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AbstractAbstract

[en] Investigations of the properties of the multigroup transport operator, width and without delayed neutrons in the diffusion and P

_{1}approximation, is performed using Keldis's theory of operator families as well as a technique . recently used for investigations into the properties of the general linearized Boltzmann operator. It is shown that in the case without delayed neutrons, multigroup transport operator in the diffusion and P_{1}approximation possesses a complete set of generalized eigenvectors. A formal solution to the initial value problem is also given. (author)Primary Subject

Secondary Subject

Source

1970; v. 2, 22 p; Fizika; Beograd (Yugoslavia); Also available from the Institute of nuclear sciences Vinca; 16 refs.

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Miscellaneous

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Carlvik, I.

AB Atomenergi, Nykoeping (Sweden)

AB Atomenergi, Nykoeping (Sweden)

AbstractAbstract

[en] Analytical formulae have been derived for the collision probabilities of homogeneous finite cylinders and cuboids. The formula for the finite cylinder contains double integrals, and the formula for the cuboid only single integrals. Collision probabilities have been calculated by means of the formulae and compared with values obtained by other authors. It was found that the calculations using the analytical formulae are much quicker and give higher accuracy than Monte Carlo calculations

Primary Subject

Source

May 1967; 32 p; 5 refs., 8 figs., 4 tabs.

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Report

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Carlvik, I.

AB Atomenergi, Nykoeping (Sweden)

AB Atomenergi, Nykoeping (Sweden)

AbstractAbstract

[en] A method called DIT (Discrete Integral Transport) has been developed for the numerical solution of the transport equation in one-dimensional systems. The characteristic features of the method are Gaussian integration over the coordinate as described by Kobayashi and Nishihara, and a particular scheme for the calculation of matrix elements in annular and spherical geometry that has been used for collision probabilities in earlier Flurig programmes. The paper gives a general theory including such things as anisotropic scattering and multi-pole fluxes, and it gives a brief description of the Flurig scheme. Annular geometry is treated in some detail, and corresponding formulae are given for spherical and plane geometry. There are many similarities between DIT and the method of collision probabilities. DIT is in many cases faster, because for a certain accuracy in the fluxes DIT often needs fewer space points than the method of collision probabilities needs regions. Several computer codes using DIT, both one-group and multigroup, have been written. It is anticipated that experience gained in calculations with these codes will be reported in another paper

Source

Jun 1966; 70 p; 14 refs., 15 figs., 1 tab.

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Report

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AbstractAbstract

[en] The objective of this work was development of adequate method for solving the space-energy dependent neutron transport equation to obtain faster and more efficient methods for calculating the depletion of fuel during burnup. A method of space-energy points was chosen. In applying this method for calculating the burnup it was necessary to calculate the collision probabilities for space zones. The equations obtained are presented in this paper and can be directly used for programming and numerical solution

Original Title

Verovatnoce sudara za koncentricne cilindricne zone

Primary Subject

Source

Nov 1967; 12 p; IBK--598; Also available from the Institute of nuclear sciences Vinca; 18 refs, 4 figs

Record Type

Miscellaneous

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INIS VolumeINIS Volume

INIS IssueINIS Issue

Carlvik, I.

AB Atomenergi, Nykoeping (Sweden)

AB Atomenergi, Nykoeping (Sweden)

AbstractAbstract

[en] Flux distributions have been calculated mainly in one energy group, for a number of systems representing geometries interesting for reactor calculations. Integral transport methods of two kinds were utilised, collision probabilities (CP) and the discrete method (DIT). The geometries considered comprise the three one-dimensional geometries, planes, sphericals and annular, and further a square cell with a circular fuel rod and a rod cluster cell with a circular outer boundary. For the annular cells both methods (CP and DIT) were used and the results were compared. The purpose of the work is twofold, firstly to demonstrate the versatility and efficacy of integral transport methods and secondly to serve as a guide for anybody who wants to use the methods

Primary Subject

Source

May 1967; 100 p; 48 refs., 26 figs., 31 tabs.

