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.

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

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)

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

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

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 =2,3,4 s’x= 320 mrad s’y= 144 mrad From simulation Floss is ~7.3 smaller, means tloss = 292mn

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