Modeling neutron count distribution in a subcritical core by stochastic differential equations

Dubi, C.; Atar, Rami

doi:10.1016/j.anucene.2017.09.040

Cited by 12 publications

(3 citation statements)

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“…where dW (1) , dW (2) are two independent BM increments, and σ i, j i, j = 1, 2 are the amplitudes of the BM increments. In most applications, it is assumed the both and σ i, j i, j = 1, 2 are constant [5,6]. This is often due to a first-order approximation, and in their true nature, σ i, j i, j = 1, 2 may be functions of P and C [5,6].…”

Section: The Point Reactor Equationmentioning

confidence: 99%

“…In most applications, it is assumed the both and σ i, j i, j = 1, 2 are constant [5,6]. This is often due to a first-order approximation, and in their true nature, σ i, j i, j = 1, 2 may be functions of P and C [5,6]. To allow a general as possible theory, we will only assume that they are bounded.…”

Section: The Point Reactor Equationmentioning

confidence: 99%

“…In recent years, originating in the work of Hayes and Allen [5], there is an ongoing effort to analyze reactor noise via stochastic differential equation (SDE) and Ito calculus. The basic SDE model is obtained by applying the central limit theorem on the master equation, an approximation referred to in the literature as the diffusion scale approximation (see also [6]). We consider [5] to be the first paper to use SDE to model reactor noise (although the Langevin equation was introduced in earlier studies, see [7] and the references within), for two reasons: first, [5] was the first to construct the amplitude of the noise term from first principles and analytically justify the use of the Brownian motion increment.…”

Section: Introductionmentioning

confidence: 99%

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Stabilization of the stochastic point reactor kinetic equation through power feedback

Stein

Dubi

2020

Eur. Phys. J. Plus

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Most basic models for the power (or equivalently, the neutron population) in a nuclear core consider the power as a function of time (with an energetic and spatial distribution) and lead to deterministic description of the reactor kinetics. While these models are of common use and are undoubtedly the main analytic tool in understanding the reactor kinetics, the true nature of the power in a reactor core is stochastic and should be considered as a stochastic process in time. The stochastic fluctuations of the power around the mean field (which is given by the deterministic models) are referred to as "reactor noise", and understanding them is a basic topic in nuclear science and engineering. Traditionally, most models for reactor noise consider a sub-critical core, reaching steady state after exposure to an external source. The focus on a sub-critical setting is driven by two main factors. First, from a practical point of view, measuring the power fluctuations in a sub-critical core (known as "noise experiments") has proven to be a very efficient tool for estimating the static and kinetic parameters of the core. Second, once we assume a critical setting, the current models become statistically unstable, while the mean field solution has a stationary solution, the variance tends to ∞ linearly in time. The instability of the stochastic models is a known problem, and it has been conjectured in the past that this (some what strange) increase in the variance-that is not observed in physical systems-can be restrained by power feedback. However, this conjecture was never proven. The outline of the present study is to present a stochastic analysis to the point reactor kinetics model, proving that once the reactivity has a negative feedback, it not only forces a specific steady-state solution (in terms of the mean field equation), but also prevents the variance to "explode", and the variance is bounded in time.

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Section: The Point Reactor Equationmentioning

confidence: 99%

Section: The Point Reactor Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stabilization of the stochastic point reactor kinetic equation through power feedback

Stein

Dubi

2020

Eur. Phys. J. Plus

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A survey of mean-square destabilization of multidimensional linear stochastic differential systems with non-normal drift

Senosiaín

2023

Numer Algor

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Mean-square stability analysis of linear stochastic differential systems obtained perturbing ordinary systems by linear terms driven by independent Wiener processes is investigated. The so obtained stochastic regions are contractions of the asymptotic stability domain of the linear ordinary system. In this work, the mean-square stability regions exact shape is provided by means of necessary and sufficient conditions in terms of the eigenvalues of the drift and the intensities of the noises. Special attention is paid to how different structures of the perturbation affect the mean-square stability of systems with non-normal drifts. In each case, the obtained explicit stability condition reveals the role played by the parameter that controls the non-normality.

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A stochastic differential equation for neutron count with detector dead time and applications to the Feynman-α formula

Dubi

Atar

2019

Annals of Nuclear Energy

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Modeling neutron count distribution in a subcritical core by stochastic differential equations

Cited by 12 publications

References 11 publications

Stabilization of the stochastic point reactor kinetic equation through power feedback

Stabilization of the stochastic point reactor kinetic equation through power feedback

A survey of mean-square destabilization of multidimensional linear stochastic differential systems with non-normal drift

A stochastic differential equation for neutron count with detector dead time and applications to the Feynman-α formula

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