Beam beam simulations with disruption (work in progress...)

1. Beam beam simulations with disruption(work in progress...) M.E.Biagini SuperB-Factory Workshop Frascati, Nov. 11th, 2005

2. Beam-beam • Beam-beam interaction in a linear collider is basically the same Coulomb interaction as in a storage ring collider. But: • Interaction occurs only once for each bunch (single pass); hence very large bunch deformations permissible not for SBF ! • Extremely high charge densities at IP lead to very intense fields; hence quantum behaviour becomes important bb code

3. Disruption • Beam-beam disruption parameter  equivalent to linear bb tune shift in storage ring • Proportional to 1/g large numberfor low energy beams • Typical values forILC < 30, 100 > SBF >1000 • The bb interaction in such a regime can be highly non linear and unstable

4. Contraddicting requests! Scaling laws • Disruption: • Luminosity • Energy spread: Decrease sz + decrease N Increase spotsize Increase N Decrease spotsize Increase sz + decrease N Increase spotsize

5. Kink instability • For high Disruption values the beams start to oscillate during collision  luminosity enhancement • Number of oscillations proportional to D • bb sensitive even to very small beam y-offsets Simulation !

6. Pinch effect • Self-focusing leads to higher luminosity for a head-on collision • The “enhancement” parameter HD depends only on the Disruption parameter • HD formula is “empirical fit” to beam-beam simulation result  good for small Dx,y only

7. Disruption angle • Disruption angle after collision also depend on Disruption: • Important in designing IR • For SBF: spent-beam has to be recovered ! • Emittances after collision have to be kept as small as possible  smaller damping times in DR

8. Beamsstrahlung • Large number of high-energy photons interact with electron (positron) beam and generatee+e- pairs • e+e- pairsare a potential major source of background • Beamsstrahlung degrades Luminosity Spectrum

9. SBF energy spread • U(4S) FWHM = 20 MeV beam energy spread has to be smaller • PEP-II cm energy spread is ~5 MeV, depends on HER and LER energy spreads, which in turn depend on dipole bending radius and energy • For “linear colliding” beams a large contribution to the energy spread comes from the bb interaction • Due to the high fields at interaction the beams lose more energy and the cm energy spread increases

10. GUINEAPIG • Strong-strong regime requires simulation. Analytical treatments limited • Code by D. Schulte (CERN) • Includes backgrounds calculations, pinch effect, kink instability, quantum effects, energy loss, luminosity spectrum • Built initially for TESLA  500 GeV collisions, low rep rate, low currents, low disruption • Results affected by errors if grid sizes and n. of macro-particles are insufficient

11. Parameters optimization • Choice of sufficiently good “simulation parameters” (compared to CPU time)…took time • Luminosity  scan of emittances, betas, bunch length, number of particles/bunch • Outgoing beam divergences and emittances • Average beam losses • Luminosity spectrum • cm energy spread • Backgrounds

12. D Energy spread Luminosity & sE vs N. of bunches at fixed total current = 7.2 A (6.2 Km ring) Working point

13. Working point parameter listfor following plots… • ELER = 3.94 GeV, EHER = 7.1 GeV (bg = 0.3) • Collision frequency = 120 Hz • bx = 1 mm • by = 1 mm • exLER = 0.8 nm, exHER = 0.4 nm DR • ey/ex =1/100 • szLER = 0.8 mm, szHER = 0.6 mm Bunch comp • Npart/bunch = 4x1010 • Nbunch = 24000 DR kickers • Incoming sE = 10-3 Bunch comp LD = 1.2x1036 cm-2 s-1

14. Luminosity spectrum (beamsstrahlung contribution only, incoming beams energy spread 10-4) 64% of Luminosity is in 10 MeV Ecm

15. X - collision x (nm) z (micron) red  LER HER  green

16. Y - collision y (nm) z (micron) red  LER HER  green

17. Outgoing beam emittances • LER: • exout = 4.2 nm = 5 * exin • eyout = 2.9 nm = 360 * eyin • HER: • exout = 1.5 nm = 4 * exin • eyout = 1. nm = 245 * eyin Damping time required:6 t For a rep rate120 Hzt=1.5 msec needed in damping ring

18.  X LER y   X HER y  Outgoing beam phase space plots

19. L vs energy asymmetry (bg) Asymmetry helps L Chosen bg = 0.3

20. Hourglass effect • Hourglass effect limits attainable Luminosity bunch must be shorter than b* • Short bunches smaller Disruption • Long bunches smaller energy spread • Solution: “travelling focus” (Balakin)  • Arrange for finite chromaticity at IP (how?) • Create z-correlated energy spread along the bunch (how?)

21. D Energy spread Luminosity vssz Geometric L does not include hourglass For shorter bunches LD increase but energy spread also!

22. Energy spread L vs x-emittance

23. L vs y-emittance (coupling) 1% coupling is OK (smaller L has a fall off)

24. Comments • Energy asymmetry can be compensated by asymmetric currents and/or emittances and bunch lengths • Current can be higher or lower for HER wrt LER, with proper choice of emittance and bunch length ratios • Increasing x-emittance the Disruption is smaller  less time needed to damp recovered beams  loss in luminosity could be recovered by collision frequency increase • Increasing beam aspect ratio (very flat beams) also helps to overcome kink instability

25. Outgoing beams, exLER = 1.2 nm  X LER y   X HER y 

26. X – collision, baspect ratio = 100 x (nm) z (micron) red  LER HER  green

27. Y – collision, baspect ratio = 100 y (nm) z (micron) red  LER HER  green

28. Luminosity spectrumbaspect ratio = 100 Luminosity is 60% lower Dy is smaller sE is not affected by the interaction

29. Outgoing beams, baspect ratio = 100  X LER y   X HER y 

30. Outgoing beam emittancesbaspect ratio = 100 • LER: • exout = 8 nm = 10 * exin • eyout = 0.05 nm = 6 * eyin • HER: • exout = 1. nm = 2.5 * exin • eyout = 0.02 nm = 5 * eyin Damping time required :2 t With rep rate360 Hzt=1.4 msec

31. To do list… • Decrease cm energy spread • Increase luminosity • Increase X spot sizes aspect ratio  “very flat” beams (R=100) and bunch charge • New parameter scan • Increase precision  n. of micro-particles • Travelling focus • ….