Time-space fractional neutron point kinetics: Theory and simulations

Abstract

In this work the mathematical derivation and numerical analysis of a fractional nuclear reactor point kinetics in time and space (TSFNPK) is presented. The TSFNPK model was derived considering a non-Fickian law for the neutron density current where the differential operators in space and time are of fractional order. The TSFNPK equations presented in this work constitutes a novel model for nuclear reactor kinetics, thus represent an extended model with respect to other fractional models and the classical neutron point kinetics equations. The model considers two diffusion exponents: one for the differential operator dependent in time and another for the dependent operator in space. Both exponents effect is numerically analyzed considering changes of reactivity step type, and temperature feedback reactivity. A first approach of the TSFNPK is presented, without temperature effects, and then a second approach considering temperature feedback effects is analyzed. In a following work, as a demonstration of application, a detailed analysis along with verification will be presented.