Neutron Transport with Anisotropic Scattering. Theory and Applications

The Boltzmann neutron transport equation with arbitrary order anisotropic scattering is solved using the Case/Mika singular eigenfunction expansion (SEE). In order to do so, one needs to compute all discrete eigenvalues. A numerically stable and efficient method is proposed to do this in a two-step process: first the number of discrete eigenvalues is calculated and this provides a stopping criterion in the second phase: the solution of the characteristic equation for the discrete eigenvalues. The method was improved to be able to locate so-called near-singular eigenvalues (eigenvalues lying extremely close to the continuum [-1,+1]. Next to the discrete part, one also needs the continuum part. This is characterised by its angular Legendre moments and a stable and efficient method has been proposed to calculate these moments. Three applications were studied: the boundary sources method, a study of the discrete spectrum of the Henyey-Greenstein kernel and two challenges in radiative transfer.