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Muon accelerator beams are commonly produced indirectly through pion decay by interaction of a charged particle beam with a target. Efficient muon capture requires the muons to be first phase-rotated by rf cavities into a train of 21 bunches with much reduced energy spread. Since luminosity is proportional to the square of the number of muons per bunch, it is crucial for a Muon Collider to use relatively few bunches with many muons per bunch. In this paper we will describe a bunch mergingdoi:10.18429/jacow-ipac2015-tupwi040 fatcat:4nptn6phgbb6zlp5c4uk4xah74