The classical problem of neutral beam ions slowing down in a magnetic mirror geometry is revisited to provide predictive capability for the new Wisconsin HTS Axisymmetric Mirror under development at the University of Wisconsin. A Fokker–Planck model named fast beam ion solver (FBIS) is developed to include the spatial non-uniformity of a physical mirror geometry. The mathematical framework allows for efficient orbit averaging of the pitch-angle scattering operator, and permits a determination of the axial profile of the ambipolar potential confining the electrons. The numerical results from FBIS are consistent with earlier work, but further show how mirror-ratio and a near square magnetic well optimizes the fusion gain. The numerical results are also applied to inform the conceptual design of WHAM++, a low capital-cost breakeven-class magnetic mirror device.