Memorandum from Raymond L. Murray and A. C. Menius, Jr. to C. K. Beck
2 pp.
Feb. 16, 1951


Feb 16, 1951

To: C. K. Beck
CC: Members of Reactor


Internal Design of Reactor

The program to date has consisted of determining best values of critical
numbers; these should allow the design to proceed with less fear of serious error.
Those chosen are:

Auxiliary information to the above includes:

Flux: Two-group reactor theorya1 was applied to the water-graphite system as if
it were a sphere. Since this method lumps all fast neutrons into a single
"group", the predicted critical U235 mess of 0.96 kg (compared with the Los Alamos
value of .87kg) is rather good. The thermal flux at the edge of the core computed
was 3.75 x 1011 neutrons/cm²/sec as compared with tho Los Alamos value of 3 x 1011.
The theoretical attenuation in the graphite of the reflector and thermal column was
; empirical treatment of actual data gives .
The Los Alamos values are adopted without reservation on the basis of this agreement.

The [gamma]-flux may be estimated from the 10 kw power level, the number of [gamma]'s
per fission and the area of the container. A figure of 5.4 x 1011/cm²/sec of 2 MoV
energy is used.

Tolerances: The present accepted levels are: slow neutrons 1500/cm²/sec; 2 MoV [gamma]
rays 1050/cm²/sec. Those correspond to a 0.1 r/8 hour day.

Attenuation of [gamma] rays: Inverse-square spreading exponential attenuation is
assumed, with absorption coefficients ([mu] in o-[mu]x, where x
is in cm) as follows:

concrete0.09for ordinary type
0.19for "heavy" type

Attenuation of slow and fast neutrons: Data from various sources diff or widely.
All predictions, however give safety with
a 6' Shield if the concrete is "heavy". Further investigation is needed.

Thickness of concrete shield: A tentative choice of a 5 ft diameter central cavity
filled with graphite relector end the core, with the
overall dimension of 17 feet, leaves a shield thickness of 6 feet. This is proposed
as fixed unless safety is questionable, which is not the case. From the standpoint
of [gamma] rays, the effects of reflector graphite, shield concrete (ordinary type) and

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distance, reduce the flux from 5.4 x 1011 to less than 1 [gamma]/cm²/sec. From another
viewpoint the necessary thickness to reach tolerance levels is approximately 4 ft,
so a two foot safety margin is provided.

Thickness of reflector: In order to satisfy two requirements (a) a low critical
U235 mass and (b) a maximum thermal flux at the core surface,
the largest practical thickness is used. This seems to be 20". The rate of change
of critical radius and the rate of change of the ratio of wall flux to central flux
were computed by one-group theory. With this thickness, the critical volume differs
by only 3% from that for infinite graphite; the flux is within 5% of the ultimate.

Thermal column length: To achieve a length compatible with the Los Alamos reactor,
it is indicated that the end should be located near the out-
surface of the octagon, with a movable concrete slab external to the reactor
shield. If the Cd shield at the end is used, a built-in Pb block shield is needed
to stop the [gamma]'s from Cd; if Boron instead were the neutron shield, the Pb could be
eliminated. A 7 foot thermal column can easily be obtained in the space.

Load shield outside the reflector: If the thermal neutron flux from the end of the
column is to be free of reactor [gamma]'s a lead
shield must be inserted, presumably next to the reflector. One question that must
be decided is - What is [gamma] free? A slab 2" thick will cut the flux to [~=] 1400/cm²/
sec, slightly above health tolerance; a 4" slab will cut it to [~=] 110 or 1/60
tolerance. It is found that little thermal neutron absorption is encountered in
either case. Even in 4" of Pb the flux is reduced by only 6%. (The alternative, Bi,
absorbs 93% in a 4" section.)

Problems yet to be looked into further by means of calculations are listed:

Raymond L. Murray
A. C. Menius, Jr.


a1Soodak, H., Campbell, E. C., Elementary Pile Theory, Wiley (1950), p. 56.