Nonlocal Effects to Neutron Diffusion Equation in a Nuclear Reactor

Abstract

In this study, a nonlocal approach to neutron diffusion equation with a memory is constructed in terms of moments of the displacement kernel with a modified geometric buckling. This approach leads to a family of partial differential equations which belong to the class of Fisher-Kolmogorov and Swift-Hohenberg equations. The stability of the problem depends on the signs of the second and fourth moments. The energy is a conserved quantity along orbits and a constant of integration is obtained. It was observed that the buckling is affected by the types of the kernel moment and for an explicit symmetric kernel, the ratio between the maximum and the average flux for a slab reactor is less than the ratio obtained using the conventional local diffusion equation, a result which is motivating technically in nuclear reactor engineering.

Keywords:

• nonlocal effects
• neutron diffusion equation
• kernel moments
• flux

PACS NUMBERS:

• 28.20.-v
• 28.41.-i

Disclosure statement

The author declares that he has no conflicts of interest.

Funding

The author received no direct funding for this work.

Acknowledgment

The author would like to thank the group of anonymous referees for their useful remarks and valuable suggestions.