Lifetime and Tail Simulations for Beam-Beam Effects in PEP-II B Factory Page: 3 of 3
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ulation for PEP-II. The lifetime dropped from 22.9 hours
(vacuum lifetime) to 16.7 hours. We attribute this to the
elastic scattering into the resonance -vim + 4vy = k, which
perturbs the particle density distribution at large vertical
amplitudes (compare Figure lc with Figure lb).
C. Damping Time
We compared beam-beam effects for two damping times.
First we used a damping time of 5400 turns as it is in ;
second we took a damping time of 7200 turns, as proposed
in . In Figure 2, we show the dependence of the lifetime
versus beam-beam parameters for our two cases. The dif-
ference between two cases is less than the statistical error
expected in the calculations.
30 Lifetime, (hours)
Figure. 2. Beam lifetime versus ( = 'S = boy for two
damping times. Arrows indicate damping time.
D. Machine Imperfections
In order to be more sensitive to the beam-beam effects,
we did all the rest of our simulations with 1Ox = boy = 0.05.
Chromaticity. We did not find any significant effect of
chromaticity when we varied C , Cyy in the range of 500
and C S, C~yy in the range of t104, which are larger values
than we anticipate for the machine.
Tune shifts with amplitude. In our notation, typical de-
pendence of betatron tunes from amplitudes for PEP-II
corresponds to aa-=ayy~-200m-1 and asy~-1000m-1 .
Simulations with these coefficients gave qualitatively simi-
lar results to those with zero nonlinearity. By adjusting as
with ayy=any=0 we could slightly increase the strength of
the resonance 14v_ = k at a r=-200m-1 or significantly
reduce it at a =400m-1 (compare Figure 1d and Figure
3a), but both the beam lifetime and the beam core re-
mained fairly insensitive to this change. For the rest of the
simulations we used a, =-200m1.
Orbit separation at the IP. Table II contain all results.
One can see that only the vertical beam size was sensitive
to the orbit separation Ax, Ay.
Dispersion at the IP. Simulations with non-zero hori-
zontal and vertical dispersions at the IP showed that the
lifetime began to drop below 10 hours when D* > 4 cm
or D* > 0.5 cm. An example with D* = 0.53 cm is
shown in the Figure 3b. Moreover, we found that a dis-
persion D* = 2.2 cm already reduced the lifetime below 10
hours when combined with an accidental orbit separation
of Ax/o-. = 0.4.
20 ' ' 20
-5,6,0 -1 4 0
-4,2,0 0.6, 2
' 0,6,1 -
10 10 060
0 Ax 10 0 Ax '10
Figure. 3. Particle distribution contours: a) the same as
Figure id, but with a =400 m-1; b) the same as Figure
id plus D* = 0.53 cm.
Ax/oh Ay/o'o x2/o0 y2/oy Lifetime,[h]
0 0 1.10 1.46 18.9
0.2 0 1.07 1.71 18.4
0.4 0 1.12 1.93 18.4
0 0.2 1.07 1.99 19.9
0 0.4 1.07 2.57 18.6
Our study demonstrated that beam-beam effects should
not affect the performance of the PEP-II B factory if so, =
boy = 0.03. We did not find significant reduction in the
beam lifetime even for larger beam-beam parameter, but
we did see in many occasions a large increase in the vertical
Acknowledgment. We are grateful to M. Furman and M.
Zisman for many useful discussions.
 PEP-II Design Report, SLAC-Report-418, 1993.
 A. Temnykh, Third Advance ICFA Beam Dynamics
Workshop, INP, Novosibirsk, 1989, p.5.
 D.Shatilov, Preprint BINP 92-79, Novosibirsk, 1992, (in
 J. Irwin, ref.2, p.123.
 T. Chen et al., Phys. Rev. E49, 1994, p.2323.
 J. Tennyson, unpublished code 'TRS', 1989.
 M. Furman et al., CBP Note-59 (1995).
 J. Heim et al., Wiggler Insertion of the PEP-II B Fac-
tory LER, these proceedings.
 E. Forest et al., EPAC 1994, London, 1994, p.1033.
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Shatilov, D. N. & Zholents, A. A. Lifetime and Tail Simulations for Beam-Beam Effects in PEP-II B Factory, article, December 1, 1994; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc784887/m1/3/: accessed January 18, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.