A Stochastic Approach to Monoenergetic Space-Time Nuclear Reactor Kinetics

Abstract

A simplified stochastic model based on the forward stochastic model in the stochastic kinetics theory and the Itô stochastic differential equations is newly developed for treating monoenergetic space-time nuclear reactor kinetics in one dimension. The stochastic space-dependent kinetics model (SSKM) is tested against the Monte Carlo calculations for cases of uniform slab reactors with one delayed-neutron precursor group. The results show that the SSKM is in good agreement with the Monte Carlo method and can be used to describe the actual random space-time-dependent behavior of a nuclear reactor. Moreover, the SSKM can generalize the stochastic point-kinetics model.

A New Model for the Stochastic Point Reactor: Development and Comparison with Available Models

“…Additionally, the authors in [7,8] proposed a space-time reactor kinetic model using the same procedure as in [2] but adding the spatial variations. For a detailed survey of the different techniques used in analyzing the reactor dynamics, the reader can refer to [5].…”

Numerical Investigation of Dynamic Fluctuations Following Nuclear Reactor Transients Using a Simplified Stochastic Model

“…(5), the numerical solution in previous studies is adopted with the support of MATLAB. 9,10) Using the SSKM, the main purpose is to investigate the nature and characteristics of the neutron and precursor distributions under various static and transient conditions. The investigation method is similar to that by Stacey to make the results obtained by the SSKM comparable with those attained from the FSM.…”

“…Thus, it is also noted that the SSKM can be considered as a spacedependent generalization of the stochastic point-kinetics equations. 9,10,14,15) In the present study, a number of numerical experiments will be analyzed using the SSKM in order to identify the trends in dynamic fluctuations following a variety of transients in subcritical and supercritical reactors, which are expected to help elucidate the applicability of the model in modeling the intrinsic stochastic dynamic phenomena in a nuclear reactor. Detailed information is given in the following section.…”

“…[4][5][6][7][8] In previous studies, a simplified stochastic model (called the stochastic space-dependent kinetics model, SSKM) based on the forward stochastic model (FSM) in the stochastic kinetics theory and the Itô stochastic differential equations was suggested for the analysis of monoenergetic spacetime nuclear reactor kinetics in one dimension. [9][10][11][12][13][14][15] First, the FSM equations for the mean values of neutron and delayedneutron precursor populations were considered as the deterministic ones without considering their variances and covariances. Second, the system of interest was randomized again in the light of the Itô stochastic differential equations in order to derive the SSKM, thereby making possible the computation of the expected values of neutron and cumulative fission densities as well as their standard deviations.…”