The flat flux problem in one-speed neutron transport theory

Abstract

The classic flat flux problem in nuclear reactor physics, first solved by Goertzel using diffusion theory, is extended to one-speed transport theory. A numerical solution is obtained for a general two region problem in which the inner region has a flat flux and the outer one a spatially variable flux. For the exact solution, plane geometry is employed with the optical path representation. This solution allows the accuracy of a more flexible but approximate method to be assessed. A feature of the problem which has not been noted before is that in the region of flat flux the current is not zero. The reason for this is explained and is used to assess the accuracy of the approximation method. Diffusion theory is shown to be a poor but not unreasonable approximation. However, to make it viable it is necessary to introduce generalised function solutions to the diffusion equation. The theory is illustrated in detail by numerical calculations. It is shown that a flat flux in one speed theory corresponds to a maximum fuel loading. This is in contrast to the multigroup case for which it is a minimum loading.