Fractional-space neutron point kinetics (F-SNPK) equations for nuclear reactor dynamics

Abstract

The aim of this paper is the mathematical derivation, and numerical analysis of the fractional-space neutron point kinetics (F-SNPK) equations for nuclear reactor dynamics. The classic neutron point kinetics (CNPK) equations are one of the most important models of reduced order in nuclear engineering, that been the subject of countless studies and applications to understand the reactor dynamics and its effects. The F-SNPK derived in this work is an extended model respect to CNPK. The F-SNPK model was derived considering a fractional-space law for the neutron density current where the differential operator is the fractional order (FO), also known as anomalous diffusion exponent. The physical meaning is related with non-Fickian effects (anomalous diffusion), which in F-SNPK gives rise to a new term called in this work anomalous diffusion source that considers neutron leakage, and it depends on the geometric buckling and anomalous diffusion exponent. The numerical analysis shows that the neutron leakage is greater with decreasing anomalous diffusion exponent.