PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Nuclear reactions · Fission, fusion and nuclear energy
Energy from Physics, Ch The critical reactor: neutron diffusion, buckling and the size of a core
Problem
A natural-uranium, graphite-moderated reactor of the kind built for early plutonium production used metal fuel rods of radius r=1.1cm, natural-uranium metal density ρ=19.1gcm−3, set in a graphite lattice with 200 carbon atoms per uranium atom. For this moderator-to-fuel ratio the slowing-down power per fuel atom is ξΣs/NF=149b (the same homogeneous-mixture value applies whether the fuel is dispersed or lumped into rods, since it depends on the graphite-to-uranium ratio, not the fuel's shape). For long thin natural-uranium metal rods, self-shielding of the resonances is captured by the quoted correlation Ieff=2.95+25.8S/M(barns), where S/M=2/(ρr) is the rod's surface-to-mass ratio in cm2g−1. Take η=1.34, ϵ=1.03 and f=0.85 for this lumped lattice (below the homogeneous mixture's 0.92, because the thermal flux dips inside each rod), and its migration area M2=700cm2.
((a)) Find Ieff for these rods, and hence the resonance escape probability p=exp[−Ieff/(ξΣs/NF)].
((b)) Find k∞=ηϵpf and the radius of the bare critical sphere (fundamental mode ϕ∝sin(πr/R)/r, extrapolated boundary condition).
((c)) A real reactor of this kind was built with a core roughly 9m across, not a bare sphere but reflected and engineered with substantial margin. Compare its size with the bare critical sphere of part (b) and say, in one or two sentences, what the comparison shows about whether criticality alone sets the size of a built core.