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A recirculating linear accelerator (RLA) has been proposed to accelerate muons from 5 to 63 GeV for a muon collider. It should be usable both for a Higgs factory and as a stage for a higher energy collider. First, the constraints due to the beam loading are computed. Next, an expression for the longitudinal emittance growth to lowest order in the longitudinal emittance is worked out. After finding the longitudinal expression, a simplified model that describes the arcs and their approximate expression for the time of flight dependence on energy in those arcs is found. Finally, these results are used to estimate the parameters required for the RLA arcs and the linac phase.

Parameter choices for a muon recirculating linear accelerator from 5 to 63 GeV