The solitary wave in advanced nuclear energy system

TL;DR

This paper derives an analytical solution for a class of traveling wave reactors using solitary wave theory, revealing relationships between neutron flux, wave velocity, and nuclear material properties.

Contribution

It introduces an analytical approach to model the CANDLE reactor's neutron flux using solitary wave solutions, linking physical parameters to wave characteristics.

Findings

Neutron flux is proportional to wave velocity.

Flux amplitude relates to the square root of the diffusion coefficient.

Flux amplitude inversely depends on initial 238U density.

Abstract

The solitary wave naturally arises in many areas of mathematical physics, including in nonlinear optics, plasma physics, quantum field theory, and fluid mechanics. In the past few years, for an advanced nuclear energy system, a particular class of traveling wave reactor called the Constant Axial shape of Neutron flux, nuclide number densities and power shape During Life of Energy production (CANDLE) reactor has been proposed, and an analytical solution has been desired since it could reveal the global characters of the solution. In this study, from the perspective of the solitary wave, the analytical solution of this advanced nuclear energy system is demonstrated through coupling the one-group neutron diffusion equation with the burnup equation. The tanh-function method is applied to solve that nonlinear partial differential equation. The relationship between the velocity of the solitary wave, wave amplitude, or neutron flux and the evolution of the nuclide is revealed by the analytical method. The results demonstrate that the neutron flux is proportional to the wave velocity. The results also imply that the amplitude of the neutron flux is proportional to the square root of the diffusion coefficient but is inversely proportional to the initial 238U density.