Use of a moments method for the analysis of flux distributions in subcritical assemblies

Abstract

A moments method has been developed for the analysis of flux distributions in subcritical neutron-multiplying assemblies. The method determines values of the asymptotic axial and radial buckling, and of the extrapolated height and radius, from foil activation data, in terms of flux moments defined in the usual sense. Analytic expressions are derived for the axial and radial buckling and extrapolated dimensions in terms of the flux moments. These expressions have clear physical meaning and are suitable for the interpretation of conventional buckling measurements. The method treats the moment index as a variable parameter and allows freedom in the choice of the locations of the first and last data points used in the analysis. These degrees of freedom make it possible to reduce the effects of source neutrons, flux transients, and higher harmonics. As a result, the moments method can be applied successfully to very small lattices ("miniature lattices") as well as to large exponential assemblies. The moments method has been tested, in comparison with the conventional least-squares curve-fitting method, by applying the two methods to the analysis of measurements made in several uranium heavy water, and uranium oxide-heavy water lattices investigated at the M. I. T. Lattice Project. In the case of large exponential assemblies, the moments method yielded more consistent results than the curve-fitting method. In the case of miniature lattices, the moments method made it possible for the first time to determine values of axial and radial buckling and extrapolated dimensions.