1. An e+e- storage ring Higgs factory at Fermilab Tanaji Sen FNAL Accelerators for a Higgs Factory Workshop Nov 14-16, 2012

2. T. Sene+e- ring at Fermilab Outline Prelude: VLLC parameters Design strategy and choices for the site filler Beamstrahlung lifetime estimates Optimum store times Lattice and IR design, local chromaticity correction Emittance reduction Higgs factory parameters Z factory parameters Injectors for the site filler rings Magnet designs Update on 233km ring parameters (D.J. Summers)

3. T. Sene+e- ring at Fermilab VLLC; a site filler injector and collider Workshop at IIT, Chicago in 2001 Proceedings, ed. G. Dugan & A. Tollestrup Sen and Norem, PRSTAB 5, 031001 (2002) Circumference= 16.163 km 1)Collider ring at fixed energy 2) Accelerator ring for topping up.

4. T. Sene+e- ring at Fermilab 233km ring at 200 GeV SR power, both beams [MW] Luminosity [cm -2 sec -1 ] βx*, βy* [cm] Emittance [nm] Damping partitions Jx, Jy, Jz Number of bunches Single beam current [mA] Energy loss/turn [GeV] Rf voltage [GV] Longitudinal damping time [turns] Bremsstrahlung lifetime [hrs] 100 8.8 x 10 33 100, 1 3.1, 0.03 1, 1, 2 114 11 4.4 4.9 45 5

5. T. Sene+e- ring at Fermilab Higgs factory with a site filler Power limited regime. Synchrotron radiation power from both beams limited to 100 MW. Beam current is determined by Minimum number of bunches compatible with single bunch intensity limits Luminosity in terms of beam-beam parameter, beta function and power

6. T. Sene+e- ring at Fermilab Design choices Synchrotron radiation power from both beams: P T = 100 MW. The same choice made for VLLC, LEP3 1 Interaction region Beam-beam parameter: LEP observations showed the scaling with damping decrement as ξ y ~ λ d 0.4 Scaling law predicts that if it persists at 120 GeV in this ring, then ξ y ~ (0.19 – 0.31), We choose ξ y ≤ 0.1 Beta functions at the IP: limits determined by the IR chromaticity, beam size in the quads, beam-beam effects, hourglass effect, … We choose β y * ≥ 0.2 cm Arc length/Circumference = 0.8 FODO cells in the arcs with 90 degree horizontal phase advance/cell. 2 cases: (90,90) and (90,60)

7. T. Sene+e- ring at Fermilab Beamstrahlung lifetime M. Zanetti ΔE/E accept Lifetime [sec] 0.01 0.02 0.03 0.04 0.12 12.0 2149 Inf Beamstrahlung lifetime limitation from photons emitted with energies above the energy acceptance (V. Telnov) Lifetime ~ exp[(ΔE/E) accept ] Increasing the lifetime Increase energy acceptance to 3% (possible?) Increase the beam size at the IP, e.g. σx can be increased w/o luminosity decrease (backgrounds?) Top up beam in collider more frequently Decrease bunch intensity, but L ~ N P T, so at constant P T, L decreases βx*=20 cm, βy*=0.2 cm

8. T. Sene+e- ring at Fermilab Store time and average luminosity Average luminosity relative to initial luminosity, assuming no refills during a store 1) If the refill time is 1 min and τ L = 10min, the optimum store time = 4 min and the average luminosity nearly 70% of initial 2) If the refill takes 30 min and τ L = 10min, optimum store time=18 min and average luminosity about 17% of initial.

9. T. Sene+e- ring at Fermilab Optics Preliminary optics design uses (90/90) and alternative (90,60) degree FODO cells & standard dispersion suppressors 1 straight section for the Rf for now. More Rf straight sections will be added to control energy deviations around the ring. 1 IR straight section with doublets followed by a matching section. Local chromaticity correction with dipoles in the IR. 1 family of local sextupoles in each plane. Symmetric about IP. β y * = 0.5cm L* = 2.5 m E. Gianfelice-Wendt

10. T. Sene+e- ring at Fermilab Lattice functions & Chromaticity corretion Chromaticity correction with IR & arc sextupole families. Momentum aperture nearly ± 1.6% with the (90/90) lattice Arc D sextupoles are 22% weaker with (90/60) optics. Local scheme under study Tune scan required for dynamic aperture optimization. βx*=20cm, βy*=0.5cm E. Gianfelice-Wendt Gradients ≤ 24 T/m (βxmax, βymax) = (3497, 4558)m

11. T. Sene+e- ring at Fermilab Emittance reduction at 120 GeV Ways of decreasing the emittance 1) DBA, TBA or MBA lattices, used in light sources 2) Shift in the Rf frequency 3) Gradient magnets with negative field index 4) Damping wiggler placed in a zero dispersion region Rf frequency shift, gradient magnets and wigglers increase the energy spread Natural emittance in a lattice However, Gradients at 120 GeV are large : B’ = 53 T/m Q’ about 40% larger than equivalent FODO

12. T. Sene+e- ring at Fermilab Shift in Rf frequency Shift in Rf frequency changes the damping partition numbers This changes the partition numbers and emittances as The rf voltage has to be increased to provide a sufficient quantum lifetime with the increased energy spread.

