Comparison of 6D ring cooler schemes and dipole cooler for μ+ μ- collider development

We discuss the various schemes to use ring coolers for 6D cooling for mu⁺mu^- colliders. The earliest successful cooler used dipoles and quadrupoles and a high dispersion low beta region. This was also proposed in the form of solenoids. Recently there have been many new ideas. The simplest is to use a simple dipole ring with high-pressure gas absorber or Li hydride. We show the results of simulations and compare with the results for other cooler schemes.