# [P19] The solution of the neutron point kinetics equation with stochastic extension: an analysis of two moments

### Conference paper

Proceedings of 7th INAC: International Nuclear Atlantic Conference, São Paulo, Brazil, 2015 Oct

**ABSTRACT:**The neutron point kinetics equation, which models the time-dependent behavior of nuclear reactors, is often used to understand the dynamics of nuclear reactor operations. It consists of a system of coupled differential equations that models the interaction between (i) the neutron population; and (ii) the concentration of the delayed neutron precursors, which are radioactive isotopes formed in the fission process that decay through neutron emission. These equations are deterministic in nature, and therefore can provide only average values of the modeled populations. However, the actual dynamical process is stochastic: the neutron density and the delayed neutron precursor concentrations vary randomly with time. To address this stochastic behavior, Hayes and Allen have generalized the standard deterministic point kinetics equation. They derived a system of stochastic differential equations that can accurately model the random behavior of the neutron density and the precursor concentrations in a point reactor. Due to the stiffness of these equations, this system was numerically implemented using a stochastic piecewise constant approximation method (Stochastic PCA). Here, we present a study of the influence of stochastic fluctuations on the results of the neutron point kinetics equation. We reproduce the stochastic formulation introduced by Hayes and Allen and compute Monte Carlo numerical results for examples with constant and time-dependent reactivity, comparing these results with stochastic and deterministic methods found in the literature. Moreover, we introduce a modified version of the stochastic method to obtain a non-stiff solution, analogue to a previously derived deterministic approach.

### Cite

**APA**

da Silva, M. W., Bodmann, B. E. J., Vilhena, M. T., & Vasques, R. (2015). [P19] The solution of the neutron point kinetics equation with stochastic extension: an analysis of two moments. In Proceedings of 7th INAC: International Nuclear Atlantic Conference. São Paulo, Brazil.

**Chicago/Turabian**

Silva, Milena Wollmann da, Bardo E. J. Bodmann, Marco T. Vilhena, and Richard Vasques. “[P19] The Solution of the Neutron Point Kinetics Equation with Stochastic Extension: an Analysis of Two Moments.” In Proceedings of 7th INAC: International Nuclear Atlantic Conference. São Paulo, Brazil, 2015.

**MLA**

da Silva, Milena Wollmann, et al. “[P19] The Solution of the Neutron Point Kinetics Equation with Stochastic Extension: an Analysis of Two Moments.” Proceedings of 7th INAC: International Nuclear Atlantic Conference, 2015.