Spatial Effects in Low Neutron Source Start-up and Associated Stochastic Phenomena

This work concerns the calculation of the neutron source strength necessary to start up a nuclear reactor such that the likelihood of an undesirable stochastic transient is reduced to a specified value (e.g. 10−8). We extend our earlier point model work on low source calculations to include the spatial variation of the neutron source. Results for the source multiplier for a given safety factor are obtained for slab, cylindrical and spherical systems. The spatial term in the Pál-Bell equation is dealt with by Chebyshev-Gauss-Lobatto collocation methods and this enables an extrapolation distance to be included, thereby simulating a reflector. Results are given for a range of system sizes, and corresponding source multipliers for safe source determination are obtained. The saddlepoint method is used to invert the generating function. In addition to the low source calculations, we have also tested the collocation method on the survival probability in a sphere which demonstrates excellent convergence. We also comment on the usefulness of the Gamma pdf for spatially dependent problems. For clarity of presentation, some of the detailed mathematical work is relegated to Appendices

The energy dependent Pál–Bell equation and the influence of the neutron energy on the survival probability in a supercritical medium

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CALLISTO-SPK: A Stochastic Point Kinetics Code for Performing Low Source Nuclear Power Plant Start-up and Power Ascension Calculations

This paper presents the theory and application of a code called CALLISTO which is used for performing NPP start-up and power ascension calculations. The CALLISTO code is designed to calculate various values relating to the neutron population of a nuclear system which contains a low number of neutrons. These variables include the moments of the PDF of the neutron population, the maturity time and the source multiplier. The code itself is based upon the mathematics presented in another paper and utilises representations of the neutron population which are independent of both space and angle but allows for the specification of an arbitrary number of energy groups. Five examples of the use of the code are presented. Comparison is performed against results found in the literature and the degree of agreement is discussed. In general the agreement is found to be good and, where it is not, plausible explanations for discrepancies are presented. The final two cases presented examine the effect of the number of neutron groups included and finds that, for the systems simulated, there is no significant difference in the key results of the code

Wetting-induced volumetric collapse of UO2 powder beds and the consequence on transient nuclear criticality excursions

Mathematical and computational models are proposed to simulate wetting-induced volumetric collapse of fissile powder beds. Slumping, nuclear thermal hydraulics, radiolytic gas, and steam production models are coupled with point neutron kinetics to investigate transient nuclear criticality excursions in two 5-wt% enriched UO2 fissile powder beds with varying levels of wetting-induced volumetric collapse. The two beds are distinguished by their mean powder particle size of 30 μm and 100 μm. For the UO2 powder beds modelled, the re-distribution of UO2 powder and moderator due to slumping introduced a negative reactivity into the system. This increased the amount of time taken for a delayed critical state to be reached once infiltration began, and also reduced the total fission energy generated over the course of the simulated transient. The total fission energy generated ranged from 42 MJ to 48 MJ 100 seconds after the initial nuclear criticality excursion was observed for the 30 μm sized UO2 powder bed. The fission energy of the larger sized powder bed (100 μm), varied from 42 MJ to 57 MJ. Larger discrepancies between the slumped and un-slumped initial peak power are predicted. Peak powers varied from 29.2 MW to 106 MW for the smaller-sized powder particles, whereas for larger particles, the peak powers varied from 255 MW to 501 MW

Transient nuclear criticality excursion analysis of highly dispersed particulate three-phase fluidised systems

The aim of this study was to perform sensitivity analysis, investigating how different fluidisation and sedimentation characteristics of three-phase wetted UO2 powder beds, may affect a transient nuclear criticality excursion initiated through the addition of water into a fissile powder bed. This type of postulated nuclear criticality accident scenario may occur in nuclear fuel fabrication facilities when a fire is fought through the use of water, supplied via an automatic or manual fire-suppression system. A similar scenario may also develop as a result of water leaks or flooding of the process area housing UO2 powder. The article introduces a model for gas-bubble induced fluidisation of a UO2 powder bed and examines how this phenomenon may affect the neutron kinetic response of a three-phase fluidised fissile powder system. Empirical analysis has shown that fissile suspensions form agglomerated structures when suspended in water, at agglomerate sizes that range from 18 to 40 . Simulation results indicate that both the critical gas velocity and rate of fluidisation may significantly affect transient nuclear criticality excursion dynamics. The re-distribution of fissile mass into a highly dispersed suspension generally reduces the reactivity of the system, however, depending on the H/U ratio, a positive reactivity may be added to the system. Low Péclet numbers in the suspension suggest that gas-bubble induced motion of the suspension causes a highly dispersive flow field. An oscillatory power response is predicted for low critical gas velocities where the reactivity of the system is predominantly governed by the re-distribution of fissile mass within the system. The frequency of these oscillations is greater for a higher hindered settling rate of powder particles. At a higher critical gas velocity, the transient nuclear criticality excursion is governed by the voidage reactivity feedback, making the response quite independent of fluidisation. In all cases, large volumes of UO2 powder may leave the domain due to overflowing of the suspension. Transient nuclear criticality excursions in UO2 powder beds with a low critical gas velocity are terminated once the bed becomes fully saturated

