A heavy-water-moderated lattice runs on natural uranium metal fuel
PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Fission, fusion and nuclear energy · Fission, fusion and nuclear energy
Energy from Physics, Ch The critical reactor: neutron diffusion, buckling and the size of a core
Problem
A heavy-water-moderated lattice runs on natural uranium metal fuel. Because deuterium absorbs neutrons far more weakly than hydrogen, the same natural-uranium fuel now sits in a lattice with thermal utilisation f=0.85 and resonance escape probability p=0.90 (both higher than a light-water lattice's f=0.80 and p=0.82 for the same fuel). Take η=1.34 (natural uranium, as before) and a fast fission factor ϵ=1.03. The lattice's migration area is M2=190cm2 (heavy water's much longer diffusion length outweighs its smaller water fraction).
((a)) Compute k∞=ηϵpf for this lattice, and explain in terms of f and p why natural uranium can sustain a chain reaction in heavy water when it cannot in ordinary water.
((b)) Find the radius of the bare critical sphere of this lattice, using the fundamental mode ϕ∝sin(πr/R)/r and the extrapolated boundary condition.