1. Optics with Large Momentum Acceptance for Higgs Factory Yunhai Cai SLAC National Accelerator Laboratory Future Circular Collider Kick-off Meeting, February 12-16, 2014, Geneva, Switzerland

2. Acknowledgements This work was done with my colleagues: Alex Chao, Yuri Nosochkov, Uli Wienands (SLAC) and Frank Zimmermann (CERN) Most results are reported in: SLAC-PUB-15416, April 2013 2 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

3. Luminosity Bunch luminosity where R h is a geometrical reduction from the hourglass effect and is written as Total luminosity 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland3

4. Beam-Beam Limit Given the beam-beam parameter The luminosity can be re-written as where I A =17045 A. Smaller  y * is absolutely necessary. For example, in our design we have I=7.2 mA, E 0 =120 GeV,  y =0.07, R h =0.76,  y *=1mm, gives 1x10 34 cm -2 s -1 in luminosity. So what is the beam-beam limit for Higgs factory? 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland4

5. LEP2 Experience R. Assmann and K. Cornelis, Proceeding of EPAC 2000, Vienna, Austria 5 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

6. Power Limitation Synchrotron radiation Beam power given by RF Limits the total beam current I For example, E 0 =120 GeV,  =2.6 km, U 0 =6.97 GeV, I=7.2 mA, lead to P b =50 MW in our design. 6 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

7. Scaling of Luminosity If there is a beam-beam limit as suggested by the simulation and beam power is also limited, the luminosity can be re-written as where P A = mc 2 I A /e = 8.7 GW. This scaling was first given by B. Richter, Nucl. Instr. Meth. 136 (1976) 47-60. 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland7

8. Beamstrahlung Effects Beam lifetime due to large single photon emission (for 30 minutes, V.I. Telnov, 2012) Large RF-buckets and large momentum aperture  Large  z and  x. Favors longer and larger horizontal beam size. Limits bunch population N b Are there any reasonable solutions? 8 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

9. Analysis of Design Constraints To achieve the beam-beam parameter and assuming  y =    x and  y =    x we have To have adequate beam lifetime (due to beamstrahlung) Clearly, smaller coupling  e is better and larger momentum acceptance  is better but they have their own limits. 9 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

10. Solution of the Constraints Given a momentum acceptance , we solve Note that it does not depend on   We can use    to adjust the bunch population N b or the number of bunches n b. Clearly, there are many possible solutions. But is there any self-consistent one? The requirement of accommodating beamstrahlung is translated to design a low emttance lattice. Normally, the emittance scales as  2. This relation requires a scaling of  -4, indicating a difficulty to design a machine with much higher energy than 120 GeV. 10 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

11. Design Parameters LEP2LEP3 ? Beam Energy [GeV]104.5120 Circumference [km]26.7 Beam current [mA] 4 7.2 Number of bunches450 Bunch population [10 10 ]57.58.0 Horizontal emittance [nm]484.3 Vertical emittance [nm]0.250.0108 Momentum compaction factor18.5x10 -5 2.4x10 -5  x * [mm] 1500100  y * [mm] 501 Hourglass factor0.980.76 SR power [MW]1150 Bunch length [mm]16.11.5 Beam-beam parameter0.07 Luminosity [10 34 cm -2 s -1 ]0.01251.01 11 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

12. 90 0 /60 0 Arc Cell 12 cells make an achromat (unit transformation). 12 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

13. Quasi (4 th Order) Achromat 3 rd order driving terms 4 th order driving terms The cancellation occurs in every 12 cells in arcs. Only non-vanishing resonance is 4 x. 13 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

14. Arc Design 90 0 /60 0 FODO Lattice Dynamic/Momentum Aperture Emittance: where  is the bending angle in a cell. Natural emittance:  x =4.3 nm and cell length is 28.375 m  >4% 14 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

15. Lattice of Collider Ring at IP:  x =100 mm  y =1 mm L*=4 m 15 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

16. Final Focus System at IP:  x =100 mm  y =1 mm L*=4 m 16 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

17. Local Chromatic Correction Use six pairs of sextupole reaching residual of 0.05%. 17 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

18. Chromatic Beating in Collider Ring 18 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

19. Betatron Tunes vs. Momentum Horizontal Vertical Four families of sextupole used in the optimization, achieving ±2.5% momentum bandwidth. 19 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

20. Beta Functions at IP vs. Momentum Horizontal Vertical Good region of ±0.4% in  p/p is necessary for the core in beam distribution. 20 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

21. Dynamic Aperture for On-Momentum Particles 21 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland 10  x 33  y Effects due to finite length of sextupoles are compensated up to O[L] 5.

22. Effects of Finite Length of Sextupoles in Final Focusing System -I K 2 K 1 K 2 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland22 L kL L kL L Cancel up to O[L] 5 if

23. Lattice Issues Ultra-low beta (1mm) IR design with large momentum bandwidth (2%) Low emittance lattice and ultra-low beta IR with adequate dynamic aperture (10  ) Large synchrotron radiation, saw-tooth (1-2%) in arcs of two beams in single ring Machine tolerances, especially alignment tolerance and orbit stability 23 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

24. Risks & Mitigations & RD Items Ultra-low beta* with large energy bandwidth in ring  y *=1 mm and  > 2% (lower emittance) RF parameters: frequency, voltage, gradient? What length is necessary for RF system (f RF =700 MHz and V RF =12 GV) ? is HOM a problem? What is the shortest bunch we can make? Coherent synchrotron radiation, heating What is energy reach of ring? How large it can be? How about 100 km? 24 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland

25. Summary Impact on design due to beamstrahlung is analyzed. We found a formula of minimum natural emittance that is necessary for beam lifetime. A systematic design procedure is outlined. There are many possible solutions. The final choice should be made with other considerations, including the interaction region design. We have achieved 2% momentum bandwidth in a lattice with an ultra-low beta interaction region 25 2/14/2014 Yunhai Cai, FCC 2014, Geneva, Switzerland