Exact Solution of a Critical Problem for a Slab

Abstract

By using the Case method of expansion of the angular neutron distribution into series with respect to eigenfunctions of the plane Boltzmann equation, the critical problem of a slab has been formulated. By means of symmetry considerations, the problem of boundary condition has been reduced to one singular integral equation, which has been treated by classical methods. This treatment has given an integral equation for expansion coefficients, which by means of a simple transformation can be reduced to a Fredholm type with a regular kernel, and an additional equation, which plays the role of an exact critical condition. The methods and results of numerical calculations will be published soon.