Small muon beams increase the luminosity of a muon collider. Reducing the momentum and position spreads of muons reduces emittance and leads to small, cool beams. Ionization cooling has been observed at the Muon Ionization Cooling Experiment. 6D emittance reduction by a factor of 100, 000 has been achieved in simulation. Another factor of 5 in cooling would meet the basic requirements of a high luminosity muon collider. In this paper we compare, for the first time, the amount of RF needed in a cooling channel to previous linacs. We also outline three methods aimed to help achieve a final factor of 5 in 6D cooling.
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