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SUBJECT: Water Window Thickness A. Thermal Column

The position of the window relative to the thermal column and nearest

exposure port is shown below:

To obtain the order of magnitude of radiation at the window scattered

from the thermal beam, a calculation of the flux at the point P (see figure

above) was made.

The flux at this point due to the scattering from a volume d[sigma]d[chi] is

given by

in which we have taken the probability of the neutron reaching P after

scattering to be unity. This is realistic in that the mean free path in

air for the neutron is several thousand centimeters. Also [phi] is considered

constant along [chi]. This is a good approximation and is on the safe side.

The above equation can be written as

Assuming that the increase in the [phi]s contribution on the left of the

center line in beam will nearly be compensated by decrease on the right, we

may

The average number of atoms will be

= 0.89 x 6 x 1019 = 5.4 x 1019

and since the weighted (O and N) thermal scattering cross-section is

about 9 x 10-24 cm², we have

[sigma]s = 4.9 x 10-4

Assuming a 4' x 4' beam with a flux of 107 m/cm²sec and Ro = 19' we have

at a point 7' from the edge of window a flux of

= 2.5 x 104 m/cm²sec

The above value is based upon calculations assuming a collimated bean.

This will not be exactly true. For a bean which is not collimated we can

write

= 3.5 x 104 n/cm²sec.

The correct value will be somewhere between the two. Assuming the

larger value to be correct and a tolerance of 1000 n/sec cm² for thermal

neutrons, the window thickness should be given by

This leads to a thickness of

x = 10cm.

At the experimental ports when open there will be a collimated flux of

2 x l08 n/cm²sec for fast neutrons and 1.2 x 107 n/cm²sec. slow neutrons.

Substituting in the first equation with A = 180 cm² and [sigma]s = 5.4 x 10-3

= 720 n/cm²sec

Since H20 is comparable to Portland cement in attenuation of fast

neutrons, a 6" window will reduce the fast neutron component below tolerance.

The slow neutron flux at the window will be given by

[~=] 3.25 x 104 n/cm²sec.

Adding to this the fast neutron flux which has been assumed thermalized

gives a window thickness as before of ~ 10 cm.

To be completely safe it is believed a window of 6 inches should be

used with Borax added to enhance slow neutron absorption as well as some

fast.