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 number for low energy beams
Typical values for ILC < 30, 100 > SBF >1000
The bb interaction in such a regime can be highly non linear and unstable

4. Scaling laws Disruption: Luminosity Energy spread:
Decrease sz + decrease N
Increase spotsize
Increase N
Decrease spotsize
Contraddicting
requests!
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 generate e+e- pairs
e+e- pairs are 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. Luminosity & sE vs N. of bunches at fixed total current = 7. 2 A (6
Luminosity & sE vs N. of bunches at fixed total current = 7.2 A (6.2 Km ring)
Working point D
Energy spread

13. Working point parameter list for 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 =  DR kickers
Incoming sE =  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)
HER  green
red  LER

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

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 rate 120 Hz  t = 1.5 msec
needed in damping ring

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

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

22. L vs x-emittance
Energy spread

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
y 
 X
HER
y 

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

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

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

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

30. Outgoing beam emittances b aspect ratio = 100
LER:
exout = 8 nm = 10 * exin
eyout = nm = 6 * eyin
HER:
exout = 1. nm = 2.5 * exin
eyout = 0.02 nm = 5 * eyin
Damping time required : 2 t
With rep rate 360 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 ….