6D “Garren” snake cooler and ring cooler for µ± cooling of a muon collider

Six dimensional cooling of large emittance µ+ and µ− beams is required in order to obtain the desired luminosity for a muon collider. In our previous study, we demonstrated that a 6D “Garren” ring cooler using both dipoles and solenoids in four 900 achromatic arcs can give substantial cooling in all six phase space dimensions. In this paper, we describe the injection/extraction requirements of this four-sided ring. We also present the performance of an achromat-based 6D “Garren” snake cooler. The achromatic design permits the design to easily switch between a closed ring and a snaking geometry on injection or extraction from the ring.