Analysis of fractional-order point reactor kinetics model with adiabatic temperature feedback for nuclear reactor with subdiffusive neutron transport

Abstract

In this paper, a fractional-order nonlinear model is developed for the nuclear reactor with subdiffusive neutron transport. The proposed fractional-order point reactor kinetics model is a system of three coupled, nonlinear differential equations. The model represents subprompt critical condition. The nonlinearity in the model is due to the adiabatic temperature feedback of reactivity. This model originates from the fact that neutron transport inside the reactor core is subdiffusion and should be better modeled using fractional-order differential equations. The proposed fractional-order model is analyzed for step and sinusoidal reactivity inputs. The stiff system of differential equations is solved numerically with Adams-Bashforth- Moultonmethod. The proposed model is stable with self-limitting power excursions. The issue of convergence of this method for the proposed model for different values of fractional derivative order is also discussed.