BOOK REVIEW: "Neutron Noise: A Treatise on the Physics of Branching Processes," I. PÁZSIT and L. PÁL

Pázsit, Imre; Пал, Л.

doi:10.1142/s0219477508004209

Cited by 58 publications

(154 citation statements)

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“…The precursors conceptually represent the delayed neutrons being in a 'virtual state' before the β − decay of the fission fragments, which sets them free into the system. There exists a joint probability P i,j of generating i neutrons and j precursors at the fission event, the realization {i, j} being possibly correlated [1,2]. We will denote by λ the decay rate of the β − reaction, upon which the precursors disappear to give rise to a delayed neutron.…”

Section: A Prototype Model Of Fission Chains In Nuclear Reactorsmentioning

confidence: 99%

“…Examples are widespread and encompass neutron multiplication [1][2][3], nuclear collision cascades [3][4][5], epidemics and ecology [6][7][8], bacterial growth [9,10], and genetics [11][12][13]. Neglecting particleparticle correlations and non-linear effects, the evolution of such systems can be effectively explained by the Galton-Watson model [3].…”

Section: Introductionmentioning

confidence: 99%

“…In the intermediate regime, the population stays constant on average, and the system is said to be exactly critical. A prominent example of a system operating at (or close to) the critical point is provided by the self-sustaining fission chains of neutrons in nuclear reactors [1,2].…”

Section: Introductionmentioning

confidence: 99%

“…In view of the relevance of neutron clustering in the context of nuclear reactor physics, in this paper we will investigate the spatial and temporal behaviour of a collection of neutrons undergoing scattering (random displacements), fission (reproduction) and absorption (death). As illustrated in the following, a prototype model of a nuclear reactor can be described in terms of a multi-type branching process involving an equilibrium between neutrons and a second species of particles, the so-called precursors [1][2][3]. Upon fission, a random number of secondary neutrons (called prompt) are emitted almost instantaneously.…”

Section: Introductionmentioning

confidence: 99%

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Neutron fluctuations: The importance of being delayed

et al. 2015

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The neutron population in a nuclear reactor is subject to fluctuations in time and in space due to the competition of diffusion by scattering, births by fission events, and deaths by absorptions. As such, fission chains provide a prototype model for the study of spatial clustering phenomena. In order for the reactor to be operated in stationary conditions at the critical point, the population of prompt neutrons instantaneously emitted at fission must be in equilibrium with the much smaller population of delayed neutrons, emitted after a Poissonian time by nuclear decay of the fissioned nuclei. In this work, we will show that the delayed neutrons, although representing a tiny fraction of the total number of neutrons in the reactor, have actually a key impact on the fluctuations, and their contribution is very effective in quenching the spatial clustering.

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Section: A Prototype Model Of Fission Chains In Nuclear Reactorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Neutron fluctuations: The importance of being delayed

et al. 2015

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“…In reactor cores, the subcritical reactivity can be extracted from the variance to mean or from the temporal correlations of the detections; and in safeguards, the fissile mass can be determined from coincidence an multiplicity measurements [1]. The possibility of extracting such parameters is due to the fact that the branching, i.e.…”

Section: Introductionmentioning

confidence: 99%

Energy Correlation of Prompt Fission Neutrons

Elter

Pázsit

2016

EPJ Web of Conferences

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Abstract. In all cases where neutron fluctuations in a branching process (such as in multiplicity measurements) are treated in an energy dependent description, the energy correlations of the branching itself (energy correlations of the fission neutrons) need to be known. To date, these are not known from experiments. Such correlations can be theoretically and numerically derived by modelling the details of the fission process. It was suggested earlier that the fact that the prompt neutrons are emitted from the moving fission targets, will influence their energy and angular distributions in the lab system, which possibly induces correlations. In this paper the influence of the neutron emission process from the moving targets on the energy correlations is investigated analytically and via numerical simulations. It is shown that the correlations are generated by the random energy and direction distributions of the fission fragments. Analytical formulas are derived for the two-point energy distributions, and quantitative results are obtained by Monte-Carlo simulations. The results lend insight into the character of the two-point distributions, and give quantitative estimates of the energy correlations, which are generally small.

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Multi-species Neutron Transport Equation

et al. 2019

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The Neutron Transport Equation (NTE) describes the flux of neutrons through inhomogeneous fissile medium. Whilst well treated in the nuclear physics literature (cf. [8, 28]), the NTE has had a somewhat scattered treatment in mathematical literature with a variety of different approaches (cf. [7,26]). Within a probabilistic framework it has somewhat undeservingly received little attention in recent years; nonetheless, probabilistic treatments can be found see for example [18,27,23,30,4,3]. In this article our aim is threefold. First we want to introduce a slightly more general setting for the NTE, which gives a more complete picture of the different species of particle and radioactive fluxes that are involved in fission. Second we consolidate the classical c 0 -semigroup approach to solving the NTE with the method of stochastic representation which involves expectation semigroups. Third we provide the leading asymptotic of our multi-species NTE, which will turn out to be crucial for further stochastic analysis of the NTE in forthcoming work [14,12,5]. The methodology used in this paper harmonises the culture of expectation semigroup analysis from the theory of stochastic processes against c 0 -semigroup theory from functional analysis. In this respect, our presentation is thus part review of existing theory and part presentation of new research results based on generalisation of existing results.1. Introduction. The neutron transport equation (NTE) describes the flux of neutrons across a directional planar cross-section in an inhomogeneous fissile medium (typically measured is number of neutrons per cm 2 per second). As such, flux is described as a function of time, t, Euclidian location, r ∈ R 3 , direction of travel, Ω ∈ S 2 , speed c > 0 (and hence velocity υ = cΩ), and neutron energy, E ∈ R. It is not uncommon in the physics literature, as indeed we shall do here, to assume that energy is a function of velocity (E = m|υ| 2 /2), thereby reducing the number of variables by one. This allows us to describe the dependency of flux more simply in terms of time and, what we call, the configuration variables (r, υ) ∈ D × V where D ⊆ R 3 is a smooth, open, connected and bounded domain of concern such that ∂D has zero Lebesgue measure and V is the velocity space, which can now be taken to be V = {v ∈ R 3 : υ min < |v| < υ max }, where 0 < υ min < υ max < ∞.

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BOOK REVIEW: "Neutron Noise: A Treatise on the Physics of Branching Processes," I. PÁZSIT and L. PÁL

Cited by 58 publications

References 0 publications

Neutron fluctuations: The importance of being delayed

Neutron fluctuations: The importance of being delayed

Energy Correlation of Prompt Fission Neutrons

Multi-species Neutron Transport Equation

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