[Physics] Is a Plutonium gun-type atomic bomb really “impossible”

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I caught a pretty well done 2 hour documentary on atomic bomb history yesterday on the local PBS station. In it, they go over the paths taken for design of the first bombs, including the Thin Man Pu239 based gun design. After Segrè found the spontaneous fission rate from the reactor-produced Pu was much too high (from Pu240 contamination), that design was abandoned.

It is stated by one of the speakers in the documentary (might have been Rhodes) that such a design is "impossible" (not "was impossible"), implying that it's not feasible at all.

I did a quick back-o-the-envelope calculation as follows (I'm a mathematics guy, not a physicist, hence the question…):

Taking the ~60Kg U235 of the Little Boy, and 3*10^-4 neutrons/gram-second, ~18 neutrons/sec.

Guessing at (since it won't be as efficient as implosion) 2.5X the 6Kg mass of the Fat Man Pu239 to be used in the hypothetical gun and 0.022 neutrons/gram-second, ~330 neutrons/sec.

Taking the insertion time as 1 millisecond (which I assume could be improved with current technology), I get ~0.018 and ~0.33 neutrons/ms average for U235 mass and Pu239 mass respectively.

Assuming Poisson distribution of arrivals, I end up with ~0.98 and ~0.72 probabilities of no stray neutrons during assembly for U235 mass and Pu239 mass respectively.

While that shows a much higher possibility of a fizzle in that latter, it seems far from "impossible".

My question: Given a sufficient mass of "pure" Pu239 (say cyclotron produced, or whatever the current state-of-the-art might be to produce it), and current state-of-the-art technologies to accelerate a projectile, is such a design really impossible (cost of Pu production, efficiency, practicality aside). As in, could an actual high-yield device (as opposed to a fizzle-yield) be produced?

Best Answer

This is from The Nuclear Weapons Archive:

2.1.4.1.2 Gun Assembly

Assembling a critical mass by firing one piece of fissionable material at another is an obvious idea and was the first approach developed for designing atomic bombs. But it is probably not obvious how you take two subcritical masses and obtain the equivalent of three critical masses by bringing them together.

This can be made clear by conducting a thought-experiment. Imagine a spherical pit made up of about three critical masses of fissionable material. Now remove a core (like an apple core) from the pit with a mass slightly less than critical. Since the center of the pit is now hollow, its effective density has been reduced to 2/3 of the original density. Since we now have two critical masses remaining in the pit, and the reduction in density leads to a further reduction of (2/3)^2 = 4/9, the pit now contains only 2*(4/9) = 8/9 of a critical mass.

The two sub-critical pieces can be brought together by firing the cylindrical core down a gun barrel into the center of the hollowed-out pit. The insertion time is large - over 1 millisecond. This is the design used in Little Boy, the bomb dropped on Hiroshima (except that a slightly less efficient squat cylinder was used, rather than a spherical pit).

The primary advantage of gun assembly is simplicity. It is as close to a fool-proof design as ordinance technology allows.

The drawbacks are:

a. the lack of compression, which requires large amounts of fissionable material, and leads to low efficiency;

b. only uranium-235 (and possibly U-233) can be used due to the slow insertion speed;

c. the weight and length of the gun barrel makes the weapon heavy and fairly long.

Their website is here.

And this is from "Nuclear Weapons Design" at this website:

If plutonium -- even weapon-grade -- were used in a gun-assembly design, neutrons released from spontaneous fission of its even-numbered isotopes would likely trigger the nuclear chain reaction too soon, resulting in a "fizzle" of dramatically reduced yield.

Me again: so it seems like it might be possible to get a plutonium-based gun assembly device to actually explode rather than fizzle, but the timing would be so critical that if would fail more often that it would explode.

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