Most scenarios for accelerating muons require recirculatingacceleration. A racetrack shape for the accelerator requires particleswith lower energy in early passes to traverse almost the same length ofarc as particles with the highest energy. This extra arc length may leadto excess decays and excess cost. Changing the geometry to a "dogbone"shape, where there is a single linac and the beam turns completelyaround at the end of the linac, returning to the same end of the linacfrom which it exited, addresses this problem. In this design, the arclengths can be proportional to the particle's momentum. This paperproposes an approximate cost model for a recirculating accelerator,attempts to make cost-optimized designs for both racetrack and dogbonegeometries, and demonstrates that the dogbone geometry does appear to bemore cost effective
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