1. Alexander W. Chao (SLAC)
Beam-Beam diffusion
Alexander W. Chao (SLAC)
Cécile Rimbault (LAL)
A.C. would like to thank Eugene Perevedentsev for illuminating discussions.

2. Beam-Beam diffusion
Beam-beam diffusion caused by discrete-particle scatterings
with coulomb scattering angle :
(b=impact parameter)
This can leads to:
Reduction of beam life time (particle loss during collision)
Emittance growth
Spin diffusion
Is it a problem for SuperB?
 should be studied because SuperB’s luminosity comes from colliding a small number of particles which are sharply focussed. The small number of colliding particles implies larger statistical effects.
tests comparing kick angle from
gaussian distribution charge (GUINEA-PIG++ simulation)
and discrete point charges

3. Simulations GUINEA-PIG++ (GP++): kick calculated from gaussian field
1slice-slice interaction with
sx=8mm, sy=36nm, bx=25.3mm, by=0.25mm,
N= NB (sx/f)/sz=3 109,
E=5.3 GeV
Nmacro (M) varies from 5000 to 60000
Grid parameters have also been tested
Beam-beam diffusion
Use same as GP++ initial distribution.
Calculate a kick of 2req/gb (with q=N/M) for each
Mparticle-Mparticle collision and sum for each Mpart.
 Comparisons of the kick from gaussian (which does not contain diffusion) with the kick from Mparticles (which contains diffusion)

4. kick from gaussian field and kick from multiparticles scattering
Comparison of
kick from gaussian field and kick from multiparticles scattering
Larger angles from diffusion:
need to study particle loss

5. Emittance diffusion
Emittance diffusion and spin diffusion are charaterized by Qx and Qy
From theory , corresponding to an
emittance diffusion time of 46s and a spin diffusion time of 4.6h
From simulation Qy is 3.3 larger, means tdiff = 14s and a spin diffusion time of 1.4h

6. Beam lifetime
Beam lifetime is charaterized by the probability for a particle to be lost during the collision.
From theory , corresponding to a beam lifetime of 40mn
Floss=Nloss/M, Nloss = Nb of part. for which
with ncutoff =2,3, s’x= 320 mrad s’y= 144 mrad
From simulation Floss is ~7.3 smaller, means tloss = 292mn

7. Beam-Beam diffusion conclusion
Nice accordance between theory and simulation
 Beam life time due to beam-beam diffusion = 292mn
Emittance diffusion time = 14s
Spin diffusion time = 1.4 h
Small effects, should not be a problem for SuperB
Need to be confirmed by other theories and more simulations