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Report

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Sjoestrand, N.G.

AB Atomenergi, Nykoeping (Sweden)

AB Atomenergi, Nykoeping (Sweden)

AbstractAbstract

[en] A one-group transport equation is derived from the general Boltzmann equation with the sole assumption that the neutron velocity spectrum is independent of position and angle. It is shown that the correct way to define a diffusion constant is to form averages of the scattering cross section, not the mean free path, over the neutron spectrum. Conclusions are also drawn regarding the equivalence between moderator systems studied with pulsed neutron sources and critical reactors and regarding possible systematic differences in diffusion constants derived from stationary and pulsed source experiments. Finally, an accurate equation for the neutron spectrum is derived

Primary Subject

Source

Apr 1970; 16 p; 5 refs.

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Report

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AbstractAbstract

[en] The principle of the curved neutron guide is to transport neutrons far away from the reactor core with as minimum particle loss as possible. After a series of total reflection,the neutron beam is no longer visible from the reactor core and consequently, gamma radiations and fast neutrons emitted from the core are scattered by the walls of the guide and absorbed by the biological shielding set around the guide. The curved neutron guide provides a high-quality beam of slow neutrons. The first chapter deals with the theoretical concept of curved guide, we have determined the parameters for the setting of such a guide in the EL3 reactor at Saclay (France). The different tolerances on the state the surface, on the alignment of the different parts of the guide, on the waving of the guide wall have been assessed. The second chapter presents the technical solution chosen that complies to all the required specifications. The curved neutron guide has been designed for neutrons with wavelength of 4 Angstroms, it is 29 m long, has a bending radius of 835 m and is composed of 87 rectangular components made of glass plates on which a 1500 angstrom thick layer of nickel has been deposited. Each component is set with a fixed angle of (4±0.25)*10

^{-4}radians from the previous component in order to form the bending radius. The last chapter is dedicated to the neutron flux measurement made at the end of the neutron guideOriginal Title

Guide courbe conducteur de neutrons

Primary Subject

Source

4 Mar 1969; 110 p; 8 refs.; Available from the INIS Liaison Officer for France, see the 'INIS contacts' section of the INIS website for current contact and E-mail addresses: http://www.iaea.org/inis/Contacts/; These Docteur de l'Universite, Mention Sciences

Record Type

Report

Literature Type

Thesis/Dissertation

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Londen, S.O.

AB Atomenergi, Nykoeping (Sweden)

AB Atomenergi, Nykoeping (Sweden)

AbstractAbstract

[en] The reactivity effects of small samples of various materials have been measured, by the period method at the core centre of Assemblies 1 and 3 of the fast zero power reactor FR0. For some materials the reactivity change as a function of sample size has also been determined experimentally. The core of Assembly 1 consisted only of uranium enriched to 20 % whereas the core of Assembly 3 was diluted with 30 % graphite. The results have been compared with calculated values obtained with a second-order transport-theoretical perturbation model and using differently shielded cross sections depending upon sample size. Qualitative agreement has generally been found, although discrepancies still exist. The spectrum perturbation caused by the experimental arrangement has been analyzed and found to be rather important

Primary Subject

Source

Jan 1966; 66 p; 30 refs., 25 figs., 7 tabs.

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Report

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Nguyen-Ngoc, H.