13. T. Sene+e- ring at Fermilab Higgs Factory Parameters Circumference [km] Synchrotron Radiation power, both beams [MW] Energy [GeV] Luminosity [cm -2 sec -1 ] Hourglass factor β x *, β y * [cm] Particles/bunch Number of bunches Beam-beam parameters ξ x, ξ y Beam current [mA] Emittances [nm] Damping partition numbers Jx, Jy, Jz Energy lost/turn [GeV] Rf voltage [GV] Damping time (τ s ) [turns] Bremsstrahlung lifetime [mins] Beamstrahlung upsilon parameter 16.0 100 120 5.2 x 10 33 0.89 20, 0.2 7.9 x 10 11 2 0.067, 0.095 4.8 23, 0.1 1.5, 1, 1.5 10.5 12.8 11 18 8.8 x 10 -4

14. T. Sene+e- ring at Fermilab Z factory at 46 GeV Design strategy: operate at the beam-beam limit when synchrotron radiation power is not a limit In this regime, luminosity proportional to emittance, so increase the emittance with wigglers in areas with dispersion. Lower bunch intensity, more bunches Parasitic collisions is an issue, so need bunch trains perhaps with a crossing angle at the IP or pretzel orbits Multi-bunch feedback system may be required.

15. T. Sene+e- ring at Fermilab Z factory parameters Values Circumference [km] Energy [GeV] Luminosity [cm -2 sec -1 ] SR power, both beams [MW] β x *, β y * [cm] Particles/bunch Number of bunches Beam parameters ξ x, ξ y Beam current [A] Emittances [nm] Damping partition numbers Jx, Jy, Jz Energy lost/turn [MeV] Rf voltage [MV] Damping time (τ x ) [turns] Bremsstrahlung lifetime [hrs] Beamstrahlung upsilon parameter 16.0 46.0 3 x 10 34 60 20, 0.2 5 x 10 11 89 0.032, 0,045 0.13 78, 0.4 1, 1, 2 226 260 203 1.2 4.61x10 -5

16. T. Sene+e- ring at Fermilab Beam Dynamics Dynamic Aperture over a wide momentum range Bunch intensity limitations - TMCI: High frequency Rf cavities may pose a limit. - Synchrotron radiation from quads increases with beam size, which increase with intensity due to beam-beam Beam-beam limitations, dynamic beta, beam backgrounds, flip-flop, coherent effects, Synchro-betatron resonances with large Qs Synchrotron radiation from quadrupoles, backgrounds

17. T. Sene+e- ring at Fermilab Injection Scenarios Scenario 1: 400 MeV linac, Accumulator ring, Booster, Main Injector Scenario 2: 3 GeV linac, Accumulator ring, Main Injector Scenario 3: 1 GeV linac, Accumulator ring, Superconducting Fast Ramping Synchrotron Scenario 4: Recirculating linac, e+ damping ring

18. T. Sene+e- ring at Fermilab

19. T. Sene+e- ring at Fermilab Injectors: Scenario 3 New: 1 GeV Linac + Accumulator Ring + Fast Ramping Synchrotron Concept: H. Piekarz Circumference Damping time at 1 GeV Acceleration time B field range [T] Energy loss/turn@ 12GeV Critical energy at 12 GeV 830 m 2.8 sec 0.2 sec 0.08 – 0.9 21 MeV 41 keV Accumulator at 1 GeV The SFRS uses HTS cable, operates at 4.5 K Expected to have a generous temp. margin Magnet ramp rate is 4T/sec Stacking in: Accumulator, SFRS. May eliminate stacking in large ring. Issues Field quality at injection. May not be an issue if no stacking is done Damping time is long at 1 GeV. Can full intensity be accumulated in the SFRS at 1 GeV or higher ? High synchrotron radiation load at 12 GeV No operational experience with a SFRS

20. T. Sene+e- ring at Fermilab Conceptual Magnet Designs Fast Ramping Injector Synchrotron magnet : Built with HTS cable. Ramping speed = 4T/sec. Accelerates beam from 1GeV to 12 GeV. Under test. Accelerator ring magnet: Built with NbTi cable. Ramping speed = 0.8 T/sec. Acceleration from 12 GeV to 120 GeV. Collider ring magnet: C shaped with shims for improved field quality. Cooling provided by water channels and absorber fins. H. Piekarz Fast ramping Injector Magnet Accelerator Ring Magnet Collider Ring Magnet

21. T. Sene+e- ring at Fermilab Technical Issues Vacuum system: high synchrotron radiation load, 15 kW/m in collider, critical energy nearly 2 MeV. Also needs design in the injectors Rf system: choice of frequency, e.g. 1.3 GHz (ILC cavities) or lower. Impact on transverse impedance and bunch intensity limit. HOM losses with short bunches. Needs to be distributed in several straight sections. Machine backgrounds in detector. What is the minimum value of L*? Superconducting large aperture quadrupoles in the IR placed close to the IP

22. T. Sene+e- ring at Fermilab D.J. Summers U of Mississippi, Oxford

23. T. Sene+e- ring at Fermilab D.J. Summers U of Mississippi, Oxford

24. T. Sene+e- ring at Fermilab Conclusions Luminosity of (1-5)E33 may be possible in 1 st stage Local chromaticity correction scheme implemented. Need to improve energy aperture of scheme and dynamic aperture to 3% Beamstrahlung lifetime is adequate at a 3% energy acceptance. If use 1 ring, average luminosity < 20% of initial if refill time = 30min. With 2 rings and refill time=1min, av. Luminosity nearly 70% of initial. Both assume luminosity lifetime = 10min. Several possibilities for injectors including a superconducting fast ramping ring. Main technical issues are vacuum system design and Rf system. Upgrades to reach higher luminosities include lower emittance latttices, lower β* with improved chromaticity correction, crab waist collisions

25. T. Sene+e- ring at Fermilab Acknowledgments Credits Lattice : E. Gianfelice-Wendt, Y. Alexahin SFRS & Magnets : H. Piekarz Beamstrahlung : M. Zanetti (MIT) Vacuum : J. Noonan (ANL) Thanks to B. Brown, W. Chou, S. Henderson, V. Lebedev, J. Norem (ANL), N. Solyak, V. Shiltsev, D. Summers (U Miss), R. Zwaska