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), or Higgs Factory. To reach the design luminosities, the value of beta at collision in the two rings must be 4 cm and 14 cm, respectively. In addition, the bu...