Beam-beam update
M. Tawada and K. Ohmi
@KEKB MAC
02/22/2005

KEKB MAC 2005

Contents
Simulation code Tolerance for optics error Parasitic collision effect at KEKB Conclusion

KEKB MAC 2005

Simulation code

One turn linear map and beam-beam map
M ( s + C , s ) = M 0 ( s + C " ! , s + ! ) M BB

3D particle-in-cell code
 Beam are sliced longitudinally and particles are mappedon the transverse grid space Arbitrary beam distribution can be treated Poisson solver using FFT
 Linear interpolation between longitudinal slices
 Longitudinal beam dynamics
 Finite crossing angle and parasitic crossing Machine errors can be treated.
 Using MPI only for parameter scan.
KEKB MAC 2005
Simulation computer
Using supercomputer ofKEK (Hitachi SR8000F1)
12GFlops(peak)x100 node For typical job with
128x256x5 grids, it takes
about 8 hours for 12000
turns.
 >50% of calculation time isfor FFT.
 2x32 nodes are available
for parameter scan.
KEKB MAC 2005

Beam-beam limit

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Simulation results show particle distribution are changed due to thecollision
The incoherent effect is essential to determine beam-beam limit.

Our simulation result shows
the beam-beam parameter of 0.1
can be achieved with crab crossing.
L=2.5E35 for 10A betay=0.3cm
L = 7.6 "10 34

I(A)# y$ y* (cm)KEKB MAC 2005!

Tolerances of the optics error
Map of lattice with optics errors (crossing angle, tilt,offset…) induces coupling of freedom.
 Weak-strong simulation indicates that in a high beambeam parameter region of 0.1, optics errors easily
induce Arnold diffusion and degrade the luminosity.
 Tolerances for coupling parameter (r1-r4), dispersion,
waist and vertical offset are presented here.
 The definition of coupling parameter is#µ%%0% "r1%%"r3%0%$0!

0µ"r2"r400r4"r3µ000"r2r10µ000000100&(0(0((0(0((1'KEKB MAC 2005

Optics parameter r1, r2

1 unit for KEKB tuning:KEKB
r1=0.0008(rad),
MAC 2005

r2=0.00022 (m)r3, r4
1 unit for KEKB tuning: r3=0.07 (/m),

KEKB MAC 2005r4=0.021 (rad)Dispersion, waist
1 unit for KEKB tuning: ηy=0.00016, ηy’=0.016

KEKB MAC 2005

Vertical offset, angle

KEKB experimental data by Y. Funakoshi
Good agreement with simulation
Orbit feedback controls the orbit
fluctuation < 0.1 um, <10 urad.
KEKB MAC 2005

Parasitic collision
Long range nonlinear beam-beam force Beam-beam separation:
"x = # /2 $ lsp,min = 6.6(KEKB),9.0(Super)mm% x (lsp,min ) = % x (0) 1+l 2sp,min
4 & x2= 0.1mm!

Simulation includes dynamic beta and dynamicemittance
KEKB MAC 2005

Parasitic collision
PIC method is used for IP collision.
 Gaussian approximation is used for parasitic crossing Two methods, soft target and fixed target with gaussian
shape. Both methods give same results.
 Drift is used between parasitic and IP collision.
 1st, 2nd, 3rd … parasitic collision can be calculated.
 Particle lost are observed
at early stage of simulation
for horizontal direction.
 It might affect lifetime.
KEKB MAC 2005

Parasitic collision
w/o parasiticw/ parasitic (4bkt sp)
Parasitic collision simulation
for KEKB LER. Each graphshows the luminosity contour
plot w/o and w/ parasiticcollision.
Marker shows the history ofworking point.
Specific luminosity wasimproved by lowering LER-Vtune. But there is no direct
evidence of parasitic effect inKEKB.
KEKB MAC 2005

Parasitic collision
w/o parasitic

w/ parasitic (4bkt sp)
Parasitic collision simulation
for KEKB HER.
Synchro-beta resonance line
are observed in HER.

KEKB MAC 2005

Conclusion
Severe tolerances of optics error may be required forhigh beam-beam parameter region.
 The simulation shows the luminosity degradation due tothe parasitic collision is negligible if good working point
are chosen.
 There is no remarkable effect with many parasiticcollisions.
 Particle lost are observed at the early stage of simulation
with parasitic collision. Lifetime issue should be studied.
KEKB MAC 2005