1. Note presentation: Performance limitations of circular colliders: head-on collisions M. Koratzinos TLEP ACC meeting no. 8, 25/8/2014

2. introduction This is the first of the (many) presentations of notes regarding accelerator issues of FCC-ee I will present my note: Performance limitations of circular colliders: head-on collisions The idea is to collect in one document the (first- order) limitations on performance of a circular machine I have tried not to be FCC-ee specific as much as I could, so different tunnel diameters are discussed Only head-on collisions discussed

3. Energy reach This appears trivial, but I wanted something more than “circular colliders cannot go to high energy” So I used what I think is reasonable assumptions: – 20MV/m accelerating cavities – 90% dipole fill factor Then I plot beam energy vs bending radius for different percentages of the machine filled with RF – 1,2 and 5%

4. LEP2-LEP3 TLEP ttbar

5. Luminosity formula …is very simple and is spelled out as a formula: …or in natural units: (1)

6. Luminosity for an 11km radius machine, with 50MW power consumption, beta*_y of 1mm (and longitudinal beam size of 1.2mm) Luminosity for different beam-beam parameters

7. Beam-beam parameter

8. Max. beam-beam parameter

9. 0.57

10. …is small:

11. Condition for a ‘balanced’ machine

12. Beamstrahlung lifetime I mention both Valery and Anton formulas. Difference is small: TLEP-175 parameters with two different values of xi_y. this is simply to show that the two formulas are similar Mom. Acceptance = 2%

13. Beamstrahlung lifetime

14. Beamstrahlung bunch length The BS process tends to increase the bunch length which decreases the effect. An equilibrium point is reached. This is easiest computed using an iterative method. I am using the method of our parameter paper.

15. Hourglass effect Beta*_y is 1mm. If the bunch lenth increases from 1.2 to 2.6mm, the hourglass factor changes from 0.82 to 0.64 Performance drop going from 1mm to 2mm beta*y: ~20%

16. The two regimes So, we see that the maximum luminosity for a given machine (circumference) and power consumption has two regimes: – At low energies is limited by the beam-beam limit – At high energies by the BS lifetime It would be interesting to see where the crossover between the two regimes is To do this, we need to fix all other parameters to some ‘reasonable’ value – I have taken when possible the parameters of TLEP-175 Easy to work in the vertical beam-beam parameter space

17. Beam-beam parameter space

18. Choices of displaying results

19. Energy spread vs energy This is with TLEP-175 parameters, vertical emittance of 2pm and J s = 2 A c = 5.10 -6 Q s = 0.1 This is with TLEP-175 parameters, vertical emittance of 2pm and J s = 2 A c = 5.10 -6 Q s = 0.1 At low energies to reach such (low) lifetimes one needs to increase the bunch population so that the BS energy spread increases Figure not in the note

20. Keeping the Q s constant Vertical emittance of 2pm and 4pm shown At 175 GeV, theoretical beam beam parameter is 0.14 and we are able to run only up to 0.11 (20% lower)

21. Cross over vs ring size Here we keep sigma_z_SR fixed to 1.2mm Even for LEP3, cross over is at more than the Higgs threshold, provided we have a reasonable longitudinal beam size (not too small). Here we keep sigma_z_SR fixed to 1.2mm Even for LEP3, cross over is at more than the Higgs threshold, provided we have a reasonable longitudinal beam size (not too small).

22. Strategy at TLEP-175 Here we are (just) BS limited and lose about 20% of performance. We can recover that by increasing the longitudinal beam size due to SR, reducing the BS problem (at the expense of a small luminosity decrease due to hourglass) Energy: 175GeV, BS lifetime: 300s Current working point TLEP-175 Current lumi of TLEP-175 (but at more comfortable lifetime Figure not in the note

23. End