Analysis of some pseudo-discrete spatial decay modes of the two- and three-group neutron transport equations by analytic continuation

Abstract

The nature and location of the poles of the dispersion function of the frequency-dependent two- and three-group neutron transport equations for an infinite 3-D homogeneous multiplying medium with constant cross sections and isotropic scattering is investigated. It is shown that on the right half of the complex plane, only one pole exists on the physical sheet of the Riemann surface, which is almost identical to the one obtained in two- and three-group frequency-dependent diffusion theory, and gives rise to the well-known, in neutron noise, long attenuation length global component of the detector response. In contrast to diffusion theory, in transport theory no other pole exists on the physical sheet; the poles associated with the short spatial relaxation length ‘local component’ in homogeneous diffusion theories approaches are bifurcated and are to be found on the adjacent ‘unphysical’ sheets of the Riemann surface of the generic multivalued dispersion function. Although not on the physical sheet, the bifurcated poles are located very close to it and give rise to pseudo-discrete spatial decay modes with very similar characteristics to the local component of the detector response in homogeneous diffusion theories.