  A large admittance sector cyclotron filled with LiH wedges surrounded by
helium or hydrogen gas is explored. Muons are cooled as they spiral
adiabatically into a central swarm. As momentum approaches zero, the momentum
spread also approaches zero. Long bunch trains coalesce. Energy loss is used to
inject the muons into the outer rim of the cyclotron. The density of material
in the cyclotron decreases adiabatically with radius. The sector cyclotron
magnetic fields are transformed into an azimuthally symmetric magnetic bottle
in the center. Helium gas is used to inhibit muonium formation by positive
muons. Deuterium gas is used to allow captured negative muons to escape via the
muon catalyzed fusion process. The presence of ionized gas in the center may
automatically neutralize space charge. When a bunch train has coalesced into a
central swarm, it is ejected axially with an electric kicker pulse.
