline Introduction Space charge in the LHC proton injectors Space charge induced resonance in the PS Studies of losses in LEIR Summary & conclusions

13. CERN accelerator complex

14. Space charge in the proton injector chain PSB cycle (0.5 s) PS cycle (3.6 s) PS FB (1.2 s) SPS FB (10.8 s) Large tune spread values at injection in the PS (1.4 GeV) are critical due to the long flat bottom (present space charge bottleneck) Large tune spreads at PSB injection (50 MeV) can be handled thanks to efficient resonance compensation, dynamic working point and rapid cycling Tune spreads in the order of 0.2 seem to be acceptable at the SPS flat bottom (26 GeV) (standard) (high brightness) Large space charge tune spread in all LHC injectors due to increasing machine circumference and decreasing bunch length (despite the higher beam energy) …

15. Brightness limitations proton injector chain Present performance is limited by space charge 2015 operation close to global performance limit 2015 white area accessible excluded due to space charge Present injector complex performance

16. Brightness limitations proton injector chain Present performance is limited by space charge 2015 operation close to global performance limit LHC Injector Upgrade (LIU) aims at ~ double brightness −Linac4: H - into PSB −PSB: increased injection energy (50  160 MeV) −PS: increased injection energy (1.4  2 GeV) −SPS: RF upgrade to reach higher intensity white area accessible excluded due to space charge Expected performance after upgrade (in ~2020) LIU upgrade Emittance preservation and loss minimization is essential for maximizing luminosity in LHC LIU upgrade for double brightness is based on energy scaling of space charge detuning Understanding space charge limitations is crucial

17. Outline Introduction Space charge in the LHC proton injectors Space charge induced resonance in the PS Studies of losses in LEIR Summary & conclusions

18. Brightness limitation in the PS The tune spread is trapped between the 4 Qy = 25 and the integer resonance If vertical tune is increased to avoid growth due to the integer, losses increase because of the 4 Qy = 25 resonance Less losses with higher tune-spread because proton population becomes smaller at 4 Qy = 25 Choice of the working point is a compromise between losses and emittance blow-up Core of the beam Halo particles R. Wasef et al.

19. Studies of the resonance at Qy = 6.25 Losses due to resonance at Qy = 6.25 depend on space charge tune spread Max. space charge detuning Beam 4 : (-.01 ; -.01) Beam 3 : (-.08 ; -.07) Beam 2 : (-.18 ; -.37) Beam 1 : (-.22 ; -.40) Horizontal tune fixed at Qx = 6.23 Qy = 6.24 Qy = 6.3 Detuning comparison  Q = 0.40 R. Wasef et al.

20. 8 th order resonance excited by space-charge Loss mechanism from 8 Qy = 50 resonance (PS has a symmetry of 50): Core particles pushed at small amplitudes by integer resonance and then trapped in islands that moves to large amplitudes due to synchrotron motion Slow process requiring synchrotron periods simulation R. Wasef et al.

21. Measurements with different PS integer tunes Optics with new integer tunes (5, 7) avoids space charge induced resonance Operational implementation being studied (issues at high energy due to combined function magnets) Integer tunes (6, 6)Integer tunes (5, 7) Losses increase with higher fractional tune (tune spread overlaps more with 8 Qy = 50 resonance) Qy= 6.24Qy = 6.xx Qy= 6.24 Qy= 7.24Qy = 7.xx Qy= 7.24 No strong losses around Qy = 7.25, losses only at Qy = 7.33 (3 rd order due to magnet errors) R. Wasef et al.

22. Outline Introduction Space charge in the LHC proton injectors Space charge induced resonance in the PS Studies of losses in LEIR Summary & conclusions

23. Losses at capture in LEIR Accumulation of Pb54+ & electron cooling Coasting beam, space charge tune spread increases along with injections and cooling electron cooling

24. Losses at capture in LEIR Accumulation of Pb54+ & electron cooling Coasting beam, space charge tune spread increases along with injections and cooling Capture Space charge tune spread increases (~ factor 2) and particles are pushed onto betatron resonances  emittance blow-up and losses RF capture

25. Mitigating space charge at capture in LEIR Iso-adiabatic capture in single/double RF with and without longitudinal blow-up Clear dependence of losses on line charge density (smaller tune spread for higher bunch factors)

26. Resonance compensation at LEIR norm: ON skew: ON norm: ON skew: OFF norm: ON skew: ON norm: OFF skew: OFF Compensating sextupolar resonances with harmonic sextupoles (2 skew & 2 normal) 10-15% increase of intensity achieved with optimal sextupole settings found so far

27. Outline Introduction Space charge in the LHC proton injectors Space charge induced resonance in the PS Studies of losses in LEIR Summary & conclusions

28. Summary and conclusions Space charge effects determine performance of LHC injectors Upgrade program relies on energy scaling of space charge detuning PS is limited by space charge induced resonance 8 th order resonance at Qy = 6.25 due to lattice symmetry  halo creation and losses Alternative optics with integer tunes (5, 7) avoids this resonance Losses at RF capture in LEIR Enlarged tune spread at capture  overlaps with lattice resonances Mitigation by flattening longitudinal bunch profile (reduction of tune spread) First studies of resonance compensation demonstrated loss reduction Implications for low emittance lepton machines Space charge could become performance limitation due to losses and increased equilibrium emittances in the limit of ultra small emittances and bunch lengths (e.g. CLIC damping rings) Incoherent space charge requires different working point and nonlinear optics optimization (large tune shift for small amplitude particles)

29. Thank you for your attention!