*banhammer*is still functional: if there has been any trolling I'm sorry I wasn't on duty to crush it with characteristic barbarity. On that note, warm greetings again to all!

I'd like to share something today more related to fission than to fusion. However, the neutron time correlation technique mentioned here would be a valuable way to test assumptions about stochasticity in fusion projects or to make sure neutron detectors are free of non-random noise influences. So feel free to read on.

About a month ago, I was given a piece of the first nuclear reactor, the Chicago Pile. It came via Herbert L. Anderson's wife. Herb had been given the piece of the pile as a commemorative item for his pioneering work on the pile's physics. A photo is posted below: As can be seen, this is a bit of the graphite moderator with two recesses containing pieces of original uranium metal fuel. It is one of about 1000 blocks that contained uranium metal rather than the more-abundant "pseudosphere" oxide fuel. Mrs. Anderson was surprised when I showed her that the artifact that had spent so much time in her home was radioactive; Herb had withheld that tidbit from her. In fact, the piece has a gamma exposure rate of about 8 mR / hr on contact. Later on, I got surprised myself when I learned that the detectable radioactivity is dominated by fission products rather than natural uranium decay. The clear conclusion is that this piece not only spent three months in the first iteration of the Chicago Pile, "CP-1"--which was erected hastily under the stands at Stagg Field and spent three months there, operating sporadically and at essentially zero power--but also spent a decade in the rebuilt pile ("CP-2") outside of Chicago. The rebuilt pile had the benefit of air cooling and biological shielding, and ran at up to 10 kW. From a high-resolution gamma spectrum, I am able to calculate the fuel's burnup from the ratio of counts in the Pa-234m peaks (natural U-238 decay) to those in the Cs-137 peak (a long-lived high-yield gamma-emitting fission product). Here is the example spectrum: To calculate burnup from this type of gamma spectrum data, I first looked at the Pa-234m peaks to obtain the photopeak detection efficiency

*for this particular detector and source geometry*. I can do that because Pa-234m is in secular equilibrium with its parent, U-238, and I know the mass of the uranium (5.11 kg) having weighed the fuel elements on my kitchen scale. I obtained efficiencies of 5.01E-6 at 766 keV, and 6.15E-6 at 1001 keV. The trend implied by these numbers is one dominated by self-shielding in the source since the photopeak efficiency goes down as energy goes up; this is certainly expected since the fuel is a very thick source. Now I linearly extrapolate the photopeak efficiency for the 662-keV line from Cs-137, assuming the Cs-137 is homogeneously distributed in the source like the Pa-234m is. This extrapolation yields an expected photopeak efficiency at 662 keV of 4.13E-6. With that I can calculate the activity of Cs-137 in the nuclear fuel from the counts in the 662-keV peak, obtaining 669 microcuries. In 1954, at the conclusion of CP-2's operation, there would have been 2.65 mCi. From Cs activity, tabulated cumulative thermal-neutron fission yields of U-235, and uranium mass, we can calculate the fission density in the fuel per mass of U. (Cs-137 fission yield is commonly reported around 0.062.) Thus, the fission density is some 4.2E+14 per gram U. The energy released in each fission event is about 202 MeV...multiplying fission density by this number gives a result with dimensions of energy released per mass of uranium fuel. Conventionally, the number is reported in units of watt-days per metric ton (or kWD/MTU, MWD/MTU, or GWD/MTU). In the case of this fuel, I get 156 kWD/MTU. Is that consistent with the CP-1/CP-2 operational history? Assume for the sake of a sanity-check that CP-1 delivered essentially no burnup and that CP-2 ran at 50% availability and 5 kW for ten years. That's an exposure of about 220 kWD/MTU, similar to the calculated number, building confidence. Now how does my calculated value of burnup in the Chicago Pile compare to other familiar nuclear reactors? Well, it's pretty tiny: spent fuel discharged from a power reactor can expect to have tens of GWD/MTU, and fuel discharged from a plutonium production reactor would have on the order of tens or possibly up to a few hundred MWD/MTU. So by comparison, the Chicago Pile fuel just got lightly toasted.

