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Fusion Energy
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Conference on Nuclear Training and Education: A Biennial International Forum (CONTE 2025)
February 3–6, 2025
Amelia Island, FL|Omni Amelia Island Resort
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Christmas Night
Twas the night before Christmas when all through the houseNo electrons were flowing through even my mouse.
All devices were plugged in by the chimney with careWith the hope that St. Nikola Tesla would share.
Chen Dubi, Rami Atar
Nuclear Science and Engineering | Volume 195 | Number 3 | March 2021 | Pages 256-270
Technical Paper | doi.org/10.1080/00295639.2020.1819136
Articles are hosted by Taylor and Francis Online.
Fluctuations associated with power and detector readings in a nuclear reactor, commonly known as reactor noise, are of great importance in nuclear science and engineering. Two different types of noise are described in the literature: internal noise, which is associated with the inherent stochasticity of fission chains, and external noise, which is governed by physical fluctuations of the macroscopic system. The latter may include temperature fluctuations, vibration of regulation rods, fluent turbulence, bubble formation, and more. It is generally true that in power reactors, where high temperatures and strong hydrodynamic flows are characteristic, the external noise is dominant. The goal of this paper is to propose a stochastic differential equation (SDE) that models the effect of two types of external noise terms: the inlet temperature variations, which affect the power through reactivity feedback, and rod vibrations, which affect the reactivity directly. Although these aspects were studied in the past, they were only treated via nonstochastic equations. It is argued that the SDE approach, previously used only for modeling the effect of internal noise on nuclear reactor dynamics, is also highly suitable for modeling external noise. The main advantage of our approach is the ability to arrive at analytic formulas.
The contributions presented in this paper based on the SDE approach are as follows. Under a linear approximation of thermal feedback, the stabilizing effect of thermal feedback is explained and quantified, and a limiting distribution is analyzed in full. An analysis of the detector response on a finite time interval is carried out, leading to a version of the Feynman variance-to-mean-ratio formula in the presence of external noise. Finally, a calculation of the eigenvalues associated with the linearized system alluded to above is performed, showing that in practical cases the rod vibrations and inlet temperature fluctuations correspond to eigenvalues in distinct timescales. The significance of these finding is discussed.
