Fractional neutron point kinetic equation with ramp and sinusoidal reactivity effects

• Fractional analysis for reactivity insertion and sinusoidal form.
• A relaxation time associated with the neutron flux density variation is considered.
• Different relaxation times and anomalous diffusion exponents were analyzed.
• The model can super-predict the classical equations due to memory effects.

The Classical Neutron Point-Kinetic (CNPK) equations are a system of stiff nonlinear ordinary differential equations for the neutron density, which have been subject of countless studies and applications with different approaches in the last seventy years. In this paper we carry out the numerical analysis of the Fractional Neutron Point-Kinetics (FNPK) model for two simple cases of reactivity insertion processes: Case (1) Ramp insertion of reactivity, and Case (2) Sinusoidal form. The FNPK model considers a relaxation time associated with a rapid variation in the neutron flux density, which is considered in the differential operator of fractional order, it is known as anomalous diffusion exponent. Different values of the relaxation time with one-group of delayed neutron precursors were used for this numerical analysis. The results of the neutron flux density with the FNPK model were compared with the CNPK equations for ramp and sinusoidal reactivity insertion processes. In both cases, the neutron density behavior described by the first model, for different relaxation times and anomalous diffusion coefficient values, over-predicts the behavior obtained with the CNPK equations.