A reflection on the fractional order nuclear reactor dynamics

Abstract

• Fractional order modeling of the coupled reactor kinetic equations . • Bifurcation and instability investigated as a function of the fractional order. • More tendency towards instability in more sub-diffusive regions. Bifurcation and stability analysis in the coupled integer-fractional order dynamic equations of a nuclear reactor is carried out in this work. To this end, the dynamics of a Pressurized Water Reactor (PWR) is taken into account as a mainstay design in the water reactor technology. The effect of fractional derivative order on the stability threshold and the onset of bifurcation phenomena is inspected therein with the temperature feedback coefficient taken as the bifurcation parameter. Overall, the transport of neutrons inside the nuclear reactor core, especially in the high neutron absorbing spaces such as the fuel or control rod, resembles that of a sub-diffusion phenomenon. As such, the pertaining equations which comprise neutron diffusion terms are more carefully treated within a fractional order framework. In this work, a formal approach is examined to help readily compute system poles and the associated stable half plane. Results confirm a sensible tendency towards instability as the value of the fractional order is decreased and a more sub-diffusive regime is established.