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Licensed Unlicensed Requires Authentication Published by De Gruyter February 28, 2022

Solution of the multilayer multigroup neutron diffusion equation in cartesian geometry by fictitious borders power method

Lösung der stationären Multigruppen- und Mehrbereichs-Neutronendiffusionsgleichung in kartesischer Geometrie mit Hilfe der Potenzmethode
  • R. Zanette EMAIL logo , C. Z. Petersen , M. Schramm and J. R. Zabadal
From the journal Kerntechnik


In this paper a solution for the one-dimensional steady state Multilayer Multigroup Neutron Diffusion Equation in cartesian geometry by Fictitious Borders Power Method and a perturbative analysis of this solution is presented. For each new iteration of the power method, the neutron flux is reconstructed by polynomial interpolation, so that it always remains in a standard form. However when the domain is long, an almost singular matrix arises in the interpolation process. To eliminate this singularity the domain segmented in R regions, called fictitious regions. The last step is to solve the neutron diffusion equation for each fictitious region in analytical form locally. The results are compared with results present in the literature. In order to analyze the sensitivity of the solution, a perturbation in the nuclear parameters is inserted to determine how a perturbation interferes in numerical results of the solution.


In diesem Beitrag wird eine Lösung stationären Multigruppen- und Mehrbereichs-Neutronendiffusionsgleichung in kartesischer Geometrie durch die Potenzmethode der fiktiven Grenzen und eine Störungsanalyse dieser Lösung vorgestellt. Für jede Iteration der Potenzmethode wird der Neutronenfluss rekonstruiert durch polynomiale Interpolation, so dass er stets in der Normaldarstellung bleibt. Wenn jedoch der Definitionsbereich lang ist, erscheint eine fast singuläre Matrix in dem Interpolationsprozess. Um diese Singularität zu beseitigen, wird der Bereich in R-Regionen aufgeteilt, sogenannte fiktive Regionen. Der letzte Schritt ist die Lösung der Neutronendiffusionsgleichung für jedes fiktive Gebiet lokal in analytischer Form. Die Ergebnisse werden mit den Ergebnissen der Literatur verglichen. Zur Sensitivitätsanalyse der Lösung wird eine Störung in die Kerneckdaten eingeführt. So kann ermittelt werden, wie eine Störung die numerischen Ergebnisse der Lösung beeinflusst.


The first author is grateful indebted to Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Brazil for the financial support.


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Books · Bücher

Cosmic Ray Neutron Sensing: Use, Calibration and Validation for Soil Moisture Estimation. IAEA-TECDOC-1809, Published by the International Atomic Energy Agency 2017, ISBN 978-92-0-101017-9, 48 pp., 18.00 EUR.

Nuclear and related techniques can help develop climate-smart agricultural practices by optimizing water use efficiency. The measurement of soil water content is essential to improve the use of this resource in agriculture. However, most sensors monitor small areas (less than 1 m in radius), hence a large number of sensors are needed to obtain soil water content across a large area. This can be both costly and labour intensive and so larger scale measuring devices are needed as an alternative to traditional point-based soil moisture sensing techniques. The cosmic ray neutron sensor (CRNS) is such a device that monitors soil water content in a non-invasive and continuous way. This publication provides background information about this novel technique, and explains in detail the calibration and validation process.

This publication was developed as a partial output of the Coordinated Research Project titled: “Landscape Salinity and Water Management for Improving Water Productivity” managed by the Soil and Water Management & Crop Nutrition Subprogramme of the Joint FAO/IAEA Division. This publication is intended to serve as a guideline for scientists, technicians, and students and provides a description of the key characteristics of the technique, a review of recent literature related to its use and field validation, and procedures for installation, calibration, and validation. The data processing procedure is also described and includes corrections based on ancillary measurements of air temperature, relative humidity, and barometric pressure as well as corrections derived from publically available data of solar activity.

This publication is divided into three Chapters. Chapter one provides an introduction to the technique and the physical principles behind its function. It also illustrates the theory and parameters to be considered as well as the associated calculations and calibrations; Chapter two details the appropriate field installation procedures for a general CRNS device and the associated materials; Chapter three provides a step-by-step instruction on field calibration and validation procedures related to the use of the CRNS. Additionally, examples of validation campaigns performed by multiple academic research institutions are provided to demonstrate different validation techniques.

Received: 2017-01-31
Published Online: 2022-02-28

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