Subcritical Multiplication and Spontaneous Fission in Uranium

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Carl Willis
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Subcritical Multiplication and Spontaneous Fission in Uranium

Post by Carl Willis » Fri Nov 18, 2005 5:52 am

I have been working on some experiments whose principal relevance is to obtain measurable subcritical multiplication in uraniferous samples using a large He-3 detector and a small AmBe neutron source as a "driver". The concept is simple (neutron source is near a detector; induced fissions in a uranium sample placed near the source will increase the neutron population in the detector), but in practice this is a tricky measurement and I conclude from the preliminary data (following) that my method would take days of measuring time to get a statistically-significant "positive" for neutron multiplication. However, another interesting finding is that spontaneous fission neutrons from U-238 are easy to measure with the He-3 tube. I'll leave some suggestions for another post about how to improve the technique to better detect induced fission, since this post will be ungodly long for the sake of completeness.

The setup: See two images at bottom. A six-sided moderating reflector is composed of about 120 lb of Astorlite J-300 wax composite (has some vegetable oil mixed with paraffin). This stuff is much easier to cut into bricks than straight paraffin and that's why I used it, but on the downside it is softer and stickier. He-3 tube runs though center. The neutron source (~ 1 mCi AmBe) is rigidly held in graphite blocks at the right of tube. Other side of tube has an empty cavity for uranium samples. The uranium sample used comprised all of the following, in separate plastic bottles:

-26 g. DU metal plate
-4 g. DU metal plate
-20 g. DU3O8
(Total of 47 g uranium)

I could have used pieces of the large quantity of uranium ores on hand, some of which do have 85% non-depleted uranium by weight. I may yet try that, but I think there are large concentrations of neutron absorbers in most of this stuff (cadmium, cobalt, boron, rare earths). Having a few hundred ppm of these in the mix will totally trash a neutron experiment, whereas the loss of 3/4 of the U-235 in pure depleted U is comparably a minor reduction in fission neutron economy. One item that warrants explanation is the large quantity of wax: people might think they could get by with less, but we have to realize that the source and the sample will in reality add some moderating and reflecting capability. The goal of the large wax enclosure is to approach maximum possible reflectivity BEFORE anything else is added next to the tube, so that the reflection from those items is not going to be a significant contribution.

The method: Tube pulses were shaped and amplified (3 us, Ortec 571) and sent to Tracor-Northern MCS. An external timer (Tennelec 536) was used to drive the MCS dwell advance every 3 minutes. The neutron detector signal was aggressively windowed to discriminate against noise, gammas, and whatnot: the LLD was right below the 570 keV "step" in the absorbed-energy spectrum, and the ULD was right above the tail for the full energy peak. The order of the measurements is important because it helps add control to the experiment. In this order, the source and the uranium only need to be physically positioned in the apparatus once to get all the data. Neutron contributions are identified as those from the source (S), background (B), spontaneous fission of U-238 (SF), and induced fission mainly of U-235 (IF). The count results shown below are averages and standard deviations per three minute interval. Different numbers of samples were used for different experiments.

1. Empty sample chamber, source in (measure S + B). Result: 1057.2 +/- 2.3
2. Uranium in sample chamber, source in (measure IF + SF + S + B). Result: 1066.1 +/- 2.1
3. Uranium in sample chamber, source out (measure SF + B). Result: 19.6 +/- 0.24
4. Empty sample chamber, source out (measure B). Result: 13.80 +/- 0.31
5. 5 uCi Ra-226 ionotron strip against tube, source out (test gamma sensitivity G). Result: 13.87 +/- 0.17

The analysis and results: To isolate the IF component, the counts from Measurement 4 are first subtracted from Measurement 1 to isolate (S), taking care of course to propagate the uncertainties from the raw data through the subtraction; Measurement 3 is subtracted from Measurement 2 to isolate (IF + S); (IF + S) is compared to (SF) using MS Excel's t-test tool (with the null hypothesis being that <S> = <IF + S>) and the probability of a difference in these means due to chance alone is determined. It was noticed then that <SF + B> looked significantly larger than <B> and the t-test between the two was used to find the approximate probability of that difference being due to chance. (It turns out to be miniscule.) Lastly, we do the t-test between Measurement 5 and Measurement 4. The null hypothesis is accepted here, since there is a very large probability (>78%) that these measurements are not different from one another.

