Calculating reactor transfer functions by Padé approximation via Lanczos algorithm

Abstract

An effective method of solving the one-speed transport equation in frequency domain is demonstrated in this paper, the so-called Padé approximation via Lanczos algorithm (PVL). The advantage of the PVL method is that implementing the calculation process over a considerably reduced model yields a pseudo-analytical expression of the transfer function over a fairly large range of frequency. As a particular application, the dynamic transfer function of a reactor, i.e. the neutron noise induced by a localised perturbation is calculated in one-speed transport theory. The problem is essentially the same as that of the “detector-field-of-view”; studied by other authors. The PVL algorithm is demonstrated through the solution of the problem and its advantages are described. The quantitative results show that although one-speed theory was used, a local component was found, and thus the local-global decomposition could be reconstructed. This shows that unlike in diffusion theory where at least two-group theory is necessary, the local behaviour can be described already by a one-speed equation in transport theory.