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Neutrino Factory/Muon Collider Document 24-v1

Analysis of the Longitudinal Collective Behavior in a 50GeVx50GeV Muon Collider Ring

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Document type:
MuCool Note
Submitted by:
John Urish
Updated by:
John Urish
Document Created:
12 Feb 1999, 12:00
Contents Revised:
12 Feb 1999, 12:00
Metadata Revised:
12 Feb 1999, 12:00
Actually Revised:
14 Sep 2006, 13:35
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\title{ Analysis of the Longitudinal Collective Behavior\\ in a
50GeV$\times$50GeV Muon Collider Ring}
\author{Eun-San Kim$^1$, Andrew M. Sessler$^2$, Jonathan S. Wurtele$^{1,2}$ \\
\small $^1$Department of Physics, University of California, Berkeley \\
\small Berkeley, California 94720 USA \\
\small $^2$Lawrence Berkeley National Laboratory, \\
\small Berkeley, California 94720 USA
\begin{center} Abstract \end{center}

Simulations of the longitudinal instability in the 50GeV$\times$50GeV muon
collider ring have been performed. Operation of the ring close to
the slippage factor $\eta_1 \simeq 10^{-6}$, such that
synchrotron motion is frozen, minimizes the need for rf to maintain
the bunch length. However, there is still an
energy spread due to the bunch wake. For design parameters of the
ring this induced energy is too large and must be controlled. This
paper demonstrates that the bunch wake may be compensated for by two rf
cavities with low rf voltages. These studies were made at the nominal
design point, and sensitivities to errors were explored. It is seen that
the small energy spread of the beam ($\delta E/E$=3$\times 10^{-5}$) in the
50GeV$\times$50GeV muon collider ring can be maintained during the 1000
turn lifetime of the muons.
Controlled beam dynamics requires proper choice
of rf parameters (rf voltage, rf frequency, phase offset) for two
cavities; these parameters depend on the ring design through the
impedance, beam pipe radius, and momentum compaction.
The simulation also shows that the computation of wake field using
bins of variable width (each with a constant number of macroparticles
in each bin) gives an accurate wake and also yields
reduced computing time compared to an evaluation of the wake as the
direct sum over the wakes of all preceding macroparticles.

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Eun-San Kim, Andrew M. Sessler, Jonathan S. Wurtele LBNL,Berkeley
Publication Information:
Phys.Rev.Special Topics:Accelerators and Beams
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