This video is just a little more interesting than watching paint dry—until you realize that it is sound causing that little bright dot in the center! Sonoluminescence, light emitted by a plasma created at the center of a converging spherical sound wave, can be yours for about $100. Here are the instructions and here is a Scientific American article on the phenomena, which is closely related to the UD3 neutron generator.

I’ve been thinking about a small detail involving UD3 imitators ever since Jeffrey first published his very interesting post showing A. Q. Khan in front of a blackboard detailing Pakistan’s bomb design: why uranium deuteride? The uranium doesn’t participate in the nuclear aspects of the neutron generation, so why use it? I’m still not convinced I’ve understood the reasons behind this choice of material but the process of trying to understand it has been very enlightening.

Of course, one answer might be purely practical: there’s a whole bunch of uranium sitting in a bomb not doing anything until the first burst of neutrons is generated. Why not use it in the initiator? Such practical considerations undoubtedly do play an important role. But uranium has a very nice property that deuterium gas, for instance, does not: it’s very massive, an important consideration for shock compression. That mass, and how it’s packaged, might play a critical role in generating the pressure spike that compresses and heats up the deuterium to the 12 million degrees as reported in the Chinese paper.

What potential benefits does that mass bring to the initiator? The internal energy caused by the shock of the collision at the center of the device is proportional to the density of the material. Not the density of deuterium alone, but the total mass density. And the change in internal energy is also proportional to the shock pressure associated with this collision, which is much, much more intense than the shockwave that propagated through the UD3 to get it accelerating toward the center.

I’ve been trying to guess how fast that initial shock velocity was; another thing the Chinese paper—by not fully describing their experimental set up (they only give the outer radius of the high explosive as 8 cm)—has managed to conceal. I’ve estimated it as between 7 and 17 km/s, depending on how big the air gap between the aluminum and steel liner and the core really is. (The particle velocity is less than that.) One possible measure of just how important the uranium mass is comes from the paper reviewing Kaliski’s experiments using D2 gas, as pointed to by Robert Cross in Jeffrey’s original post. Through a fairly complex apparatus for focusing the shockwaves from a shaped charge (complicated if you wanted to place it next to a nuclear weapon’s pit, that is), Kaliski reported a particle velocity striking the deuterium gas of 50 km/s. Needless to say, the smaller the required velocity of the “strike,” the easier it should be to cause fusion.

But It’s More Than Just the Mass

Of course, just because deuterium is bonded to uranium doesn’t mean the compound has a high density. The theoretically maximum density of UD3 is about 11 g/cc; still quite dense if considerably less than the 19 g/cc for uranium metal. But that 11 g/cc is for a monolithic crystal. This is where material engineering really comes into play. You can increase the shock pressure—a seemingly important factor for increasing the final temperature—by increasing the density of the material. But you can also increase the temperature by making it more porous. In the language of shockwaves, you are increasing the change in “specific volume” (which is just the inverse of the density) as the material is crushed by the shock. This crushing, or compression, performs work on the material and heats it up. (That’s why the sonoluminescence experiment mentioned above needs a bubble in the center.) A monolithic crystal of UD3 would have a high pressure associated with the collision but not much work would be done—because of the relatively small compression associated with the solid crystal—and hence would not produce much of an increase in temperature. The Chinese, on the other hand, used a material with an initial density of 6 g/cm^3, which I assume is in the form of a sintered powder.

The effects of increasing the porosity of a material has been well documented in the open literature. Furthermore, increases in temperature appear to increase with increasing density of the porous metal’s “parent material” (bulk copper, for instance, is the parent material of copper powder). But most reproducible results involve temperature changes less than 10,000 K; about a factor a thousand less than the Chinese report. Of course, it is possible that the results mentioned in the literature were based on bulk temperatures and the fusion-type environments only happen over a very small volume that can only be measured by looking for the fusion-induced neutrons. (Just to be clear, I’m purposely grasping at straws here.) On the other hand, the Chinese measured a maximum of 48 neutrons in their detector and “corrected” that value by a whopping big factor to infer a yield of 50 thousand neutrons. To make maters worse, I saw nothing in the Chinese paper to indicate that they measured the effects of setting off 252 high speed detonators close to the sensitive preamps attached to their barium fluoride proportional counters. That might cause a lot of ringing in the signals.

Figure from the Chinese paper. After reading their caption, try saying “preamp noise” to see how that fits. (The darker black areas are in the original article.)

At the end of this process, I still don’t know why it is uranium deuteride. Can such high density materials like uranium be used to provide exactly the right balance between the two countervailing needs: high shock pressure and crushability? Or is UD3 a red herring and that famous (or infamous?) blackboard photograph an instance of carefully constructed of misdirection? As you might have guessed, I’ve become increasingly skeptical about the possibility of using UD3 as a source of fusion neutrons initiated by conventional explosives.

Note on Proliferation: I’ve tried mightily to extract the UD3 shock Hugeniot from the Chinese paper and haven’t figured out a way of doing it. Through a carefully selected set of information actually published, I think the Chinese have managed to convey their results without creating a proliferation problem since that Hugeniot is really what you need to design an initiator. However, just because I can’t do it doesn’t mean it is impossible so I agree with Jeffery’s decision not publish the paper here. This, of course, just propagates the problems arising from censoring science: a lack of full peer review etc.

I’d like to thank Prof. Andrew Higgins for pointing me to a number of important papers in the literature and helpful pointers as I tried to understand this issue. I highly recommend one of Andrew’s suggestions: Paul Cooper’s “Explosive Engineering” Of course, any mistakes I’ve made here are entirely mine.

Appendix: Hugoniots “Explained”

Once again, it has been pointed out to me that I’m way too techno-wonky on this one and failed to explain what a Hugoniot is. Of course, the best way to learn about them would be to read chapters 14 through 17 from Explosives Engineering. (Don’t worry, the book is excellent and you can jump in right to those chapters, which give a very readable physical explanation of shock waves. They get progressively more “mathy” but its all algebra and I urge you to work through them. If you don’t feel like that, just read Chapter 14, which doesn’t use any math at all.) But for the skinny, let me say that a material’s response to shocks can be characterized almost entirely by one graph and that graph can, for most materials, be characterized by a single number. The graph is a plot of the shock velocity vs. the velocity of the particle and the single number is the slope of that line in what is, in most cases, a straight line. This is called the U-u Hugoniot and other Hugoniots associated with the material are simply derived from it.

As you might expect, a shock wave, which is just a pressure wave has a higher velocity that the particles that get accelerated by the shock as it pass over them. But once the these parameters have been determined, it can be used to plot the same Hugoniot line but in terms of different variables, all of which are related to the original line by the laws of physics. In particular, you can plot the pressure of the shock wave verse the “specific volume,” the inverse of the density. This plot is important because the area under a line drawn from the initial, unshocked state, to the state after the shock wave has passed through is equal to the internal energy of the material. In our case here, by increasing the porosity of the material, we have increased the area under the graph and hence the total internal energy. A word of warning: the temperature is different from the total internal energy.


An example of a typical Hugoniot where pressure is plotted against specific volume (i.e. the inverse of density). The area under the Raleigh line is equal to the shock induced internal energy (including potential energy stored in chemical bonds of compressed materials.)