In diffusion theory, what does the condition φ = 0 at the extrapolated boundary enforce?

• A. φ is infinite at boundary
• B. No net neutron current crossing the boundary in the diffusion approximation
• C. φ equals the boundary flux gradient
• D. φ is constant anywhere

Answer: (B)

In diffusion theory, you need a boundary condition that links the inside flux to what happens outside the region being modeled. The extrapolated boundary condition says the scalar flux is zero at a fictitious point just outside the physical boundary. This choice effectively enforces that there is no net neutron current crossing that boundary in the diffusion approximation, since the outside region is treated as vacuum with no support for incoming particles. The actual leakage from the material is then captured by how the flux varies near the real boundary, with the extrapolated distance typically about 0.7104 times the transport mean free path. So, setting φ to zero at the extrapolated boundary is a way to represent zero net current crossing the boundary within diffusion theory.