Asymptotic solutions in transport theory part I—One velocity with isotropic scattering

Abstract

We report here some results of an extensive series of calculations on the asymptotic behaviour of a neutron pulse injected into a slab and a sphere using monoenergetic transport theory with isotropic scattering cross section in the laboratory system. These results are compared with the infinite medium solutions with exp (iBx) spatial dependence. Two definitions of buckling are considered and the corresponding extrapolation distances are calculated; both the quantities are of considerable interest in the study of neutron thermalization. The characteristic angular peaking of neutrons leaking from slabs of extremely small thicknesses has been found. The spatial variation of the fundamental mode eigenfunction has been calculated and it has been found that the flux shape (except very close to the boundary) can be fitted accurately to the fundamental mode of the scalar Helmholtz equation ▽²Φ + B²Φ = 0. The results obtained from simple diffusion theory, with extrapolation distance assumed to be given by the Milne value, (independent of the size of the assembly), has been found to compare well with the exact calculations of the fundamental mode eigenvalue for thicknesses exceeding one mean free path. The theoretical results are compared with the recent pulsed neutron experiments in fast non-multiplying non-moderating assemblies.