LHC beam-beam compensation studies at RHIC Page: 4 of 5
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Proceedings of PAC09, Vancouver, BC, Canada
One important goal of the experiments is to benchmark
simulations. In several simulations the onset of large losses
as a function of the distance between wire and beam was re-
produced within about 1 o- [17, 21, 24, 25]. One such com-
parison is shown in Fig. 7.
If a collision of a proton beam with another proton beam
is followed by a collision with an electron beam, the head-
on beam-beam effect can be canceled exactly if the follow-
ing 3 conditions are met:
1. The proton and the electron beam produce the same
amplitude dependent force.
2. The phase advance between the two beam-beam col-
lisions is a multiple of 7r in both transverse planes.
3. There are no nonlinearities between the two collisions.
In practice this cannot be achieved, and the goal of the
simulation studies is to find out how far one can deviate
from these three condition. With tolerances established one
can then assess if these can be achieved with the technology
Electron Lenses in RHIC
Two electron lenses are currently installed in the Teva-
tron  where they are reliably used as an operational gap
cleaner . They were also shown to improve the life-
time of antiproton bunches suffering from PACMAN ef-
fects . The experience with the construction and op-
eration of the Tevatron electron lenses provides invaluable
input into an assessment of the practicability of head-on
beam-beam compensation. In RHIC it is planned to install
2 electron lenses near IP10 with parameters close to those
of the Tevatron. (Fig. 1, Table 4). A successful demonstra-
tion of head-on beam-beam compensation in RHIC would
also allow to use this technique in the LHC.
A number of simplifications are used for the simulations
so far. First, the electron lenses are exactly at IP10, while
2 lenses for both beams would need to be installed with a
few meters offset from the IP. Second, the electron beam
of the electron lens is infinitely stiff (see Refs. [30, 31] for
a discussion). Third, a lattice for polarized proton opera-
tion at 250 GeV is used with * 0.5 m in IP6 and IP8,
and * 10 m in all other IPs (see Fig. 1 and Table 1).
Table 4: Parameters for RHIC Electron Lenses ,
Adapted from the Tevatron Electron Lenses 
quantity unit value
electron kinetic energy Ke keV 5.0
electron speed 3e c ... 0.14c
electron transverse rms size mm 0.57
effective length L,,e,, m 2.0
full head-on compensation
no of electron in lens Ne 1011 3.5
electron beam current Ic A 1.2
- - -
Figure 8: Tune diffusion without beam-beam interaction
(top left), with beam-beam interaction (top right), with half
(bottom left), and with full beam-beam compensation .
20 30 40 50 60 ,0 80 90 1
""r f "5
Figure 9: Beam lifetime simulations for increased bunch
intensity and different phase advances between the IP and
e-lens. Note that without compensation the beam-beam
tune generated tune spread could not be accommodated for
these bunch intensities.
The phase advance in the horizontal plane between IP6 and
IP10 is close to a multiple of 7r, as well as in the vertical
plane between IP8 and IP10. No optimization of the phase
advance was done in this lattice.
Tune footprints can be compressed with electron lenses
but this is not sufficient to improve the beam lifetime. At
large compensation strength the tune footprints are folded
over which leads to reduced stability. The folding can be
avoided with a partial compensation.
It was found that almost all particles are chaotic with
and without compensation , and that therefore chaotic
borders cannot be used to evaluate head-on problems. Dy-
namic aperture calculations proved insensitive since they
evaluate the stability of motion at large betatron ampli-
tudes, where the beam-beam forces are small.
Other short-term measures calculated were tune diffu-
sion (Fig. 8) and Lyapunov exponent maps , and diffu-
sion coefficients sampled at a number of locations in phase
space and fitted with an analytic function . In all cases
we find that the stability of motion is increased at ampli-
tudes below 3 o- and decreased at amplitudes above 4 o-.
Beam Dynamics and Electromagnetic Fields D02 - Non-Linear Dynamics - Resonances, Tracking, Higher Order
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Fischer, W.; Luo, Y.; Abreu, N.; DeMaria, R.; Calaga, R.; Montag, C. et al. LHC beam-beam compensation studies at RHIC, article, May 1, 2009; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc1012170/m1/4/: accessed January 21, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.