Progress on six dimensional ionization muon cooling with relatively small rings of magnets is described. Lattices being explored include scaling sector cyclotrons with edge focusing and strong focusing, fixed field alternating gradient (FFAG) rings. Ionization cooling is provided by high pressure hydrogen gas which removes both transverse and longitudinal momentum. Lost longitudinal momentum is replaced using radio frequency (RF) cavities, giving a net transverse emittance reduction. The longer path length in the hydrogen of higher momentum muons decreases longitudinal emittance at the expense of transverse emittance. Thus emittance exchange allows these rings to cool in all six dimensions and not just transversely. Alternatively, if the RF is located after the ring, it may be possible to cool the muons by stopping them as they spiral adiabatically into a central swarm. As momentum goes to zero, the momentum spread goes to zero. The resulting cooled muons can lead to an intense muon beam which could be a source for neutrino factories or muon colliders.
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