Beam-beam studies for Super KEKB

1. Beam-beam studies for Super KEKB K. Ohmi & M Tawada (KEK) Super B factories workshop in Hawaii 20-23 Apr. 2005

2. Luminosity limit • Fundamental limit due to the beam-beam interaction. • Super B factories target the fundamental limit. • How high is the beam-beam limit? • The beam-beam limit is discussed in two papers, K. Ohmi et al, PRL 92, 214801 (2004). Beam-beam limit in Super KEKB K. Ohmi et al, PRST 7, 104401 (2004). Crossing angle effect in KEKB • The beam-beam limit can be understood by using strong-strong simulation (based on the Particle in cell method). • Design of super KEKB is discussed from the view of the beam-beam limit using the simulation.

3. Parameter table of super KEKB KEKB

4. Tune scan • Bunch luminosity v.s. tune • Total luminosity = 5000x bunch luminosity • Green line sketches progress of KEKB. Ltot = 4x1035 cm-2 s-1 By M. Tawada

5. Luminosity evolution • Equilibrium state is realized for equal damping times. • Design damping time is 4000 and 6000 turns for HER and LER, respectively. • Slow luminosity decrease is observed for unequal damping times. bx=30 cm 20cm

6. Difference of the damping time • Beam size asymmetry and luminosity decrease arise. • Emittance equalization is required. Equal damping time (6000 turn) 4000 (HER) & 6000 (LER) turn

7. What disturb to achieve the fundamental beam-beam limit? • Nonlinear diffusion • Linear coupling of arc • Nonlinearity of arc lattice • External diffusion • Phase jitter of crab and accelerating cavities • Feedback noise • Parasitic interaction • Other issues • Heating, bunch lengthening, electron cloud …

8. Optics error at the collision point • One turn map is multiplication of beam-beam interaction and map of arc section. • Total luminosity performance is determined by the map of arc section, which is controllable by us. • X-y coupling, dispersion (xy-d coupling) and crossing angle (x-z coupling) • A symplectic diffusion is induced by the couplings. Mixing of degree of freedom seems to enhance Arnold diffusion.

9. Vertical dispersion Gaussian approx. • Diffusion behavior due to dispersion in a system without synchrotron radiation. • Luminosity and beam size are degraded. PIC simulation

10. X-y coupling Gaussian approx. • Diffusion due to x-y coupling. • Luminosity and beam size degradation. PIC simulation

11. Crossing angle • Crossing angle is equivalent to x-z coupling. • Diffusion and luminosity degradation due to crossing angle Gaussian approx. PIC simulation

12. Nonlinear terms • Effect of chromaticity, dn/dd, db/dd, da/dd, has been studied. • The effect was very weak for dn/dd ~7. • Life time degradation may be issue. • Higher nonlinearity using a Taylor map will be included in the beam-beam simulation. • Detailed studies will be done.

13. External diffusion: Vertical offset noise • Since the beam-beam system is chaotic, such noise enhances the diffusion of the system. • Luminosity degradation for the noise without correlation between turns.

14. Orbit offset (static) • Static vertical offset. Tolerance is easier than the fast noise. • For slower variation than radiation damping time, emittance can be an adiabatic invariant.

15. Phase jitters of RF systems: horizontal offset noise • Noise of RF system. Deviation of RF phase, dj. • Phase error between two crab cavities. • The transverse offset affects the beam-beam performance.

16. Effect on the beam-beam performance of the phase jitter of RF’s • Luminosity and beam size as functions of dx. • Correlation time of the jitter, 1 or 10 turns, is important for the degradation. • Since Q=200,000 and H=5120, the correlation time will be larger than 10 turns. • Tolerance is 0.05 degree.

17. Parasitic collision • Nonlinear force (~1/r) with very large amplitude • Separation at the parasitic collision • Dynamic beta and emittance (simulation)

18. Luminosity with or without parasitic interaction • In fixed parasitic beam model, no effect is observed. • When parasitic beam is treated as soft Gaussian, a stable solution was not obtained by beam loss at the early stage (unmatched). • It may be critical situation, especially forthe beamlife time or injection.

19. Toward Higher luminosityHigher bunch currentwith keeping total current • Luminosity saturates for increasing bunch current. Beam-beam limit. • Only HOM loss increases.

20. Toward higher luminosity, 1036 cm-2 s-1 • Two beam collision is limited by strong nonlinear diffusion coupled to synchrotron radiation around 4x1035 cm-2 s-1 . • Compensation scheme is one of limited choices. • Our first study (Ohnishi & Ohmi) did not give better results than that of the two beam collision.

21. 4 eigenmodes of four-beam collision Rich unstable mode and no Landau damping x,y No tune shift n=n0 z Focusing n=n0+x Defocusing n=n0-x Unstable modes

22. Summary • Design and tolerance for Ltot = 4x1035 cm-2 s-1 were studied. • Reduce optics error at the collision point. Maybe acceptable. • Reduce external diffusions especially those with fast frequency component. • Arc nonlinearity and life time issues will be studied soon by collaboration with BINP (D. Shatilov). • Efforts on higher luminosity are continued.