On the stability of linear fractional-space neutron point kinetics (F-SNPK) models for nuclear reactor dynamics

The aim of this work is to investigate the stability of linear fractional-space neutron point kinetics (F-SNPK) models for nuclear reactor dynamics, using three methods: root locus, Bode plot and unit step response. The F-SNPK is based on an approximation non-Fickian that is modeled considering that the differential operator of neutron density current is of fractional order, known as anomalous diffusion exponent. Two rector geometries for different values of anomalous diffusion exponent where analyzed. The results obtained with F-SNPK were compared with the classical neutron point kinetic (CNPK) equations. It has been found that the F-SNPK models are open-loop as well as closed-loop stable for both the geometries. The models are also found to exhibit faster dynamics with increase in subdiffusivity.