Question 22.9: A bare homogeneous reactor is surrounded by a reflector that......
A bare homogeneous reactor is surrounded by a reflector that has almost no measureable reflectivity. If it then follows that Σ_s ≈ 0 in the area occupied by the reflector, how far from the edge of the core must we set the neutron flux equal to zero if we want to obtain an accurate solution to the flux shape ϕ(x) using the one-group neutron diffusion equation? Assume that the transport mean free path at the core–reflector interface is 5 cm.
In this case, the extrapolated boundary condition can be used. The extrapolation distance is L_{EXT} = 0.7104λ_{TR}. For a transport mean free path λ_{TR} of ≈5 cm, the extrapolation distance is L_{EXT} = 0.7104λ_{TR} = 0.7104 × 5 ≈ 3.55 cm. Strictly speaking, this expression can only be used for a slab reactor. However, most reactors are generally large enough
that the slab reactor approximation is accurate to within a few percent.