The Green's dyadic method for the analytic solution of multigroup neutron transport boundary value problems

An extension of the Green's function method is developed for the exact solution of the multigroup neutron transport equation. The method is based on the treatment of the steady-state, plane geometry multigroup equations for general anisotropic scattering in a homogenous medium. The problem of a system of N coupled integrodifferential equations is reduced to the evaluation of an NXN dyadic by the Green's dyadic method. Each dyadic element represents neutron scatterring from one energy group to another.In this technique, all elements of the dyadic will be coupled if the multigroup transport equation describes both slowing down and energy gain mechanism of the neutrons. As a result of neglecting scattering to higher energy groups, the diagonal elements of the dyadic become the one-speed Green's functions. The singular eigenfunction method is used in order to determine the Green's functions. These functions, which are available for the cases of infinite and semi-infinite media in the literature, are extended for the slab case. This extension provides an iterative answer for the slab Green's function. It is shown that the diagonal elements are fundamental in evaluation of the off-diagonal elements also. A final solution for the group angular fluxes is constructed from elementary solutions of the one-speed homogeneous transport equation.The advantage of this technique manifests itself in two ways. First, the determination of the spectrum of the multigroup operator, which has been a common approach so far in the literature has been eliminated. Second, the orthogonality relations which are available in the literature were used to find the expansion coefficients. The developed formalism is applied to well-known neutron transport boundary value problems in two groups. The Green's dyadic method provides a systematic solution technique for these problems. The group angular fluxes are determined in a homogenous mesh for the solution of model transport problems which are chosen as the albedo, slab criticality and two adjacent slabs problems.U of I OnlyETDs are only available to UIUC Users without author permissio