On the solution of the Boltzmann transport equation in two-dimensions (Q2540251)

The Boltzmann integrodifferential equation of monoenergetic neutron transport is written in rectangular two-dimensional coordinates. One spatial variable is removed by a Fourier transformation, and the resultant equation is cast into a one-dimensional form having a complex neutron direction of motion. Elementary solutions to this equation can be obtained by separation of variables and they have been shown to form a complete set of functions. Hence the solutions for the flux from a line source in a full- and a half-space are obtained in the transformed domain. Certain identities are developed to simplify several relevant two-dimensional integrals. When these identities are applied to the full-space problem and the solution inverted, the known result obtains. The same simplifying procedure works in the half-space problem as well, and this result is shown to agree with the Wiener-Hopf solution to the problem.