Neutron counting statistics in a subcritical cyclo-stationary multiplying system I: Die-away experiment

Abstract

This paper is the first of two which deal with the neutron counting statistics in a subcritical, cyclo-stationary, nuclear reactor explicitly taking into account the delayed neutrons. In the framework of the one-velocity point-reactor model, the backward Kolmogorov equation is used to study the branching processes in a system assumed to contain a time dependent neutron source and a set of counters. Analytical expressions for the moments up to the second order of the number of counts measured by one or two of the detectors are obtained. These expressions are then specialized for the die-away experiment modelled as a regular sequence of rectangular neutron pulses. The explicit expressions thereby obtained allow the calculation of the variance-covariance matrix required for estimating the kinetic parameters from the experimental data. Results are reported and a Fortran IV program for computing the moments is available.