Newton’s second law analogy for the traveling wave of nuclear burning

Vitalii Urbanevych,Viktor Tarasov,Vitaliy Rusov,Igor Sharph

doi:10.1051/epjn/2020012

Vitalii Urbanevych, Viktor Tarasov + Show 2 more

Open Access

https://doi.org/10.1051/epjn/2020012

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Abstract

We consider a model of neutron-nuclear wave burning. The traveling wave of nuclear burning of the medium is initiated by an external neutron source and is the basis for the new generation reactors the so-called “traveling-wave reactors”. We develop a model of nuclear traveling wave burning, for which it is possible to draw a Newton’s second law analogy with a mechanical dissipative system. On the basis of this analogy, we find that the wave velocity has a continuous spectrum bounded below. Within the framework of the new model, we show the autowave to be possible for certain neutron energies only. Also we find that two burning modes are possible depending on the control parameters: a traveling autowave and a wave driven by an external neutron source.

Highlights

The idea of autowave regime in the medium with diffusion and multiplication of neutrons was suggested in the paper [1] more than 30 yr ago
We show all the neutron energies, for which we found the minimum of potential energy, as a set of points in the graph, where the neutron energy is along the X-axis and the parameter nPu is along the Y -axis
A kinetic system of equations, describing the wave mode of neutron-nuclear burning in the uranium-plutonium medium is formulated

Summary

Introduction

The idea of autowave (or traveling-wave) regime in the medium with diffusion and multiplication of neutrons was suggested in the paper [1] more than 30 yr ago. The ball in the elastic pendulum, which is brought out of the equilibrium in a very viscous medium will be able just to return to the equilibrium point, but not to oscillate It will be shown below, that the “dissipative” contribution is directly connected to the β-decay processes, which are not taken into account in [5,9], and it is appeared to be proportional to the autowave velocity. A similar way of finding the wave velocity is used in [9], but using only the part of the trajectory, which corresponds to the positive (that is physical) values of neutron flux This path is being built with the help of integral, which can lead to an unphysical branch with negative values because of the square of neutrons’ flux in it.

System of kinetic equations

The analogy to Newton’s second law

Finding a criterion for the wave velocity

Numerical solution of the non-stationary system of equations

Conclusions