Solutions of the one-group neutron transport equation are provided for point-beam and finite isotropic line sources in a homogeneous 3-D infinite medium with isotropic scattering. The solution is obtained via Fourier transforms and analytical/numerical inversions. The transport equation is cast into a 2-D equivalent form, which can ultimately be put in terms of a 1-D problem, thereby providing analytical leverage. The inversions use standard numerical techniques such as Gauss-Legendre quadrature and summation of infinite series. Even though the solution obtained here uses equivalent forms in fewer dimensions, it does represent a true 3-D analytical benchmark which is useful for both code verification and educational enrichment.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics