Memorandum from R. L. Murray to Dr. Clifford K. Beck

%MurNBeffect070551; ]> Memorandum from R. L. Murray to Dr. Clifford K. Beck [a machine-readable transcription] Murray, Raymond L. Creation of machine-readable version: Russell S. Koonts Creation of digital images: Russell S. Koonts Conversion to TEI.2-conformant markup: NCSU Science and Technology Electronic Text Center. ca. 9 kilobytes NCSU Libraries. Raleigh, NC. Modern English, MurNBeffect070551

Available from: NC State University Archives

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URL: http://www.lib.ncsu.edu/archives/etext/engineering/reactor/murray/

2000

Nuclear Reactor Digitization Project

Raymond L. Murray Reactor Project Notebook

Illustrations have been included from the print version. Scanned by Russell Koonts with Photoshop 5.0 software. Memorandum from R. L. Murray to Dr. Clifford K. Beck <author>Raymond L. Murray</author> <respStmt> <resp/> <name/> </respStmt> </titleStmt> <editionStmt> </editionStmt> <extent>1 p.</extent> <publicationStmt> <publisher></publisher> <pubPlace></pubPlace> <date></date> <idno>Manuscript copy consulted: NCSU Libraries call number UA105.16</idno> </publicationStmt> <seriesStmt> </seriesStmt> <notesStmt> <note></note> </notesStmt> </biblFull> </sourceDesc> </fileDesc> <encodingDesc> <projectDesc> Prepared for the NCSU Libraries Science and Technology Electronic Text Project. </projectDesc> <editorialDecl> Spell-check and verification made against printed text using Notetab spell checker. The lineation of the manuscript has been maintained and all end-of-line hyphens have been preserved. The images exist as archived TIFF images, one or more JPEG versions for general use, and thumbnails. Keywords in the header are a local Electronic Text Center scheme to aid in establishing analytical groupings. </editorialDecl> <refsDecl> ID elements are given for each page element and are composed of the text's unique cryptogram and the given page number, as in NEprop033050a for the title page of Clifford Beck's Proposal. </refsDecl> <classDecl> <taxonomy id="LCSH"> <bibl> <title>Library of Congress Subject Headings July 5, 1951 English non-fiction; prose LCSH 24-bit color; 400 dpi Memorandum from R. L. Murray to Dr. Clifford K. Beck Typescript 2 pp. July 5, 1951 MurNBeffect070551

MurrayJuly 5, 1951NCSC-23 TO: Clifford K. Beck FROM: R. L. Murray COPIES TO: Reactor Committee SUBJECT: Effect of Pb and Bismuth in Thermal Column.

Information was received from Los Alamos that there was a factor of 10 dif- ference in neutron flux at the end of the thermal column between the cases of lead and bismuth gamma shielding. The shield thickness used there is 8"; our calculations had indicated that 4" of Pb was adequate, for which it had been thought that the neutron attenuation was not serious.

As a check on the Los Alamos quotations however, the flux values are computed, for an 8" spherical shell, as sketched below.

Analysis: the flux equations for the carbon and shield are

where K takes on the value Kc in carbon, Ks in the shield

In the three regions, solutions are assumed

Where the thermal column is assumed to be infinite in extent for calculation purposes.

Boundary conditions are taken as follows: φI = 1 at the surface of the core. Normalization to any known value can be made later.

A comparison between the coefficients E for lead and bismuth serves to de- termine the relative attenuation, since the shape of the flux curve will be the same in the two cases.

By the application of standard, methods of solution (Soodak and Campbell) including calculation of the K's (reciprocals of the thermal neutron diffusion lengths) and the λ's (transport mean free paths), the coefficient E is computed.

The general solution is:

where =

, and

The constants used were: Kc = 0.020 cm-1 ; λc = 2.72 cm r1 = 66 cmKpb = 0.085 cm-1 ; λPb = 2.33 cm r2 = 86.3 cmKBi = 0.0187 cm-1; λBi = 3.85 cm

For the case of 8" of lead, E is 0.185; for 8" of bismuth E is approximately 1, (which is expected because the diffusion lengths for C and Bi are about the same). Thus the flux with a lead shield is about 1/5 that with a bismuth shield. No account is taken of impurities in either case. A separate calculation with a 4" lead shield leads to a factor of 1/3, which would not be too serious a drop. The problem thus rests on the necessary shield thickness for protection against gammas.