A bare spherical core has infinite multiplication factor and migration area

PHYSICS · Subjective · 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 bare spherical core has infinite multiplication factor

k_\infty = 1.15

and migration area

M^2 = 70\,\mathrm{cm^2}

. The fundamental-mode geometric buckling of a bare sphere of radius

R

B_g^2 = (\pi/R)^2

. Compute the critical radius

R