PROGRESS IN DESIGNING A MUON COOLING RING WITH LITHIUM LENSES.

We discuss particle tracking simulations in a storage ring with lithium lens inserts designed for the six-dimensional phase space cooling of muons by the ionization cooling. The ring design contains one or more lithium lens absorbers for transverse cooling that transmit the beam with very small beta-function values, in addition to liquid-hydrogen wedge-shaped absorbers in dispersive locations for longitudinal cooling. Such a ring could comprise the final component of a cooling system for use in a muon collider. The beam matching between dipole-quadrupole lattices and the lithium lenses is of particular interest.