Full calculation of the long-time-interval limit of noise in reactors

Abstract

The analysis of the stochastic behavior of detected signals is useful in multiplicative systems such as nuclear reactors. In this work, we derive a simple, exact expression for the long-time limit of the variance-to-mean ratio of neutron detection near a reactor using the probability generating function technique. The obtained result incorporates continuous energy and spatial effects and depends only on the steady-state flux and its adjoint. We then perform MCNP simulations to calculate the adjoint flux in the Israeli Research Reactor no. 1 (IRR-1). This allows us to explicitly calculate the said values for different configurations of varying homogeneity and criticality, and to compare the results of the simulations to the Feynman α point model results. In the comparison we find significant deviations of 10%-80%, with strong dependence on the core's multiplication factor, accentuating the need for spatial corrections.