RECENT PROGRESS IN SIX-DIMENSIONAL IONIZATION COOLING TECHNIQUES FOR MUON-BASED MACHINES ∗

Ionization cooling is an essential component of a neutrino factory or a muon collider. Ionization cooling in the transverse dimensions is reasonably straightforward, and has been incorporated in published neutrino factory studies. Achieving cooling in the longitudinal dimensions is more difficult, but has the potential to greatly improve the performance of neutrino factories, and is essential to muon colliders. Much progress has recently been made in describing ring cooling lattices which achieve cooling in all three phase space planes, and in the design of the required, but difficult, injection systems. Ring cooling lattices also have the potential of significantly reduced cost compared to single-pass cooling systems with comparable performance. We will present some recent lattice designs, describing their theory, features, and performance, including injection and extraction systems.