Modifying the neutron diffusion equation using spatial fractional operators and developed diffusion coefficients

Normal diffusion process is quite valid for media without production and absorption. In these media particles move by scattering reaction and mean square displacement of particles is linear function of time (〈r(t)2〉∼t). In the nuclear reactors both production and absorption are present and consequently normal diffusion fails to describe neutrons behavior. In this circumstance sub or super diffusion (also called anomalous diffusion) phenomena are occurred. We have developed a new scheme of diffusion equation which is established on the spatial-fractional derivatives, neutron fractional diffusion equation (NFDE). The NFDE uses an arbitrary order of differential operators and it can model anomalous diffusion in the more accurate manner. The second drawback of diffusion equation is related to high absorption (or production) regions where a steep spatial gradient is existent. Based on the Fick's law, if gradient of flux is very large the neutron current will exceed the scalar flux (|J→|>ϕ). In order to dump this effect, the flux limited diffusion theory is used to calculate diffusion coefficient. The proposed model is validated against experimental measurements of DIMPLE reactor.