1. A First Look at the Performance for Pb-Pb and p-Pb collisions in FCC-hh Michaela Schaumann (CERN, RWTH Aachen) In collaboration with J.M. Jowett and R. Versteegen (CERN) 14 th February 2014 FCC Study Kickoff Meeting, Geneva

2. Outline M. Schaumann, Pb-Pb and p-Pb performance of FCC 2 2014/02/14 General assumptions (Pre-accelerator chain, ring and beam parameters) Estimates for: IBS and radiation damping Luminosity and beam evolution Beam-beam tune shift Power in secondary beams emerging from collision point Parameter table Conclusions

3. General FCC-hh Parameters 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 3 UnitsInjectionCollision Circumference[km]80 Main dipole strength[T]1.220 Bending radius[m] 8339.1 Proton equivalent energy[TeV]350 Lead ion energy[TeV]2464100 Lead ion energy/nucleon[TeV]1.219.7 [TeV]2.439.4 Based on a working p-p collider exists.

4. Heavy Ion Pre-Accelerator Chain 4 2014/02/14 Straw-man assumption to estimate (conservative) beam parameters and luminosity: LHC, as it is today, but cycling to 3 Z TeV, is assumed to be the injector for FCC-hh. The requirements and performance of the pre-accelerator chain for FCC are not studied yet. Present heavy-ion pre-injectors LEIRHI source + Linac 3 Inject one LHC beam into 1/3 FCC, no waiting. Will see later that injector cycle time is similar to time taken to burn-off all beam in FCC. PS SPS LHC FCC M. Schaumann, Pb-Pb and p-Pb performance of FCC R&D

5. Pb Beam Parameters in LHC and FCC-hh LHC Design LHC 2011 LHC 2013 FCC-hh Beam Energy [Z TeV]73.5450 β-function at the IP [m]0.51.00.81.1 0.71.4 1.5 15.933.926.68.8 7.9410 Number of bunches592358 432 1110 (p-Pb)? M. Schaumann, Pb-Pb and p-Pb performance of FCC 5 2014/02/14 Best injector performance achieved in 2013 p-Pb run. Average beam parameters from 2013 are assumed as VERY conservative baseline for FCC-hh! → Improvements are already under study for HL-LHC!

6. Effects on the Emittance – a new regime 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 6 Intra-Beam Scattering (IBS)Radiation Damping Emittance GrowthEmittance Shrinkage twice as fast as for protons!! Growth rate dynamically changing with beam properties: Damping rate is constant for a given energy: Damping Times UnitFCC collision [h]0.16 [h]0.31 [h]0.31 Growth Times UnitFCC collision [h]144.7 [h]39.1 [h] IBS is weak for initial beam parameters, but increases with decreasing emittance. Fast emittance decrease at the beginning of the fill, until IBS becomes strong enough to counteract the radiation damping.

7. Beam Evolution in Pb-Pb Collisions (1 Experiment) 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 7 Horizontal Emittance Vertical Emittance Intensity

8. Pb-Pb Luminosity Evolution (1 Experiment) 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 8 Unitper Bunchwhole Beam [Hz/mb]0.00753.2 [Hz/mb]0.02912.7 0.283 1 experiment in collisions R&D

9. Beam-Beam Tune Shift 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 9 Beam-Beam Parameter per Experiment UnitLHC Design p-p LHC Design Pb-Pb FCC Pb-Pb Initial3.70.180.37 Peak3.70.182.0 Beam-beam tune shift per experiment. For round beams : The tune shift due to beam-beam interactions remains well below assumed limit.

10. p-Pb Luminosity Evolution (1 Experiment) 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 10 “Analytical calculation” only! – Neglecting IBS Unitper Bunchwhole Beam [Hz/mb]0.6267 [Hz/mb]135477 7030240

11. BFPP Beam Power 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 11 Main: 208-Pb-82+ BFPP1: 208-Pb-81+ BFPP2: 208-Pb-80+ EMD1: 207-Pb-82+ EMD2: 206-Pb-82+ LHC Example: LHC Pb beam right of IP2 Countermeasures (e.g., DS collimators) have to be considered in initial lattice & hardware design. Main contribution to fast Pb-Pb burn-off: R&D FCC-PbPb

12. Summary Table (1) 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 12 UnitLHC DesignFCC Injection FCC Collision FCC Collision Operation mode-Pb-PbPbPb-Pbp-Pb Particle type-Pb p Beam Energy[TeV]574246410050 Lead ion energy/nucleon[TeV]2.761.219.750 Relativistic γ-factor-296312702116853290 Number of bunches-592432 No. Ions per bunch0.71.4 115 Transv. normalised emittance1.5 3.75 RMS bunch length7.9410 Synchrotron frequency[Hz]23.05.51.9 Longitudinal emittance (4σ)[eVs/charge]2.5423 RMS energy spread1.13.31.1 Circulating beam current[mA]6.123.0 Stored beam energy[MJ]3.812.440 Longitudinal IBS emit. growth time[h]7.716.9144.7 Horizontal IBS emit. growth time[h]138.539.1 Longitudinal emit. rad. damping time[h]6.37250.160.32 Horizontal emit. rad. damping time[h]12.614510.310.63

