Status of Studies of Achromat-based 6D Ionization Cooling Rings for Muons

Six dimensional ionization cooling of muons is needed to achieve the necessary luminosity for a muon collider. If that cooling could occur over multiple turns in a closed ring, there would be significant cost savings over a single-pass cooling channel. We report on the status of a cooling ring with achromatic arcs. The achromatic design permits the design to easily switch between a closed ring and a snaking geometry on injection or extraction from the ring. The ring is designed with sufficient space in each superperiod for injection and extraction magnets. We describe the ring's lattice design, performance, and injection/extraction requirements.