The Neutron Point Kinetics Equation: Suppression of Fractional Derivative Effects by Temperature Feedback

Fractional point kinetics fractional point kinetics has been discussed recently as one of the novel approaches that describes the short-term evolution of neutron densities as well as precursor concentrations in nuclear reactor theory. Kinetics may be derived from an original transport problem introducing simplifications that allow to decouple the time from spatial degrees of freedom. One of the motivations to extend the traditional point kinetics by additional terms that contain a fractional derivative is to improve the solution in the sense to compensate effects due to the simplifications mentioned above. Works on the fractional derivative point kinetics equation found in the literature (Espinosa-Paredes et al., Ann. Nucl. Eng. 35:1963–1967, 2008; Espinosa-Paredes et al., Energy 38:207–330, 2011; Nec and Nepomnyashchy, J. Phys. A Math. Theor. 40(49):14687–14702, 2007; Saha Ray and Patra, Ann. Nucl. Eng. 41:61–66, 2012) treat the extended kinetics problem, whereas in the present work we consider additionally temperature feedback on the reactivity (El Tokhy and Mahmoud, Ann. Nucl. Eng. 68:228–233, 2014; Nahla, Nucl. Eng. Des. 241:1502–1505, 2011; Silva et al., Int. J. Nucl. Eng. Sci. Technol. 8(2):131–140, 2014), which mimics influences of thermohydraulics on neutronics and thus may be considered beside being a novelty also a more realistic model in comparison with the previous works.