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We outline a plan for final muon ionization cooling with quadrupole doubletsfocusing onto short absorbers followed by emittance exchange in vacuum toachieve the small transverse beam sizes needed by a muon collider. A flat muonbeam with a series of quadrupole doublet half cells appears to provide thestrong focusing required for final cooling. Each quadrupole doublet has a lowbeta region occupied by a dense, low Z absorber. After final cooling,normalized xyz emittances of (0.071, 0.141, 2.4) mm-rad are exchanged into(0.025, 0.025, 70) mm-rad. Thin electrostatic septa efficiently slice the bunchinto 17 parts. The 17 bunches are interleaved into a 3.7 meter long train withRF deflector cavities. Snap bunch coalescence combines the muon bunch trainlongitudinally in a 21 GeV ring in 55 microseconds, one quarter of asynchrotron oscillation period. A linear long wavelength RF bucket gives eachbunch a different energy causing the bunches to drift until they merge into onebunch and can be captured in a short wavelength RF bucket with a 13% muon decayloss and a packing fraction as high as 87%.

Final Muon Emittance Exchange in Vacuum for a Collider