The eigenvalues of the discrete ordinates equations in slab geometry

The discrete ordinates approximation of the one-group, source-free, neutron transport equation has been solved analytically for slab geometry. The resulting eigenvalues are functions of both the angular quadrature and the spatial mesh used in the discrete ordinates equations. The dependence of the eigenvalues on the angular quadrature has been examined for the three limiting cases of c << 1, mod(1-c) << 1 and c >> 1, where c = sigma(sub(s))/sigma(sub(t)). Both the diamond difference and step function approximations have been considered in the evaluation of the eigenvalue dependence on the spatial mesh size. When the neutron flux is well described by a function of the form exp(-KX), the diamond difference approximation gives an eigenvalue Ksup(d) approximately equal to K(1 + (K Δ)2/12), where K is the eigenvalue for small values of the mesh size Δ, while the step function approximation gives an eigenvalue Ksup(s) approximately equal to K(1-0.4 sigma(sub(t))Δ). (author)