The Scientific Contribution of the Kaniadakis Entropy to Nuclear Reactor Physics: A Brief Review

Abstract

In nuclear reactors, tracking the loss and production of neutrons is crucial for the safe operation of such devices. In this regard, the microscopic cross section with the Doppler broadening function is a way to represent the thermal agitation movement in a reactor core. This function usually considers the Maxwell-Boltzmann statistics for the velocity distribution. However, this distribution cannot be applied on every occasion, i.e., in conditions outside the thermal equilibrium. In order to overcome this potential limitation, Kaniadakis entropy has been used over the last seven years to generate generalised nuclear data. This short review article summarises what has been conducted so far and what has to be conducted yet.

Keywords: Doppler broadening function; Kaniadakis entropy; nuclear reactor physics.

Figure 1

The temperature rise causes the Doppler broadening effect in a resonance curve [28]. Source: de Abreu (2020, p. 14).

Figure 2

The comparison between the ${\psi }_{\kappa =0.3}\left(\xi ,x\right)$ (blue) and $\psi \left(\xi ,x\right)$ (green) curves [28]. It is possible to see the peak’s attenuation.

Figure 3

The comparison between the ${\psi }_{\kappa =0.5}\left(\xi ,x\right)$ (blue) and $\psi \left(\xi ,x\right)$ (green) curves. It is possible to see the peak’s attenuation.

Figure 4

A comparison between the analytical and numerical results for the radiative capture cross-sections using the Kaniadakis distribution [28]. Source: de Abreu (2020, p. 90, our translation).

Figure 5

A plot of the deformed radiative capture cross section for plutonium 238 considering $k=0.1$ and the 9.98 eV peak generated by the FRENDY data processing code [23]. Source: de Abreu et al. (2022, p. 10).

Figure 6

A plot of the deformed radiative capture cross section for gadolinium 155 considering $k=0.1$ and the 95.7 eV peak generated by the FRENDY data processing code [23]. Source: de Abreu et al. (2022, p. 12).