  We propose a novel scheme for final muon ionization cooling with quadrupole
doublets followed by emittance exchange in vacuum to achieve the small beam
sizes needed by a muon collider. A flat muon beam with a series of quadrupole
doublet half cells appears to provide the strong focusing required for final
cooling. Each quadrupole doublet has a low beta region occupied by a dense, low
Z absorber. After final cooling, normalized transverse, longitudinal, and
angular momentum emittances of 0.100, 2.5, and 0.200 mm-rad are exchanged into
0.025, 70, and 0.0 mm-rad. A skew quadrupole triplet transforms a round muon
bunch with modest angular momentum into a flat bunch with no angular momentum.
Thin electrostatic septa efficiently slice the flat bunch into 17 parts. The 17
bunches are interleaved into a 3.7 meter long train with RF deflector cavities.
Snap bunch coalescence combines the muon bunch train longitudinally in a 21 GeV
ring in 55 microseconds, one quarter of a synchrotron oscillation period. A
linear long wavelength RF bucket gives each bunch a different energy causing
the bunches to drift in the ring until they merge into one bunch and can be
captured in a short wavelength RF bucket with a 13% muon decay loss and a
packing fraction as high as 87%.
