A Variational Approach for the Determination of Neutron Flux Spectra from Detector Activation

Abstract

The problem of determining neutron flux spectra through detector activation is of wide and continued interest in the nuclear industry. Analysis of this problem has historically been divided into two areas of concern. The first area is the evaluation of the perturbation introduced into the flux field by the detector. The second area is the determination of the unperturbed energy-dependent neutron flux from the integral relationship of neutron flux to detector activity.An expression was derived which relates detector activity to the unperturbed neutron flux and the adjoint difference flux through the use of a variational approach and a transport theory description of the system. The equation was cast in discrete ordinates formalism to permit numerical solution. The self-contained adjoint problem was solved using standard techniques. The unperturbed flux was expanded as a series of Laguerre polynomials, the coefficients of which were determined through inversion of the resulting rectangular matrix.The theoretical model was examined through application to several synthetic problems. A water-moderated spectrum was examined with both perturbed and unperturbed calculations. Direct calculation of perturbed activities showed good agreement with standard activity calculations. Comparable calculations of flux spectra with perturbed and unperturbed activities showed close agreement. The flux spectrum calculations yielded good results in the thermal energy range, and analysis showed that difficulties encountered in the epithermal range were due to the polynomial expansion scheme, as has been previously observed.