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Errors due to the cylindrical cell approximation in lattice calculations

Technical Report:

Abstract

It is shown that serious errors in fine structure calculations may arise through the use of the cylindrical cell approximation together with transport theory methods. The effect of this approximation is to overestimate the ratio of the flux in the moderator to the flux in the fuel. It is demonstrated that the use of the cylindrical cell approximation gives a flux in the moderator which is considerably higher than in the fuel, even when the cell dimensions in units of mean free path tend to zero; whereas, for the case of real cells (e.g. square or hexagonal), the flux ratio must tend to unity. It is also shown that, for cylindrical cells of any size, the ratio of the flux in the moderator to flux in the fuel tends to infinity as the total neutron cross section in the moderator tends to zero; whereas the ratio remains finite for real cells. (author)
Authors:
Newmarch, D A [1] 
  1. Reactor Development Division, Atomic Energy Establishment, Winfrith, Dorchester, Dorset (United Kingdom)
Publication Date:
Jun 15, 1960
Product Type:
Technical Report
Report Number:
AEEW-R-34
Resource Relation:
Other Information: Country of input: International Atomic Energy Agency (IAEA); 2 refs, 2 figs, 2 tabs
Subject:
22 GENERAL STUDIES OF NUCLEAR REACTORS; APPROXIMATIONS; CROSS SECTIONS; CYLINDRICAL CONFIGURATION; ERRORS; MEAN FREE PATH; MODERATORS; NEUTRONS; REACTOR LATTICES; TRANSPORT THEORY
OSTI ID:
20883389
Research Organizations:
United Kingdom Atomic Energy Authority, Reactor Group, Winfrith (United Kingdom)
Country of Origin:
United Kingdom
Language:
English
Other Identifying Numbers:
TRN: GB07A0163048779
Availability:
Available from INIS in electronic form; Also available from H.M. Stationery Office
Submitting Site:
GBN
Size:
26 pages
Announcement Date:
Jul 14, 2007

Technical Report:

Citation Formats

Newmarch, D A. Errors due to the cylindrical cell approximation in lattice calculations. United Kingdom: N. p., 1960. Web.
Newmarch, D A. Errors due to the cylindrical cell approximation in lattice calculations. United Kingdom.
Newmarch, D A. 1960. "Errors due to the cylindrical cell approximation in lattice calculations." United Kingdom.
@misc{etde_20883389,
title = {Errors due to the cylindrical cell approximation in lattice calculations}
author = {Newmarch, D A}
abstractNote = {It is shown that serious errors in fine structure calculations may arise through the use of the cylindrical cell approximation together with transport theory methods. The effect of this approximation is to overestimate the ratio of the flux in the moderator to the flux in the fuel. It is demonstrated that the use of the cylindrical cell approximation gives a flux in the moderator which is considerably higher than in the fuel, even when the cell dimensions in units of mean free path tend to zero; whereas, for the case of real cells (e.g. square or hexagonal), the flux ratio must tend to unity. It is also shown that, for cylindrical cells of any size, the ratio of the flux in the moderator to flux in the fuel tends to infinity as the total neutron cross section in the moderator tends to zero; whereas the ratio remains finite for real cells. (author)}
place = {United Kingdom}
year = {1960}
month = {Jun}
}