1. Beam-beam simulations
M.E. Biagini, P. Raimondi
LNF/INFN, SLAC
2nd Workshop on SuperB, Frascati 16th March 2006

2. Outline Round or flat? 4 beams scheme
2 beams scheme with asymmetric energies
Conclusions

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”
Optimization of beam parameters must include Damping Ring optimization and Final Focus design

4. Round or Flat ?
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)
Round and Flat beams have been considered
Optimization of beam parameters performed with Mathematica + GuineaPig (see next talk by E. Paoloni)

5. 4 Beams Scheme
Option of colliding 4 beams in a “charge compensation” scheme considered
GuineaPig modified to allow 4 beams (many thanks to D. Schulte !!!)
4 identical beams (energy, beam sizes, current) simulated
Parameters from optimization studies

6. Linear SuperB Double Pass
e- Gun
2GeV
e+ DR IP
5 GeV e+ & 3.5GeV e- SC Linac
e- Dump
0.5GeV SC Linac
7GeV e+
4 GeV e- e- e+
2 GeV e+ injection
1st LNF Workshop on SuperB, Nov. 2005

7. SuperB ILCDR-like ILC ring with ILC FF ILC compressor
Decompressor
DeCompressor IP
Optional
Acceleration
and deceleration FF
ILC ring with ILC FF
ILC compressor
Colliding every 50 turn
Acceleration optional
Crossing angle optional

8. Optimized Round case EP parameter set: Npart = 7.x1010
I = 5.6 A (for a 3Km ring)
sx = sy = mm
sz = 0.8 mm
bx = by = mm

9. Round case Phase space after collision
x,x’
y,y’
z,dE/E
Round case
Phase space
after collision
(x,x’), (y,y’), (z,dE/E)
2 Beams
x,x’
y,y’
z,dE/E
4 Beams

10. 4 beams, Round case

11. 2 beams, Round case

12. Optimized Flat case PR parameter set: Npart = 2.x1010
I = 1.6 A (for a 3Km ring)
sx = mm
sy = 12.6 nm
sz = 4. mm
bx = 2.5 mm
by = 80. mm

13. Flat Case Phase space after collision
x,x’
z,dE/E
y,y’
Flat Case
Phase space
after collision
(x,x’), (y,y’), (z,dE/E)
2 beams
x,x’
z,dE/E
y,y’
4 beams

14. 4 beams, Flat case
Large blow up of all 4 beams

15. 2 beams, Flat case
Smaller blow up of 2 beams

16. Possible choice for ILC !!!!
4 Beams conclusions
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 !!!!

17. 2 beams asymmetric energies
Studied the 2-beams scheme with asymmetric energies
4x7 GeV case
PR parameter set:
Npart = 2.x1010
I = 1.6 A (for a 3Km ring)
sx = mm
sy = 12.6 nm
sz = 4. mm
bx = 2.5 mm
by = 80. mm

18. Symmetric energies
Y emittance blow-up: 3.x10-3

19. Asymmetric energies (4x7 GeV)
Y emittance blow-up: 4 GeV  5x10-3
7 GeV  3x10-3

20. Asymmetric energies (4x7 GeV) with transparency condition (I)
Np(4 GeV) = 2.65x1010
Np(7 GeV) = 1.51x1010
I(4 GeV) = 2.1 A
I(7 GeV) = 1.2 A
Y emittance blow-up: 4 GeV  3.5x10-3
7 GeV  3.6x10-3

21. Asymmetric energies (4x7 GeV) with asymmetric bunch lengths
Np(4 GeV) = 2x1010
Np(7 GeV) = 2x1010
I(4 GeV) = 1.6 A
I(7 GeV) = 1.6 A
sz(4 GeV) = 3.02 mm
sz(7 GeV) = 5.29 mm
Y emittance blow-up: 4 GeV  4. x10-3
7 GeV  4. x10-3

22. Alternative scheme for beam-beam compensation of energy asymmetryz x e- e+
HER: larger by*, smaller ey,ex
LER: smaller by*, larger ey,ex
No need for high current in LER
Better for IBS, Touschek in LER
Work in progress, coordination with DR design

23. Conclusions
More work is needed to understand if the 4 beams scheme can work at low energy
For the asymmetric energies “equal blow up” can be obtained with transparency condition (asymmetric I, or sz)
Alternative scheme is possible
Optimization work will continue to finalize the beam-beam parameters