Numerical comparison of mathematical and computational models for the simulation of stochastic neutron kinetics problems

This paper concerns numerical comparisons between five mathematical models capable of modelling the stochastic behaviour of neutrons in low extraneous (extrinsic or fixed) neutron source applications. These models include analog Monte-Carlo (AMC), forward probability balance equations (FPB), generating function form of the forward probability balance equations (FGF), generating function form of the backward probability balance equations (P´al-Bell), and an Itˆo calculus model using both an explicit and implicit Euler-Maruyama discretization scheme. Results such as the survival probability, extinction probability, neutron population mean and standard deviation, and neutron population cumulative distribution function have all been compared. The least computationally demanding mathematical model has been found to be the use of the P´al-Bell equations which on average take four orders of magnitude less time to compute than the other methods in this study. The accuracy of the AMC and FPB models have been found to be strongly linked to the computational e ciency of the models. The computational e ciency of the models decrease significantly as the maximum allowable neutron population is approached. The Itˆo calculus methods, utilising explicit and implicit Euler-Maruyama discretization schemes, have been found to be unsuitable for modelling very low neutron populations. However, improved results, using the Itˆo calculus methods, have been achieved for systems containing a greater number of neutrons

Development and verification of a one-dimensional collision probability based neutron transport code to model axially heterogeneous cylindrical vessels containing aqueous and organic plutonium nitrate

This paper presents the development and verification of a collision probability (CP) code, capable of modelling neutron transport in one-dimensional slabs and axially heterogeneous cylinders with varying radii. The CP code is used to model layered systems of aqueous and organic plutonium nitrate, as process criticality accidents are more likely to occur in these systems compared to dry systems. The use of the CP code is desired as it offers a computationally inexpensive method for calculating neutron transport when compared to higher fidelity codes such as MCNP. For slab geometries, the CP code can be used effectively, given they contain at least 0.7 g cm−2 plutonium. The approximation employed by the CP code to model heterogeneous cylinders overestimated the rate of radial neutron leakage such that vessels with radii of 30.0 cm could not reliably calculate reactivity to within 1 $of MCNP. Increasing the radii to 40.0 cm improved the accuracy of the CP code to within 1$ of MCNP for systems containing at least 2.75 kg plutonium. The error in the CP code increased when used to model cylindrical geometries with dished ends and complete vessels with dished ends, such that systems with large dished ends and low plutonium content should be avoided. As a simple, neutronics based model, the CP code could be used as part of rough order of magnitude calculations for criticality transients, where high levels of accuracy are not required, given that potential errors in results have been previously identified

Search for new phenomena in final states with an energetic jet and large missing transverse momentum in pp collisions at √ s = 8 TeV with the ATLAS detector

Results of a search for new phenomena in final states with an energetic jet and large missing transverse momentum are reported. The search uses 20.3 fb−1 of √ s = 8 TeV data collected in 2012 with the ATLAS detector at the LHC. Events are required to have at least one jet with pT > 120 GeV and no leptons. Nine signal regions are considered with increasing missing transverse momentum requirements between Emiss T > 150 GeV and Emiss T > 700 GeV. Good agreement is observed between the number of events in data and Standard Model expectations. The results are translated into exclusion limits on models with either large extra spatial dimensions, pair production of weakly interacting dark matter candidates, or production of very light gravitinos in a gauge-mediated supersymmetric model. In addition, limits on the production of an invisibly decaying Higgs-like boson leading to similar topologies in the final state are presente

Conservation of freshwater bivalves at the global scale: diversity, threats and research needs

Bivalves are ubiquitous members of freshwater ecosystems and responsible for important functions and services. The present paper revises freshwater bivalve diversity, conservation status and threats at the global scale and discusses future research needs and management actions. The diversity patterns are uneven across the globe with hotspots in the interior basin in the United States of America (USA), Central America, Indian subcontinent and Southeast Asia. Freshwater bivalves are affected by multiple threats that vary across the globe; however, pollution and natural system (habitat) modifications being consistently found as the most impacting. Freshwater bivalves are among the most threatened groups in the world with 40% of the species being near threatened, threatened or extinct, and among them the order Unionida is the most endangered. We suggest that global cooperation between scientists, managers, politicians and general public, and application of new technologies (new generation sequencing and remote sensing, among others) will strengthen the quality of studies on the natural history and conservation of freshwater bivalves. Finally, we introduce the articles published in this special issue of Hydrobiologia under the scope of the Second International Meeting on Biology and Conservation of Freshwater Bivalves held in 2015 in Buffalo, New York, USA.This work was supported by FCT—Foundation for Science and Technology, Project 3599—Promote the Scientific Production and Technological Development and Thematic 3599-PPCDT by FEDER as part of the project FRESHCO: multiple implications of invasive species on Freshwater Mussel co-extinction processes (Contract: PTDC/AGRFOR/1627/2014). FCT also supported MLL under Grant (SFRH/BD/115728/2016)