Fourier mode analysis of reflected slab and sphere criticality

Abstract

Abstract The criticality solution to one-speed neutron transport equation using Fourier mode analysis is described for reflected slab and spheres. The variation of critical distances under different specular reflection conditions is investigated considering linearly anisotropic media. For the spherical case the pseudo-slab approach is not required. The critical equations are derived for both cases. The critical half thicknesses and critical radii are determined for a given critical eigenvalue, reflection coefficient and anisotropy parameter. Numerical calculations verify that both the Fourier mode and P N method results are identical.