Lattice design for a 50 on 50 GeV muon collider

Two modes are being considered for a 50 on 50-GeV muon collider: one being a high-luminosity ring with broad momentum acceptance (dp/p of ~0.12%, rms) and the other lower luminosity with narrow momentum acceptance (dp/p of ~0.003%, rms). To reach the design luminosities, the value of beta at collision in the two rings must be 4 cm and 13 cm, respectively. In addition, the bunch length must be held comparable to the value of the collision beta to avoid luminosity dilution due to the hour-glass effect. To assist the rf system in preventing the bunch from spreading in time, the constraint of isochronicity is also imposed on the lattice. Finally, the circumference must be kept as small as possible to minimize luminosity degradation due to muon decay. Two lattice designs will be presented which meet all of these conditions. Furthermore, the lattice designs have been successfully merged into one physical ring with mutual components; the only difference being a short chicane required to match dispersion and floor coordinates from one lattice into the other