Which condition is NOT a scenario where diffusion approximation may be inadequate?

• A. Near boundaries
• B. Strong anisotropy
• C. Low scattering
• D. Deep in a large, uniform medium

Answer: (D)

Diffusion approximation works best when particles scatter many times and come to a near-isotropic distribution, with flux changing slowly over space. It relies on smoothing out the angular dependence and ignoring detailed transport along straight paths. Near boundaries, you get boundary layers where the interface alters the angular distribution and flux, so diffusion can miss important directional effects. If scattering is strongly anisotropic, there’s a persistent forward component that keeps the transport more beam-like than diffusive, breaking the isotropy assumption. When scattering is weak, particles travel longer distances between collisions, so ballistic transport dominates and diffusion no longer describes the motion well.

Deep inside a large, uniform medium, these problematic conditions disappear: there are no nearby boundaries to create boundary layers, scattering is typically frequent enough to randomize directions, and the flux varies slowly over many mean free paths. In this regime the diffusion equation provides an accurate description of how the fluence changes in space, making this the scenario where diffusion approximation is least likely to be inadequate.