Chapter 4 - Fractional-order neutron current density

Abstract

The fractional-order neutron density is a constitutive law for the neutron motion in nuclear reactors without restrictions. The fractional constitutive law has a fractional exponent of the differential operator, which is the new unknown that is known as the anomalous diffusion coefficient. The application of the fractional constitutive law in the neutron balance equation leads to the fractional diffusion equation with time relaxation of the fractional order. This representation has an important physical meaning because it considers that the effects of neutron transport are not instantaneous (time memory or space memory) and nonlocal. The time-fractional diffusion equation is the starting point to derive the time-fractional point reactor kinetics model. The time-fractional point model is widely discussed with numerical solutions in order to establish the importance of three terms of fractional order as well as the analysis of the insertion of reactivities (ramp and sinusoidal), reactor start-up, temperature feedback, and ATWS boron analysis.