1. Beam-beam limit estimated by a quasi-strong-strong simulation
K. Ohmi (KEK)
e+e- Factories
13-16 Oct. 2003

2. Introduction
Equilibrium distribution of two beams is estimated by PIC based quasi-strong-strong simulation.
Luminosity beam-beam limit due to incoherent effect is given.
Coherent motion is assumed to be suppressed.

3. Equilibrium distribution of two beams
Vlasov equation
Fokker Plank equation
D:rad. damping
B:rad. excit.

4. Quasi-strong-strong method
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Beam-distribution used potential calculation is averaged and revised in every n0 turn.

5. Briefly speaking Repetition of weak-strong simulation.
Strong beam is determined by average of previous weak-strong cycle.

6. Characteristics
Self consistent equilibrium distribution can be obtained by PIC method with very high statistics (>10M) and with short calculation time (30min for 1M turns at KEK super computer).
Coherent motion is completely suppressed.

7. Luminosity of Super KEKB
2D PIC Particle , n0=500 : Npn0=5M
L beam-beam parameter
Red: quasi-strong-strong
Blue: strong-strong

8. Super KEKB sy
Quasi Strong-strong
Strong-strong

9. Beam-beam limit v.s. damping time

10. Beam-beam limit for various machine
Beam-beam limit is function of damping time.
The limit also depends on tune.
The limit is 0.1 for B factories, 0.06 for t-charm factories.
The results are not quite stable. Need more studies.

11. For longer damping time

12. For long damping time or no damping
Beam-beam limit was about 0.03 for the damping time 106 turns.
Proton beam had higher beam-beam limit.
Perhaps, diffusion which is enhanced by radiation excitation is weak for proton beam without any excitation.
Protons are unmatched due to beam-beam force. We have to study feasibility of this model for proton beam without damping.