Effective boundary conditions in the theory of neutron diffusion (A review)

Abstract

This review describes methods for determining effective boundary conditions (EBC) which ensure that in the asymptotic region a solution of the neutron diffusion equation coincides with the solution of the corresponding transport equation. We discuss EBC for mono-energetic neutrons on plane and on cylindrical surfaces of ‘black’ and of ‘grey’ bodies. Results are given for EBC in the case of cylinders of arbitrary section.

We consider the simplest problem of EBC determination for neutrons moderated in a medium of heavy atoms and with a scattering cross-section not dependent on energy. The review includes results obtained by workers both in the U.S.S.R. and abroad.