Comparison of 6D Ring Cooler Schemes and Dipole Cooler for $\mu^{+} \mu^{-}$ Collider Development

We discuss the various schemes to use ring coolers for 6D cooling for $\mu ^{+} \quad \mu ^{-}$ 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 lithium hydride. We show the recent results of simulations and compare with the results for other cooler schemes.