1. Beam-beam simulations M.E. Biagini, K. Ohmi, E. Paoloni, P. Raimondi, D. Shatilov, M. Zobov INFN Frascati, KEK, INFN Pisa, SLAC, BINP April 26th, 2006 UK SuperB Meeting, Daresbury

2. Outline GuineaPig simulations & Automatization 2 beams scheme with asymmetric energies Crab waist simulations: –DA  NE –SuperB

3. BB simulations Evolution of the SuperB layout is a consequence of the beam-beam studies Both luminosity and beam blow-up are the parameters to “watch”: figure of merit is now L/log(  blowup /  ) Optimization of beam parameters must include Damping Ring optimization and Final Focus design

4. First simulations An extensive campaign of beam-beam simulations has been carried out to find the best beam parameters set GuineaPig code by D. Schulte (CERN) has been used (same as ILC studies) in this first phase Optimization of beam parameters for round beams case was performed interfacing GuineaPig with Mathematica Round and flat, 2 and 4 beams studied

5. GuineaPig to Mathematica E. Paoloni, 2 nd SuperB LNF Workshop

6. Round case test Tested first with round beams Search of maximum L with a scan of parameters space Scan of the  x,  x plane Optimum region L/log(  blowup /  ) Scan of the  x,  z plane L/crossing E. Paoloni, 2 nd SuperB LNF Workshop

7. 4 Beams tests 4 beams are more unstable than 2 beams, highly disrupted, with larger emittance blow ups and give lower luminosity Not exhaustive analysis  not excluded we can find better working parameter set in the future Shorter beams seem to work better Larger horizontal beam size is better Higher energy definitely works better Possible choice for ILC !!!!

8. 2 beams 4 beams Flat Case comparison with 4 beams Phase space after collision (x,x’), (y,y’), (z,  E/E) x,x’ z,  E/Ey,y’ x,x’ z,  E/E y,y’

9. 2 beams asymmetric energies Studied the 2-beams scheme with asymmetric energies for 4x7 GeV case: – Npart = 2.x10 10 – I = 1.6 A (for a 3Km ring, 6000 bunches) –  x = 2.670  m –  y = 12.6 nm –  z = 4. mm –  x = 2.5 mm –  y = 80.  m –  = 2x25 mrad

10. Symmetric E Y emittance blow-up: 3x10 -3 Asymmetric E (4x7 GeV) Y emittance blow-up: 4 GeV  5x10 -3 7 GeV  3x10 -3 Study of emittance blow-up

11. Asymmetric energies (4x7 GeV) with transparency condition (I) Y emittance blow-up: 4 GeV  3.5x10 -3 7 GeV  3.6x10 -3 N p (4 GeV) = 2.65x10 10 N p (7 GeV) = 1.51x10 10 I(4 GeV) = 2.1 A I(7 GeV) = 1.2 A

12. Asymmetric energies (4x7 GeV) with asymmetric bunch lengths N p (4 GeV) = 2x10 10 N p (7 GeV) = 2x10 10 I(4 GeV) = 1.6 A I(7 GeV) = 1.6 A  z (4 GeV) = 3.02 mm  z (7 GeV) = 5.29 mm Y emittance blow-up: 4 GeV  4x10 -3 7 GeV  4x10 -3

13. Crab-waist simulations The new idea by Pantaleo is being checked by several beam-beam codes: –Guinea-Pig: strong-strong, ILC centered –BBC (Hirata): weak-strong –Lifetrack (Shatilov): weak-strong with tails growths calculation –Ohmi: weak-strong (strong-strong to be modified for long bunches and large angles) Storage rings

14. Vertical waist has to be a function of x: Z=0 for particles at –  x (-  x /2 at low current) Z=  x /2  for particles at +  x (  x /2 at low current) x 2Sz 2Sx  z 2Sx/  2Sz*  e- e+

15. GuineaPig Collisions with uncompressed beams Crossing angle = 2*25 mrad Relative Emittance growth per collision about 1.5*10 -3  y out /  y in =1.0015

16. DA  NE case (M.Zobov, LNF) Hirata’s BBC code simulation (weak-strong, strong beam stays gaussian, weak beam has double crossing angle) N p = 2.65x10 10, 110 bunches I b = 13 mA (present working current)  x = 300  m,  y = 3  m  x = 0.3 m,  y = 6.5 mm  z = 25 mm (present electron bunch length)  = 2x25 mrad Y IP = y+0.4/(  x  y’) crabbed waist shift L o =2.33x10 24 (geometrical) L(110 bunches,1.43A) = 7.7x10 32 L equil =6x10 32

17. (Geometric) Luminosity Takes into account both bb interactions and geometric factor due to crab waist n/  Peak around 0.3/  M.Zobov, LNF Scan vs crab waist n/ 

18. Vertical Tails (max amplitude after 10 damping times) Vertical Size Blow-up n/  M.Zobov, LNF

19. Present WP: x = 0.11 y = 0.19 Possible WP: x = 0.057 y = 0.097 Luminosity vs bunch current for 2 different working points M.Zobov, LNF

20. 110 bunches M.Zobov, LNF Luminosity with shorter bunch and smaller  x (preliminary)

21. Some resonances M.Zobov, LNF 2Q x = 2Q y 1Q x = 2Q y (present with crossing angle only) No crab waist Crab waist

22. Beam-Beam Tails (D.Shatilov, BINP) Without Crab WaistWith Crab Waist Bunch core blowup also reduced A y = 90 A y = 45 Vertical tails growth Greatly reduced (A is the amplitude in number of beamsize  )

23. SuperB Luminosity Ohmi’s weak-strong code K2 is the strength of the sextupolar nonlinearity introduced to have crab waist

24. SuperB vertical blow-up Ohmi’s weak-strong code

25. Conclusions For the asymmetric energies “equal blow up” can be obtained with transparency condition (asymmetric I, or  z ) The “crab waist” scheme has shown big potentiality and exciting results  LNF, BINP and KEKB physicists are working on the bb simulation with different codes to explore its properties and find the best set of parameters This scheme is promising also for increasing luminosity at existing factories, as DA  NE, KEKB and possibly PEPII