Effect of Transverse Dimensions on the Diffusion Length of Neutrons in Crystalline Moderator Assemblies

The dependence of neutron diffusion length on the size and shape of the cross-sectional area of infinitely long rectangular blocks of crystalline moderators (graphite and beryllium) has been studied using an energy-dependent transverse buckling. In conformity with the experimental results in graphite, the diffusion length is found to increase with a decrease in the transverse size of the assembly. It is further found that in assemblies with small transverse dimensions, pseudoequilibrium conditions are established fairly rapidly and reasons for this are discussed. On the other hand, in assemblies with intermediate transverse dimensions (cross-sectional area lying between 70 × 70 cm² and 50 × 50 cm² for graphite and between 30 × 30 cm² and 20 × 20 cm² for beryllium), even pseudo-equilibrium conditions are not established at very large distances from the source. Dependence of the diffusion length on the shape of the cross-sectional area is also investigated.