Subcricital multiplication:
S = 1043.4 +/- 2.3
IF + S = 1046.5 +/- 2.1
From Excel:
t Stat 0.994998
P(T<=t) one-tail 0.160149
P(T<=t) two-tail 0.320298

Spontaneous fission:
SF + B = 19.6 +/- 0.24
B = 13.80 +/- 0.31
From Excel:
t Stat 15.23779
P(T<=t) one-tail 6.73E-41
P(T<=t) two-tail 1.35E-40

Gamma rejection:
G = 13.87 +/- 0.17
B = 13.80 +/- 0.31
From Excel:
t Stat 0.27627
P(T<=t) one-tail 0.391292
P(T<=t) two-tail 0.782584

Conclusion: You'll notice that while <IF + S> is indeed larger than <S>, it is only by about 3 counts per interval. Maybe this is due to induced fission, and maybe it is just due to statistical chance. You can consider either the one-sided or two-sided probability of the measurements being not different, but either way they're rather large (16% or 32%). This is high enough that I can't say with much certainty that the difference is due to subcritical multiplication. The remedy to clear this up would be many more sample intervals. As it was, the combined measurement had 454 3-minute intervals, so it was already almost a day long. ON THE OTHER HAND, there is almost absolute certainty that <SF + B> and <B> are statistically different, giving a very strong case for spontaneous fission being measured to the tune of 2 extra counts per minute. Literature reports that U-238 gives about 0.011 n / g / s through SF, or about 30 n / minute for my sample, so the absolute detection efficiency is probably somewhere in the range of 1/15. That ain't bad for fast fission neuts. Lastly, the gamma rejection is very good. The radium source used is a much stronger beta/gamma source than the non-equilibrium uranium materials (even though the latter represents a higher total activity, ~25 uCi.). And yet there is a 78% likelihood that <G + B> is no different than <B>. If there ARE any extra counts physically associated with the radium source, my guess is that it is actual neutrons from O(a,n) in the air near it; Al(a,n) on the tube wall; or the like.
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Alex Aitken
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Re: Subcritical Multiplication and Spontaneous Fission in Uranium

Post by Alex Aitken » Fri Nov 18, 2005 2:53 pm

Something I read that stuck, but I then wasn't able to find again was discussing the problems of demonstrating fission to physics students. Or paraphrased as close as possible with my memory a lecturer once put it 'The inherent inability to demonstrate a chain reaction in a room of this size..... more than once.'

What I read described an experiment that would at least show fission. An ordinary air ionisation chamber is prepaired, coating the base plate with a thin layer of natural pitchblende powder. The chamber is then connected to a high gain audio amplifier connected to a speaker. The amp is turned up until the hiss is audable from the constant alpha emission and occasional loud clicks are heard as a result of spontanious fission of U-238. A 'chemical' neutron source is then brought in embedded in a parafin moderator and placed above the chamber, when the loud fission clicks are then heard to considerably increase. Its not a chain reaction but its probably as close as you can get.

It occurs to me given how easy fission events are to detect with an ionisation chamber, that if you can get the uranium metal as a thin foil you could do the neutron multiplication experiments and also measure the exact number of fissions with only a small alteration to the design.

I'm uncertain how easy it would be for example to make a foil from the DU, I know the metal reacts at least partially with air and water. I also dont know how thin it would need to be to transmit fission fragments with a reasonable probability, but if you can calculate the distance thick films could be extrapolated to total number of fissions.

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Re: Subcritical Multiplication and Spontaneous Fission in Uranium

Post by Richard Hull » Fri Nov 18, 2005 5:58 pm

Really a fine piece of investigative work there Carl! Well thought out and well presented.

Related to Marvin's discussion on thin U for a demo of fission.........

U metal, depending on where it was obtained is often alloyed, even if only slightly, to help it "survive" in the real world. (oxidation, corrosion and the spalling off of oxide in its travels). Regardless, of alloy they are very hard and not malleable at all.

Totally pure 99.999 U metal is listed as being relatively soft and malleable. No U metal I have ever encountered was any thing but near diamond hard. It is in the nature of many of the heavier metals to harden up with as little a 0.5% of the addition of anything. Thus, fabrication of U and Th metals can be very difficult at best. U foil is very tough to fabricate. Most alloys work harded rapidly.

