NCSC-20

TO:

FROM:

SUBJECT: Reactor Size and Mass

It has been suggested that changes in the volume of the reactor core

from the original proposal be made to

Consideration should be given to the following facts, however:

- 1. The critical mass is a rather insensitive function of the water content

in the region around NH/NU= 400. An estimate of the variation from

the minimum, Mo, from bare-reactor theory

is plotted in Figure 1. Taking the minimum critical mass to occur at

NH/NU = 360, there is no more than a 10% increase in going as low as

250 or as high as 470. - 2. The solution volume for a given mass of uranium varies inversely with

the NH/NU ratio. Neglecting the presence of other elements and ignoring

displacement, the relation is

The variation of volume is plotted on the same graph, using the relation

The conclusion is that if the critical mass of the

is actually higher than the expected 915 grams, the excess material may still be

easily

On the other hand, if the mass turns out to be lower, the mixture can be diluted

to fit the vessel.

Calculations leading to the formulas appear in the Appendix.

Assumptions:

- 1. Bare spherical reactor of critical radius R, with pure U-235 in water.
- 2. Critical equation

where k is the infinite multiplication constant, [eta]f, where [eta] = 2.1,

systems in the range of - 3. Ratio of mass of U-235 to mass (and volume) of water

- 4. Volume and mass of water

Analysis:

- 1. Assume cross sections [sigma]U = 640 barns , [sigma]H = 0.31 barns.
- 2. Solve equations (1), (2) and (3) for MU, using the approximation that

- 3. The minimum of this function occurs when the two terms in the denominator

are equal, ie at NH/NU = 360 , which checks experiment fairly well.

At that point MU = 3.2 kg = Mo which is a reasonable bare reactor mass. - 4. The ratio of M in general to the minimum mass, as quoted in the body

of this note, is computed to be - 5. The volume ratio is obtained from equations (2), (3), (5) as