Patchy nuclear chain reactions

Abstract

Stochastic fluctuations of the neutron population within a nuclear reactor are typically prevented by operating the core at a sufficient power, since a deterministic (i.e., exactly predictable) behavior of the neutron population is required by automatic safety systems to detect unwanted power excursions. In order to characterize the reactor operating conditions at which the fluctuations vanish, an experiment was designed and took place in 2017 at the Rensselaer Polytechnic Institute Reactor Critical Facility. This experiment however revealed persisting fluctuations and striking patchy spatial patterns in neutron spatial distributions. Here we report these experimental findings, interpret them by a stochastic modeling based on branching random walks, and extend them using a “numerical twin” of the reactor core. Consequences on nuclear safety will be discussed.

On Structural Rearrangements Near the Glass Transition Temperature in Amorphous Silica

“…Configurons that are generated, annihilated, and moving at relatively higher concentrations associate with each other, which is a generic feature of any collection of independent particles that move, reproduce, and die. Indeed, such collections may undergo wild fluctuations at the local and global scales, inducing characteristic patchiness in the spatial distribution of the individuals observed in the spread of epidemics [48][49][50], the growth of bacteria on Petri dishes [51,52], the dynamics of ecological communities [53], the mutation propagation of genes [54], susceptible-infected-removed spreading processes [55], and in the distribution of neutrons in nuclear reactors, which was recently shown to be an effect of clustering [56]. As long as there is a tiny number of small clusters made up of configurons, they can be neglected; however, as the temperature increases, there are more configurons and configuron clusters, which grow in size, and when the threshold value determined by percolation theory [29,57] is reached, a macroscopic percolation cluster of configurons is formed in the system, which penetrates the entire volume of the material.…”

“…The thermodynamic parameters of configurons in amorphous silica are known: H c = 237 kJ/mol and S c = 17.54 R [45], which gives the glass transition temperature of amorphous silica: T g = 1475 K. This temperature practically coincides with the experimentally known temperature T g,exp = 1480 K [1], especially when accounting for the experimental errors [32,65]. The universal critical threshold f c = ϑ c works well for silica and germania [44,45], as well as for many metallic systems [66]; however, for complex oxide systems, f c << 1, which indicates that the percolation threshold is reached at much lower concentrations of broken bonds and the effective configuron radii in these systems are larger [45,67] or there is patchiness of configuron clustering following the generic pattern of dynamic systems [48][49][50][51][52][53][54][55][56]. The formation of stable and ultrastable glasses leads to higher glass transition temperatures.…”

Space and time correlations for diffusion models with prompt and delayed birth-and-death events

“…Although mean-field zero-dimensional approaches can provide a condensed representation of the system dynamics, stochastic models accounting for the full description of the spatial behavior of the population are of utmost importance, in that they are key e.g. to characterizing the extent of epidemic outbursts [11][12][13] or to detecting possible malfunctioning or power tilts in nuclear reactors [3,6,14]. Modern state-of-the-art Monte Carlo simulation codes allow addressing real-world applications with unprecedented accuracy and have been successfully used to compute the lower-order moments of the populations, namely, the average number of individuals E[n V ](t) in a given spatial region V at time t and the two-point correlation function E[n V1 n V2 ](t 1 , t 2 ) between two regions V 1 and V 2 at times t 1 and t 2 [14][15][16][17].…”

“…to characterizing the extent of epidemic outbursts [11][12][13] or to detecting possible malfunctioning or power tilts in nuclear reactors [3,6,14]. Modern state-of-the-art Monte Carlo simulation codes allow addressing real-world applications with unprecedented accuracy and have been successfully used to compute the lower-order moments of the populations, namely, the average number of individuals E[n V ](t) in a given spatial region V at time t and the two-point correlation function E[n V1 n V2 ](t 1 , t 2 ) between two regions V 1 and V 2 at times t 1 and t 2 [14][15][16][17]. The analysis carried out with highly sophisticated simulation codes can be effectively complemented by the investigation of simplified mathematical models that avoid unnecessary complication and yet retain the key physical ingredients, possi-bly leading to semi-quantitative predictions.…”

Improvement of Geant4 Neutron-HP package: from methodology to evaluated nuclear data library

“…To this aim, the nuclear industry and nuclear engineering laboratories have been developing and using for decades dedicated Monte Carlo neutron transport codes, relying on evaluated nuclear data and subsequent nuclear data processing and treatment. Among these neutronics reference codes, MNCP (version 5 [6] and 6 [7]), SCALE [8], SERPENT [9], MORET (version 5 [10] and 6 [11]) or TRIPOLI-4 ® [12] are validated and qualified using inter-code comparisons (see for instance [13]) and large qualification data bases (using either integral or differential experiments). Combined with a large user community, these codes hence present coherent results in their respective qualification domains.…”