13. Summary Table (2) 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 13 UnitLHC DesignFCC Injection FCC Collision FCC Collision Operation mode-Pb-PbPbPb-Pbp-Pb Peak RF voltage[MV]161122 RF frequency[MHz]400 Harmonic number-35640106740 Power loss per ion[W] Energy loss per ion per turn[MeV]1.120.01969.15.8 Synchrotron radiation power per ring[W]83.90.75373226587 Critical photon energy[eV]2.770.07336.75376 β-function at the IP[m]0.5-1.1 RMS beam size at IP15.9-8.8 Initial luminosity1-3.2267 Peak luminosity1-12.75477 Integrated luminosity per fill<15-8330240 Beam-beam tune shift1.8-3.7 Total cross-section[b]515-5972 Peak BFPP beam power[W]26-29470 Initial beam current lifetime (1 exp.)[h]<11.2 (2 exp.)-8.724 Initial luminosity lifetime[h]<5.6 (2 exp.)-3.73.2

14. Peak and Integrated Luminosity per Month 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 14 https://indico.cern.ch/event/288576/material/1/0 Luminosity values discussed with the Ion Physics Working Group for FCC-hh.

15. Conclusions and Outlook 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 15 Strong rad. damping, small emittances and effective intensity burn-off. R&D Watch compatibility of evolving hadron collider design with nuclear beams.

16. M. Schaumann, Pb-Pb and p-Pb performance of FCC 16 2014/02/14

17. Bunch-by-Bunch Differences after Injection in the LHC Intensity Design Horizontal / Vertical Emittance Design M. Schaumann, Pb-Pb and p-Pb performance of FCC 17 2014/02/14 1 train E = 450 Z GeV

18. Smooth Lattice Approximation 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 18 A lattice design does not yet exist! Approximations for smooth lattice functions are used where necessary. Cell Length from aperture constraints UnitLHC DesignFCC -0.78 Average β-function[m][66, 71] Average Dispersion (hor.)[m]1.4 -55.7 Assume FODO cell with

19. Intra-Beam Scattering 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 19 Handbook of Accelerator Physics and Engineering, 1 st Edition, 3 rd Print, pp. 141 A. Piwinski Formalism for IBS growth rates: Particle Type Energy Beam properties Lattice and beam sizes IBS strength changes dynamically with beam properties.

20. Intra-Beam Scattering 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 20 Growth Times UnitLHC Design FCC injection FCC collision [h]7.716.9144.7 [h]138.539.1 [h]-75000-6604 Variation of IBS growth times for initial beam conditions with FODO cell length. Effect of long. (hor.) IBS decreases (increases) with increasing cell length. At collision energy, IBS is weak for initial beam parameters. Injection Energy Collision Energy Expected Range

21. Radiation Damping 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 21 Radiation Integrals EnergyParticle TypeRing Constant depending on particle’s mass and charge Damping Rates Handbook of Accelerator Physics and Engineering, 1 st Edition, 3 rd Print, pp. 210

22. Luminosity Evolution 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 22 Consider burn off and radiation damping: IBS is weak at top energy and dominated by radiation damping: → approximate constant emittance damping time. System of two differential equations to be solved:

23. Beam Evolution Simulations 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 23 Evolution of 3 typical Pb-bunches in collisions. Head Core Tail Dashed lines: without coupling Solid lines: with coupling

24. Pb-Pb Luminosity for varying β* 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 24 CTE simulation assuming full IBS coupling. Red curve corresponds to solid red curve on slide 8.

25. p-Pb Beam Evolution 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 25 Pb emittance damps twice as fast as p emittance; assuming exponential emittance damping with constant rad. damping rate and no IBS.

26. Longitudinal Beam Parameters 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 26 UnitLHC DesignFCC [Hz]23.01.9 1.1 [eVs/charge]2.523 S.Y.Lee, Accelerator Physics, 3 rd edition at top energy

27. Circulating Beam Current and Stored Beam Energy 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 27 Circulating beam current: Stored beam energy: UnitLHC Design FCC injection FCC collision [mA]6.122.98 [MJ]3.812.3839.73

28. Energy Loss per Turn 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 28 Radiated power per ion: Radiated power per beam: Energy loss per ion per turn: Damping Times UnitLHC DesignFCC injection FCC collision [W] [MeV]1.120.01969.1 [W]83.90.753732 [eV]2.770.07336.7 Critical photon energy: Handbook of Accelerator Physics and Engineering, 2 nd Edition, pp. 215

29. Initial Beam Current Lifetime 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 29 Lifetime due to burn-off only! UnitLHC Design (2 experiments) FCC (1 experiment) FCC (2 experiments) [h]11.28.74.3 Total cross-section at 50Z TeV: H. Meier et al, Phys. Rev. A, vol. 63, 032713. 02/2011

30. Cycle with LHC as Last Injector 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 30 Intensity Evolution in FCC with 1 exp. in collisions

31. Smaller Z Ions – Impact on Luminosity 2014/02/14 M. Schaumann, Pb-Pb and p-Pb performance of FCC 31