Solution of the fractional neutron point kinetics equations considering time derivative of the reactivity

Abstract

In this paper, we present a numerical solution for the time fractional neutron point kinetics equations (FNPK) model with Newtonian temperature feedback effects on finite medium. We consider reformulation of the FNPK model to include the time derivative of the reactivity. The model of FNPK describes a finite bare reactor core associated with values of the nuclear parameters which are adjusted to preserve the criticality of the reactor at the steady state. The modified model is compared with the earlier published models and we have found that they are consistent when the reactivity is constant. Implicit difference method is proposed to solve the model of the FNPK with six groups of delayed neutron precursors. The method is based on approximating the Caputo fractional derivative by shifted Grünwald-Letnikov fractional derivative. Stability of the method is discussed and it has proved that the method is unconditionally stable. The neutron density results with temperature reactivity feedback, for different values of fractional orders(0<α≤1), are shown and compared with the classical neutron point kinetics equations.