A new simplified analytical solution to solve the neutron point kinetics equations using the Laplace transform method

A new analytical solution of the neutron point kinetics equations is developed in the present work, which considers more families of delayed neutrons as well as constant reactivity. The proposed solution is obtained by the Laplace transform method as well as the Heaviside and the Convolution theorems, and it is expressed as two different equations, one for the neutron density, and other one for the concentration of delayed neutron precursors. Both equations are written as linear combination of exponentials functions that involve the roots of a polynomial related to the Inhour Equation. One of the main novelties of the developed solution is that it does not require to apply matrix methods to obtain its coefficients, like other reported solutions do, and instead it uses an algebraic method that is based only on polynomials, which are given in a very reduced and explicit way. Additionally, a set of improvements is developed in the present work to simplify nested sums that commonly appear in other reported analytical solutions, using a recursive and a combinatorial approach. Numerical experiments show that the developed analytical solution produces accurate results for step, ramp and feedback reactivities, comparing with other approaches that are reported in literature.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

In this work, a new analytical solution for the neutron point kinetics equations is developed, considering additional families of delayed neutrons and constant reactivity. The solution is obtained using Laplace transform method and theorems of Heaviside and Convolution. It does not require matrix methods for coefficient calculation and simplifies nested sums found in other analytical solutions.