A light-water lattice has two volumes of water for every volume of oxide 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 light-water lattice has two volumes of water for every volume of oxide fuel, giving a fast fission factor

\epsilon=1.03

and a resonance escape probability

p=0.82

regardless of enrichment (both are set mainly by the moderator-to-fuel ratio, not the uranium-235 content). At natural enrichment (

0.72\%

) the reproduction factor is

\eta=1.34

and the thermal utilisation is

f=0.80

; at

3\%

enrichment

\eta=1.84

and

f=0.92

. The lattice's migration area is

M^2=60\,\mathrm{cm^2}

at either enrichment. ((a)) Compute

k_\infty=\eta\epsilon pf

at natural enrichment and at

3\%

enrichment, and say what the natural-enrichment result implies for a chain reaction in this lattice. ((b)) For the

3\%

lattice, find the radius of the bare critical sphere, using the fundamental mode

\phi\propto\sin(\pi r/R)/r

and the extrapolated boundary condition

\phi(R)=0