CEA Saclay, 91 - Gif-sur-Yvette (France)

CEA Saclay, 91 - Gif-sur-Yvette (France)

AbstractAbstract

[en] In order to reduce computing time, two and three-dimensional multigroup neutron diffusion equations in cylindrical, rectangular (X, Y), (X, Y, Z) and hexagonal geometries are solved by the method of synthesis using an appropriate variational principle (stationary principle). The basic idea is to reduce the number of independent variables by constructing two or three-dimensional solutions from solutions of fewer variables, hence the name 'synthesis method'. Whatever the geometry, we are led to solve a system of ordinary differential equations with matrix coefficients to which one can apply well-known numerical methods: CHEBYSHEV's polynomial method, Gaussian elimination. Numerical results furnished by synthesis programs written for the IBM 7094, the IBM 360-75 and the CDC 6600 computers, are confronted with those which are given by programs employing the classical finite difference method

[fr]

En vue de reduire le-temps de calcul, les equations de diffusion neutronique, multigroupe, a deux et trois dimensions d'espace dans les geometries cylindrique, rectangulaire (X, Y), (X, Y, Z) et hexagonale sont resolues par la methode de synthese utilisant un principe variationnel approprie (principe stationnaire). L'idee consiste a reduire le nombre de variables independantes par construction d'une solution bi ou tridimensionnelle au moyen de solutions dependant d'un nombre inferieur de variables, d'ou le nom de la methode. Dans tous les cas de geometrie, nous sommes conduits a resoudre un systeme d'equations differentielles a coefficients matriciels auquel peuvent s'appliquer les methodes numeriques courantes; methode polynomiale de TCHEBYCHEFF et methode d'elimination de GAUSS. Les resultats numeriques obtenus par nos codes de synthese programmes sur IBM 7094, IBM 360-75 et CDC 6600, sont confrontes avec ceux que fournissent les programmes adoptant la methode classique des differences finies. (auteur)Original Title

Synthese spatiale: une application de la methode de synthese aux equations de diffusion neutronique multigroupe a deux et trois dimensions

Primary Subject

Source

1969; [68 p.]

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Report

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AbstractAbstract

[en] Previously published collision probability method for calculation thermal neutron flux distribution in cylindrical reactor cell, was developed for multigroup neutron transport calculation in this paper. As in case of thermal neutrons basic efficiency of this method is: Spatial distribution of neutron flux as a solution of integral transport equation, for a particular energy group and particular material region is determined in form of series expansion of even exponents of radius. Computer code SPEKTAR for ZUSE-Z-23K computer was written based on this method, using group cross sections from the literature. Test case was the problem of fast fission in the RA reactor cell

[sr]

Ranije publikovana metoda verovatnoce sudara za odredjivanje raspodele termalnog neutronskog fliksa u cilindricnoj reaktorkoj celiji osposobljena je u ovom radu za visegrupni proracun transporta neutrona. Kao i pri tretiranju termalne grupe neutrona osnovna postavka koja ovu metodu cini efikasnom je: prostorna raspodela neutronskog fluksa kao resenje integralne transportne jednacine, za odredjenu energetsku grupu neutrona i za odredjenu prostornu materijalnu zonu, trazimo u obliku reda po parnim stepenima radijusa. Na osnovu ove metode, koristeci grupne preseke iz literature, napravljen je program SPEKTAR za racunsku masinu ZUSE-Z 23K. Kao test proracun tretiran je problem brze fisije u celiji reaktora RA u VinciOriginal Title

Resenja enegretski zavisne integralne transportne jednacine u cilindicnoj geometriji

Primary Subject

Source

1970; 10 p; IBK--940; Also available from the Institute of nuclear sciences Vinca; 3 figs., 2 refs.

Record Type

Miscellaneous

Report Number

Country of publication

CALCULATION METHODS, COMPUTER CODES, CROSS SECTIONS, ENRICHED URANIUM REACTORS, HEAVY WATER COOLED REACTORS, HEAVY WATER MODERATED REACTORS, IRRADIATION REACTORS, ISOTOPE PRODUCTION REACTORS, MATHEMATICAL SOLUTIONS, NEUTRON TRANSPORT THEORY, NUMERICAL SOLUTION, REACTORS, RESEARCH AND TEST REACTORS, RESEARCH REACTORS, TANK TYPE REACTORS, THERMAL REACTORS, TRANSPORT THEORY

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