COPIES TO: Reactor Committee
SUBJECT: Effect of Pb and Bismuth in Thermal Column.
Information was received from
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
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
Boundary conditions are taken as follows:
[phi]I = 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
the same in the two cases.
By the application of standard, methods of solution (
including calculation of the K's (reciprocals of the thermal neutron diffusion
lengths) and the [lambda]'s (transport mean free paths), the coefficient E is
The general solution is:
The constants used were:
|Kc = 0.020 cm-1 ;||[lambda]c = 2.72 cm||r1 = 66 cm|
|Kpb = 0.085 cm-1 ;||[lambda]Pb = 2.33 cm||r2 = 86.3 cm|
|KBi = 0.0187 cm-1;||[lambda]Bi = 3.85 cm|