A LATTICE FOR THE 50 GEV MUON COLLIDER RING.

A resent progress report on the lattice design of the 50-50 GeV muon collider is presented. The ring circumference needs to be as small as possible due to the short lifetime of the 50 GeV muons. The background at the detector is affected by the continuous decay of muons into electrons which requires a dipole between the high focusing quadrupoles and the detector. To obtain a luminosity on the order of 1 x 10{sup 33} cm{sup {minus}2} S{sup {minus}1} it is required to have beam intensities on the order of 1 x 10{sup 12} particles per bunch. The rms momentum spread of the beam is equal to 0.12% and the beta functions at the interaction point are equal to 4 cm. The maxima of the betatron functions at these quadrupoles are 1300 m, resulting in large chromaticities which must be corrected by local chromatic correction. Pairs of horizontal and vertical chromatic sextupoles are located at locations where the corresponding betatron functions are 100 m and the values of the horizontal dispersion functions are 3 and 2 m, respectively. They are carefully placed so that most of their nonlinear effects are canceled. The dynamic aperture is larger than 7 times the mean size of the beam for the momentum offsets larger than {minus}6 and +10 sigmas