An analytical solution for an external source problem with delayed neutrons using the telegraphers equation

Different current and planned experiments are designed to study the zero power neutron physical behavior of accelerator driven systems (ADS). However, the analysis of these experiments is mostly based on point kinetics. To improve this situation and to overcome the limitations resulting from the separation of space and time, the paper presents a fully analytical approximation solution for a space-time dependent neutron transport problem in a one dimensional system consisting of a homogenized medium with a central neutron source. The basic solution without delayed neutrons is derived with Green's functions without separation of space and time. The delayed neutron production is later on implemented by means of the multiple scale expansion method. This way of separating the different time scales avoids the stiff problem arising in a closed form solution. Finally, a fully analytic approximation solution is generated for the switch on of a localized external neutron source in the center of the homogenized subcritical system. Space time dependent results based on a cross section set for a light water reactor configuration are presented to demonstrate the potential of the developed analytical approximation solution. The development is the first step towards improving the methods for the analysis of kinetic ADS experiments. It is the final goal to provide an improved tool for on site analysis of kinetics ADS experiments. (authors)