Mixed singular-regular boundary conditions in multislab radiation transport

On the development of computational tools for the design of beam assemblies for boron neutron capture therapy

“…1-3, apart from computational finite arithmetic considerations and regardless of R, N and the dimensions of and materials for the layers. The ESGF method was developed by the present author in recent years, and has found application to more general radiation transport problems [21][22][23][24][25]. The basic equations of the ESGF method are the N boundary Eqs.…”

“…6 are determined on a layerby-layer basis. For a given layer, we impose that the local eigenfunction expansion solution [21] of Eq. 1 be preserved by Eq.…”

“…A detailed description of the direct numerical scheme employed for computing the constants θ r,m,p for all layers and angular directions can be found in Ref. [21]. Equations 2-4 and 6 are the basic equations of the ESGF method, and they are all we need to derive a multi-layer matrix operator for neutron transmission computations.…”

“…2-4 and 6 can be found in Ref. [21]. Once this system is solved and the layer-edge fluxes are determined, the ESGF method goes into its next computational step: the analytical reconstruction of the angular neutron fluxes ψ r,m (x) on a layer-by-layer basis.…”

“…This article is the first in a series devoted to the development of efficient and accurate computational tools for the design of beam assemblies for boron neutron capture therapy within the framework of discrete ordinates spectral nodal methods of neutron transport theory [21][22][23][24]. Keeping always an eye on more realistic multidimensional energy-angle-dependent transport models, we begin our study here with a multi-layer energy-independent discrete ordinates model for the transport of neutrons through a bare assembly, and we attempt to solve the beam transport problem cited in the above paragraph-we are given a multi-layer domain that represents a trial assembly configuration and a source that shines the assembly with neutrons on one side, and we are asked to determine the distribution of neutrons that are transmitted through and leave the assembly across the opposite (patient) side-in an efficient and accurate manner.…”