Analytic neutron wall loading from spin-polarized fusion in axisymmetric geometries

Spin-polarized nuclei can be used to enhance the fusion reaction rate, preferentially direct neutrons and alpha particles, or do some combination of these. In this paper we present formulas for the neutron wall load (NWL) on the walls of an axisymmetric torus with a convex cross section from filamentary ring sources with arbitrary fuel polarizations and arbitrary local magnetic field directions. While the NWL does not include neutron scattering, which would require a more sophisticated treatment, these formulas can be evaluated very quickly. This can help a fusion machine designer build intuition about the effects of spin-polarization on neutron wall loading. The formulas are also fully differentiable, so they could be included in a fusion systems optimization code. As an example, we present sets of first wall shapes optimized to have a uniform NWL for each of the main polarization modes.