1. Crab Waist at DAFNE: Numerical Simulations versus Experimental Results
M. Zobov, C. Milardi (INFN LNF, Frascati)
E. Levichev, P. Piminov, D. Shatilov (BINP, Novosibirsk)
K. Ohmi (KEK, Tsukuba)
Y. Zhang (IHEP, Beijing)
SuperB Workshop
LAL, Orsay, February 15-18, 2009

2. Instead of Introduction
1. SuperB Mini-MAC (July 16-17, 2008):
“..exploit the DAFNE experiment to benchmark and validate simulation…”
2. Report on the INFN Super Flavour Factory Project (Working Group set up by ECFA, 20 November 2008):
“…Comprehensive simulation studies are still required in order to fully understand the DAFNE test and to extrapolate safely to the Super Flavour Factory environment…”

3. OUTLINE
Numerical Codes Used: Advantages and Limitations for Crab Waist Collision Studies
Comparison with Experiment
Factors Limiting Luminosity
DAFNE Dynamic Aperture
Beam-Beam Collision in DAFNE Nonlinear Lattice
Conclusions

4. DAFNE Tune Shifts x ex, mm mrad bx, m by, cm Parameter Date Sept. 2005
KLOE
FINUDA
SIDDHARTA
Date
Sept. 2005
Apr. 2007
Dec. 2008
Luminosity, cm-2 s-1
1.53x1032
1.60x1032
4.05x1032
e- current, A
1.38
1.50
1.43
e+ current, A
1.18
1.10
Number of bunches
111
106
ex, mm mrad
0.34
0.25
bx, m
1.5
2.0
by, cm
1.8
1.9
0.93 x
0.0245
0.0291
0.0361(0.042)

5. Numerical Codes Used Weak-Strong Codes Strong-Strong Codes
BBC (K. Hirata, Phys.Rev.Lett.74, 2228 (1995))
LIFETRAC (D. Shatilov, Part.Accel.52, 65 (1996))
BBWS (K. Ohmi)
Strong-Strong Codes
BBSS (K. Ohmi, PRSTAB 7, , (2004))
SBBE (Y. Zhang, K. Ohmi, PAC2005)
Beam-beam + nonlinear lattice
For Nonlinear Studies We Use
MAD (DAFNE lattice model)
ACCELERATICUM (P. Piminov, 6D symplectic tracking)
The codes have been successfully used for e+e- factories:
KEKB, DAFNE, BEPCII and colliders: VEPP4M, VEPP2000.

6. Strong-Strong Simulations
Advantages: better reproduce collisions scheme:
6D, fully self-consistent, both beams can be blown up, non-gaussian
Crab waist transformation can be applied to both beams
Limitations: very long CPU time due to long damping time (DAFNE) and many longitudinal slices required (SuperB) due to
Dense collision area is much smaller than bunch length
Beta function redistribution over this small area
K. Ohmi : PIC simulations for the central dense area + Gaussian approximation for tail slices!
New

7. Blowup versus Number of Slices
Example e+ e+

8. Single Bunch Luminosity versus Number of Slices
Example

9. Weak-Strong Simulations
Advantages:
Very fast (in comparison with strong-strong): suitable for optimization, luminosity scans etc.
Special techniques are used for non-gaussian tail simulations and lifetime determination (LIFETRAC)
Ay/sy
Limitations:
Strong beam remains gaussian, no blow up due to beam-beam interaction
Crab waist transformation is applied only to the weak beam
Ax/sx
Idea
D. Shatilov : crabbed distribution for the strong beam

10. Crab Waist Collisions at f1 = -q, f2 = q

11. Geometric Luminosity Gain due to Crab Sextupoles
(DAFNE Example)
Strong-strong
DL, %
Weak-strong
Normalised sextupole strength
Normalised sextupole strength

12. Initial Weak-Strong Simulations
Normalised crab sextupole strength
Ay/sy
DAFNE case
Ax/sx
Normalised emittance blowup
For present DAFNE parameters both beams are blown up
Strong-strong simulatios are
more relevant

13. Strong-Strong Beam-Beam Simulations (K. Ohmi)
Single Bunch Luminosity
(Damping time = turns)
Crab Waist On
105 bunches
Crab Waist Off
about 35% lower

14. Vertical Size Blow Up
Crab Off
Crab On

15. Other Factors Affecting Luminosity
Lattice nonlinearities
Electron cloud (beam size blow up, tune spread)
Ions of residual gas (incoherent effects, trapped ions)
Wake fields (single and multibunch effects)
Gap transients (different bunch synchronous phases)
Feedback noise (and also in other devices)
Low lifetime (not enough time for fine tuning)
Space charge effects
Touschek scattering
Other effects
=> 1.34

16. Horizontal Tune Spread Along Bunch Train
Courtesy A. Drago (40th ICFA Workshop)
Courtesy T. Demma (EPAC08)

17. Tune Spread on Luminosity Diagram
Dny *
Dnx
Head bunches should have higher luminosity!

18. Bunch Pattern at the End of Fill

19. 20 Bunches Collisions (mod. 4)
L > 5x1030 cm-2 s-1
(single bunch)
xy = 0.042

20. Strong-Strong Beam-Beam Simulations (K. Ohmi)
Single Bunch Luminosity
(Damping time = turns)
Crab Waist On
20 bunches
Crab Waist Off
about 20% lower

21. DAFNE Dynamic Aperture for (5.1065, 5.1750)
Dp/p = 0%
Dp/p = +0.3%
Dp/p = -0.3%
takes into account the QDO fringe field sextupoles

22. DAFNE Dynamic Aperture Scan (4D)
Nonlinear lattice adds several typical sextupole resonances

23. DAFNE Dynamic Aperture Scan (6D, Dp/p = 0 %)
No harmful resonances in the vicinity of the working point

24. DAFNE Dynamic Aperture Scan (6D, Dp/p = 0.3 %)
Reasonable energy acceptance

25. Beam Tails with Crab On Comparable Emittance Blowup Linear Lattice
Nonlinear Lattice e- e+ e+
Comparable Emittance Blowup

26. Beam Tails with Crab Sextupoles Off
One can expect lifetime problems already at 10 mA per bunch...

27. Collisions without Crab Sextupoles
Bigger blowup
Sharp lifetime reduction for bunch currents > mA
February 2009
Courtesy G. Mazzitelli

28. Conclusions Discussion
Crab waist works, strong-strong simulations agree within 20% with experimental results
Much lower luminosity is acheved with crab sextupoles off. Besides stronger blowup, a sharp lifetime reduction is observed for bunch currents > 8-10 mA. This is in accordance with beam-beam simulations taking into account the realitic DAFNE nonlinear lattice.
Discussion
Existing numerical codes are reliable to predict ideal beam-beam interaction. However, for SuperB low emittance design other factors limiting luminosity (e-cloud, ions, impedances, space charge, noise etc.) become much more important.....

29. Simulations for SuperB
Strong-Strong
Weak-Strong
Quasi-Strong-Strong
K. Ohmi

30. Weak-Strong Simualtions for SuperB Nonlinear Lattice
x 10^36 Nb
Piminov, Shatilov, Zobov