A number of experiments with muons are limited by the poor phase
space quality of the muon beams currently available. The muCool project
aims at developing a phase-space cooling method to transform a surface
\mu^+μ+
beam with 4 MeV energy and 1 cm size into a slow muon beam with eV
energy and 1 mm size. In this process the phase space is reduced by a
factor of 10^{9}-10^{10}109−1010
with efficiencies of 2\cdot 10^{-5}-2\cdot 10^{-4}2⋅10−5−2⋅10−4.
The beam is then re-accelerated to keV-MeV energies. Such a beam opens
up new avenues for research in fundamental particle physics with muons
and muonium atoms as well as in the field of
\muμSR
spectroscopy.
We discuss particle tracking simulations in a storage ring with Lithium lens inserts designed for the transverse phase space cooling of muons by the ionization cooling. In a hard-edged magnetic element model, we demonstrate the equilibrium normalized transverse emittance of 0.3 mm*rad which is necessary for a Higgs Factory, a low energy mu+mu- Collider. For the 6 dimensional phase space cooling of muons, a method of using bent Lithium lenses were discussed.