1. Lattice design for FCC-ee Bastian Haerer (CERN BE-ABP-LAT, Karlsruhe Institute of Technology (KIT)) 1 8 th Gentner Day, 28 October 2015

2. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) Future Circular Collider Study 100 km storage ring FCC-hh (=long-term goal):  High-energy hadron collider  Push the energy frontier to 100 TeV FCC-ee (TLEP):  e + /e - -collider as intermediate step FCC-he  Hadron-lepton collider option  Deep inelastic scattering 2

3. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) Physics goals of FCC-ee Provide highest possible luminosity for a wide physics program ranging from the Z pole to the tt production threshold.  Beam energy range from 45 GeV to 175 GeV Main physics programs / energies (+ scan around central values):  Z (45.5 GeV): Z pole, high precision of M Z and Γ Z,  W (80 GeV): W pair production threshold,  H (120 GeV): H production,  T (175 GeV): tt threshold. All energies quoted refer to BEAM energies 3

4. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) Coupling precision 4 J. Ellis & P. Janot

5. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) Particles with energy deviation: δ = Δp/p Linear Beam Dynamics 5 Particle trajectory: Beta Function β Dispersion function D A = πε Emittance ε x’ x

6. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) Challenges: the parameter list Design & optimize a lattice for 4 different energies Interaction region layout for a large number of bunches Horizontal emittance is increasing with reduced energy Extremely small vert. beta* (β y * = 1 mm)  High chromaticity  Challenging dynamic aperture High synchrotron radiation losses include sophisticated absorber design in the lattice ZWHtt Beam energy [GeV]45.580120175 Beam current [mA]1450152306.6 Bunches / beam1670044901330160 Bunch population [10 11 ]1.80.70.460.83 Transverse emittance ε - Horizontal [nm] - Vertical [nm] 29.2 0.06 3.3 0.007 0.94 0.0019 2 0.002 Momentum comp. [10 -5 ]1820.5 Betatron function at IP β* - Horizontal [mm] - Vertical [mm] 500 1 500 1 500 1 1000 1 Energy loss / turn [GeV]0.030.331.677.55 Total RF voltage [GV]2.545.511 6

7. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) 7 FCC-ee Layout P. Lebrun & J. Osborne S B Q Q B B B S Q S S B = bending magnet, Q = quadrupole, S = sextupole 50 m FODO cell 100 km circumference 2 experiments

8. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) Optical functions (175 GeV) 8 Arc FODO cell Mini straight section

9. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) My PhD thesis so far: Maintain the lattice for FCC-ee (Arcs) Horizontal emittance tuning Chromaticity correction using the arcs 9 Baseline parameter list: Beam energy [GeV]45.580120175 Horizontal emittance ε [nm]29.23.30.942

10. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) 1) Emittance tuning L cell = 100m L cell = 50m L cell = 150m 10

11. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) Lattices for 80 and 45.5 GeV 11 175 GeV and 120 GeV: L cell = 50 m, Ψ = 90°/60° 80 GeV: L cell = 100 m, Ψ = 90°/60° Dispersion Suppressor Arc cellsStraight matching section (with RF) Straight cells (with RF) Half-bend dispersion suppressor Dispersion suppressor based on quadrupoles 45.5 GeV: L cell = 300 m, Ψ = 90°/60° 200 m 250 m 200 m

12. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) Optics with larger cell lengths 12 80 GeV beam energy MADX Emit:ε x = 1.70 nm 45.5 GeV beam energy MADX Emit:ε x = 14.2 nm

13. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) Optics with larger cell lengths 13 80 GeV beam energy MADX Emit:ε x = 1.70 nm Re-matched Dispersion Suppressor

14. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) 2) Chromaticity 14 Dispersion in the quadrupoles modifies focusing strength Quadrupole δ > 0 δ < 0 δ = 0 Tune 1 st order2 nd order 3 rd order chromaticity  Tune shift for particles with energy deviation δ = Δp/p  Particles hit resonances and get lost

15. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) Chromaticity correction 15 δ > 0 δ < 0 δ = 0 Correction with sextupole magnets in non-dispersive regions QuadrupoleSextupole

16. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) 16 Phase advance FD – 1 st Sext. μ y = n*π μ x = m*π Final doubletFirst arc FODO cell MQDIR1MQFIR1 IP (m,n integer) … SF1 SD1

17. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) 17 FCC-ee sextupole scheme μ x = 90° = π/2 μ y = 60° = π/3 μ x = 180° = π (  -I transformation) Even number of sextupoles per family! SF1SF2SF1 SF2 SD1 SD2 SD3 SD1

18. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) W functions in the half-ring 18 IP V17_RT9060_1m1mm

19. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) Optimising the momentum acceptance 19 half-integer add linear chromaticity Q’ y = 0 Q’ y = 15 half-integer [-0.15%, 0.07%] [-0.21%, 0.07%]

20. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) Mom. acceptance for different β * 20 β* y = 1 mm: [-0.21%, 0.07%] β* y = 2 mm: [-0.29%, 0.11%]

21. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) 21 6 sextupole families + 12 free sextupole pairs per arc per plane 6 sextupole families per arc per plane Vary individual sextupole pairs to flatten Q(Δp/p) Different sextupole scheme [-0.49%, 0.69%]

22. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) Summary Lattice design for a future e+/e- collider Linear lattice design  Horizontal emittance tuning Non-linear dynamics  Higher order chromaticity correction  Momentum acceptance optimisation 22

23. 8 th Gentner Day 28 October 2015 Lattice Design for FCC-ee Bastian Haerer (bastian.harer@cern.ch) 23 Thank you for your attention!