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Re: Subcritical Multiplication and Spontaneous Fission in Uranium

Post by JohnCuthbert » Sat Nov 19, 2005 1:33 pm

Uranium as the metal might be very hard to make into foil but would a thin coating of some compound (eg the oxide) do the job. If so then a precipitated layer might be much easier to prepare.

On a related note, would the spontaneuos fission of natural uranium be usable as a calibration for a neutron detector?

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Re: Subcritical Multiplication and Spontaneous Fission in Uranium

Post by Andrew Seltzman » Sat Nov 19, 2005 4:23 pm

United Nuclear sells pure uranium 238 metal.
http://www.unitednuclear.com/chem.htm

In theory, if you were to have enough of these strips mounted within a borrated parifin block, could you gain some net multiplication if it was driven by the output of a fusor?

In theory how many strips would this take? 10, 50 100?
What is beryllium reflectors were used on the sides?

In theory could a system like this produce a multiplied semi-directional neutron beam (cone-ish) from the isotropic output from a fusor?

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Carl Willis
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Re: Subcritical Multiplication and Spontaneous Fission in Uranium

Post by Carl Willis » Sun Nov 20, 2005 5:27 pm

Hi Marvin,

This sounds like a description of Otto Frisch's ion chamber experiment. Courtesy of Brian Willard, I have some nice feedthroughs and ultra-high-impedance FETS which seem destined for a project like this. The chamber itself could probably be made in a paint can (stripped of its liner). I think it would work fine with air filling, but Frisch's experiment used a pressurized hydrogen-filled ion chamber if I recall correctly.

-Carl
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Carl Willis
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Re: Subcritical Multiplication and Spontaneous Fission in Uranium

Post by Carl Willis » Sun Nov 20, 2005 5:41 pm


> In theory, if you were to have enough of these strips mounted within a borrated parifin block, could you gain some net multiplication if it was driven by the output of a fusor?
>

In theory the uranium is a multiplying medium. You will get some degree of multiplication by fission regardless of whether you put it in wax and regardless of how much uranium you have. The hard part is measuring that multiplication in highly subcritical assemblies. By the way, "depleted uranium" is not entirely U-238, but still typically retains 1/4 to 1/3 of its original U-235 content also. Something that is relevant to the practice of measuring subcritical multiplication is minimizing neutron loss and leakage, or increasing the "utilization." You don't want to have borated paraffin around your uranium since it will absorb as well as moderate neutrons.

> What is beryllium reflectors were used on the sides?

That helps the neutron economy in a big way by curbing leakage from the fuel. In small subcritical geometries, having a reflector is very important in boosting your effective multiplication factor.

> In theory could a system like this produce a multiplied semi-directional neutron beam (cone-ish) from the isotropic output from a fusor?

Yes (to an extent--it is never easy to control the direction of neutrons).

-Carl
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Re: Subcritical Multiplication and Spontaneous Fission in Uranium

Post by 3l » Sat Nov 26, 2005 8:58 pm

Hi Folks:

Try looking at the Sillard Experiments at Columbia...he used around 500 pounds of regular uranium oxide. It is only a third as effective as the metal ... divide by 3 to get the equivalent weight of metal. So you are talking about 166 lbs of regular U! But depleted U requires much more metal. Multiply by 10 or more depending on the enrichment method ... if you are talking about
gas diffusion the equivalent metal weight of 1660 pounds will be needed for this multiplier experiment. Sillard's neutron source was 2 grams of Radium in a beryllium cylinder.
Not Exactly science fair material.

Happy Fusoring!
Larry Leins
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Re: Subcritical Multiplication and Spontaneous Fission in Uranium

Post by Alex Aitken » Sun Nov 27, 2005 8:00 pm

1/3rd by weight to get the metal content? That doesn't sound right. Atomic mass of oxygen is around 16, uranium is around 238, so considering typical oxides like UO2 and U3O8......

Of course the density would suffer somewhat also.

2 grams of radium could produce in the region of 2 million neutrons a second.

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Re: Subcritical Multiplication and Spontaneous Fission in Uranium

Post by Starfire » Sun Nov 27, 2005 10:07 pm

And thats a lot of clock hands :)

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