Analytical study and tracking simulations of the beam-beam compensation at Tevatron Page: 1 of 3
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Jt Fermilab
WVFERMILAB-Conf-01/161-T June 2001
ANALYTICAL STUDY AND TRACKING SIMULATIONS OF THE
BEAM-BEAM COMPENSATION AT TEVATRON
D. Shatilov, BINP, Novosibirsk, Russia
Y. Alexahin, V. Shiltsev, FNAL, Batavia, IL 60510, USAAbstract
Head-on and long-range induced tunespread of about
0.025 in the Tevatron collider at Run II (together with the
increased strength of the resonances) can significantly de-
teriorate the p lifetime and the collider luminosity. It was
proposed to employ the so-called Tevatron Electron Lenses
(TEL) to compress the beam-beam footprint and eliminate
completely the bunch-to-bunch tunespread (PACMAN ef-
fect) for small amplitude particles. The first lens has been
recently installed and tested [1]. This report presents re-
sults of analytical studies and tracking simulations of the
linear beam-beam compensation (elimination of the bunch-
to-bunch tune variation). Compression of the beam-beam
footprint (nonlinear compensation) is discussed in [2].
1 INTRODUCTION
During RUN II with 36 bunches in each beam, the bunch-
to-bunch tune spread will be about 8v S 0.007, while
the single bunch tune spread will be about Av 0.018
(see Fig. 1). The main problem occurs with the first and the
last bunches in the 3 identical trains of 12 bunches each.
Tunes of bunches #1 and #12 are shifted down and left, re-
spectively, compared to all other bunches, that results in
their lifetime deterioration (so-called PACMAN effect). An
electron lens, consisting of low energy, high current elec-
tron beam colliding with antiprotons, can induce a tuneshift
of the antiproton bunches. The electron beam current is
modulated, so each antiproton bunch collides with the dif-
ferent electron beam density. With appropriate choice of
parameters two such lenses could provide effective com-
pensation of the bunch-to-bunch tunespread.
2 NUMERICAL SIMULATIONS
2.1 Simulation Goals
The main goal of our simulations is to demonstrate the
possibility of using TEL for eliminating the bunch-to-bunch
tune spread. We studied how the TEL affects the nonlinear
beam dynamics and what general conditions (e-beam radius
and profile, misalignment, stability, etc.) must be satisfied
in order to keep p-beam stable. We assume here that these
conditions should be more or less general, that is do not de-
pend very much on the working point (if it is chosen prop-
erly, of course).
We started with a small betatron tune scan around some
working point. The tune variations were about the bunch-
to-bunch spread, and the goal was to find some "good" and0 600
0 585 0 590 0 595 0 600 0 805 0 610
0.585 0.590 0.595 0.600 0.805 0.6100 601
0.58c
Figure 1: Tunes for the particles with the different betatron
amplitudes, for different bunches in the train. The bare lat-
tice tunes are (20.585, 20.575). Resonances up to 12th order
are shown.
"bad" working points within this area. Then, we applied
the TEL in the "bad" working point in order to shift it to
the "good" one and to see the positive effect. After that we
varied different TEL parameters and applied some pertur-
bations to see how they affect the resulting p distribution.
Comparison with the natural "good" working point give us
important information how the TEL itself introduces pertur-
bations (linear and non-linear) to the p-beam.
2.2 Choice of the Working Point
As the analytical study [3] shows, the standard Teva-
tron working point (20.586, 20.576) is not a good one due
to the proximity of 5th and 12th order resonances (see
Fig. 1), and we decided to look at the vicinity of the point
(20.566, 20.556) surrounded by resonances of higher or-
der (7th). Then, we tried to find such a pair of the "bad"
and "good" points that the "bad" one could be shifted to
the "good" with only one TEL of two, to simplify the fur-
ther studies. We found, after a small tune scan, the pair
of (20.566, 20.556) and (20.556, 20.546) points, which re-
quires only TEL2 located at FO (as planned initially), where
the beta-functions are approximately equal. Now the other
location is chosen for TEL2, with i, <3y, while it >> it
at TELL. Besides the better operation conditions for the
tune shifts, using two TELs with unequal beta-functions
strongly reduces excitation of coupling resonances by TELs
themselves [3], so the present results can be regarded as a
conservative estimate of the effect.
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Shatilov, Dmitry; Alexahin, Yuri & Shiltsev, Vladimir. Analytical study and tracking simulations of the beam-beam compensation at Tevatron, article, July 2, 2001; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc717867/m1/1/: accessed March 27, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.