Some Observations on Transverse Leakage Approximations in Multidimensional Transport Theory

An analysis is made of the accuracy of the buckling approximation for the transverse leakage, used in various one- and two-dimensional transport theory computer codes. We find that the resulting approximate integro-differential form of the transport equation is not suitable for calculating accurate values of the angle-dependent flux for any case where transverse leakage has an appreciable effect on the solution. We have taken four problems, namely, critical equation, pulsed neutron and diffusion length problems, and extrapolated endpoints, and have solved them exactly using an equation derived in an earlier paper; we then solve the same problem by means of the buckling equation. In all cases, important deviations are noted that restrict the use of the buckling approximation.