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This note describes the design of an ionization cooling ring that uses an alternating polarity solenoid lattice. The ring is approximately 33 m in circumference and has 12 cells. Each cell has two opposing focusing solenoids placed either side of a hydrogen wedge absorber. The solenoid coils are located outside pillbox rf cavities. Bending is provided by tipping the solenoid coils. The simulated merit factor (≈ the increase in six-dimensional phase-space density) is 81.

Muon Colliders have unique technical and physics advantages and disadvantages when compared with both hadron and electron machines. They should thus be regarded as complementary. Parameters are given of 4 TeV and 0.5 TeV high luminosity µ + µ − colliders, and of a 0.5 TeV lower luminosity demonstration machine. We discuss the various systems in such muon colliders, starting from the proton accelerator needed to generate the muons and proceeding through muon cooling, acceleration and storage in a collider ring. Problems of detector background are also discussed.