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The reduction of the phase-space volume of the beam (cooling) is essential for both muon colliders and neutrino factories. In a muon collider, in particular, the six-dimensional (6D) emittance must be reduced by six orders of magnitude. Cooling the beam in all phase space dimensions can be done through emittance exchange, where the beam loses energy passing through wedge-shaped absorbers in a dispersive magnetic field, designed in a way that fast muons go through more absorber material than slow ones and lose more energy. The longitudinal momentum is then regained using RF cavities. We simulate ring coolers, in which the beam undergoes 6-dimensional cooling through emittance exchange while rotating several times in the ring. The simulation software is a Geant3-based package, specially designed this purpose, with changing electric fields in RF cavities treated correctly. Magnetic fields are read from external maps. Some ring cooler designs and cooling simulation results are presented.
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