Analytical solution of modified point kinetics equations for linear reactivity variation in subcritical nuclear reactors adopting an incomplete gamma function approximation

Abstract

The present work aims to achieve a fast and accurate analytical solution of the point kinetics equations applied to subcritical reactors such as ADS (Accelerator-Driven System), assuming a linear reactivity and external source variation. It was used a new set of point kinetics equations for subcritical systems based on the model proposed by Gandini & Salvatores. In this work it was employed the integrating factor method. The analytical solution for the case of interest was obtained by using only an approximation which consists of disregarding the term of the second derivative for neutron density in relation to time when compared with the other terms of the equation. And also, it is proposed an approximation for the upper incomplete gamma function found in the solution in order to make the computational processing faster. In addition, for purposes of validation and comparison a numerical solution was obtained by the finite differences method. Finally, it can be concluded that the obtained solution is accurate and has fast numerical processing time, especially when compared with the results of numerical solution by finite difference. One can also observe that the gamma approximation used achieve a high accuracy for the usual parameters. Thus we got satisfactory results when the solution is applied to practical situations, such as a reactor startup.