******

Now let me share another experiment I did on the CP-1 block, this time to detect neutrons from fission processes in the nuclear fuel. Simple radioactive decay is considered to be a random process in which one emission is uncorrelated in time with the next, but fission is a notable exception. In an individual fission event, multiple products (e.g. neutrons) are released simultaneously. Moreover, in a multiplying medium consisting of an assembly of fissile material and moderator, one neutron can in turn give rise to chains of further neutron emission. In the special case of nuclear criticality, the chains are self-sustaining. These are two types of time correlation potentially expected in the neutron signature of a fission source that you wouldn't expect to see in a fusion neutron source or a radiochemical (e.g. AmBe or RaBe) source. Time correlation means that, compared to the Poisson statistics of a random process, there will be excess variance observed. To measure this variance in nuclear metrology, the Feynman Y statistic is often used. It is defined as:

Y = (sigma^2/mu)-1

Sigma^2 represents the variance of number of counts observed in the data; mu is the mean number of counts. If the data are Poissonian, Y = 0. To measure Y, I set up an experiment in which a reflective HDPE brick "doghouse" surrounds a He-3 tube slab detector for neutrons and the object(s) under test. The counts from the He-3 tubes are recorded in the time bins of a multichannel scaler (MCS) whose dwell time is fixed at 30 microseconds. I wrote an auxiliary LabVIEW program to re-bin the data from the MCS according to various time intervals, up to about 5 milliseconds. When one looks at the bin time dependence of Y, one should be able to discern the characteristic time scale of the correlation effects being observed: as bin duration is reduced toward zero, you'd expect to see lower excess variance if the characteristic timing of the correlated events takes place on the order of, say, milliseconds. On the other hand, if the bin duration is extended much longer than the relevant correlation time, the value of Y would be expected to reach an asymptotic value. Below is a Feynman-Y plot of a variety of sources and objects under test. I've got a lead brick (which produces neutrons by cosmic-ray-induced spallation), a weak AmBe source by itself, the CP-1 block by itself, the CP-1 block with the AmBe source, and the empty "doghouse:"

The results are interesting but rather predictable in light of the previous discussion. We can see very strong excess variance (read: correlation) in the counts from just the CP-1 brick; this represents the inherent spontaneous fission source from U-238 possibly driving some detectable subcritical fission chains. The characteristic timescale of correlation is about a millisecond, due to how long it takes neutrons to slow down, become stored in the moderating materials, leak out, and get detected in the He-3. Next down is the Pb brick. Its correlated neutrons come from spallation, where many may be formed in a single event. However, although the correlation is strong, the neutron source presented by lead is exceedingly weak. Note the large error bars. The CP-1 block driven by the AmBe source has much lower correlation than just the CP-1 block; I attribute this to lots of leakage and penetration of source neutrons through the CP-1 piece. The AmBe source itself produces a Y = 0 line. This is exactly what I'd expect, given that it is driven by simple Poissonian alpha radioactive decay.

What I am hoping is that someone exists out there who has done a lot of neutron correlation experiments and can help me separate the influences of fission chains from those due to spontaneous fission using the data expressed in these graphs. I am still trying to wrap my head around this challenge.

Anyway, I feel uniquely privileged to have such an historic item at my disposal for nuclear experiments. Its heritage belongs to all of us, not just me, so I am actively pursuing options for loaning it to museums and institutions where it will be appreciated by a broader public. I also am interested in putting together opportunities to scientifically study it, as it is a unique record of the first (anthropogenic) nuclear reactor's construction and operation. Got ideas?? Let me know!

EDIT: I made a descriptive YouTube video about this artifact, available here:

http://www.youtube.com/watch?v=1Es4_tz7_7E

-Carl