Smallest possible plutonium implosion device

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sevenperforce
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Smallest possible plutonium implosion device

Postby sevenperforce » Mon Apr 06, 2015 10:42 pm UTC

Disclaimer: while the following is a legitimate discussion of potential nuclear weapon designs, it is purely theoretical and contains no classified or protected information. All statements comprise either publicly-available/declassified information or are my own personal speculations. Any suggested designs would be impossible to realize without advanced knowledge of criticality geometry.

The Davy Crockett W54 and W48 nuclear warheads were the smallest nuclear devices that the United States ever deployed, at 280 and 155 mm respectively. Neither the United States nor Russia has ever acknowledged designing smaller weapons, though physicist Ted Taylor claimed that 105-mm-wide devices were possible, and Russian defector Stanislav Lunev claims that the Soviet Union deployed 50-60 lb "suitcase bombs" on US soil during the Cold War. Israel is also widely believed to possess suitcase-sized nukes. Given that a bare-sphere critical mass of plutonium is 99 mm in diameter, a 105-mm warhead is pretty darn small.

I'm curious as to whether there's any way to go smaller. I thought that perhaps by combining elements from gun-type bombs, linear-implosion-type bombs, and basic nuclear reactor physics, it might be possible to make a nuke even smaller. Of course, as I mentioned in the disclaimer above, "possible" isn't the same as "realizeable", at least without the sponsorship of a major government.

Consider a bare cylinder of Plutonium-239 exactly 99 mm in diameter.

bare cylinder 1.png
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Because a 99 mm sphere of 239Pu is critical all on its own, this configuration is necessarily supercritical. Now, if we maintain this cylindrical shape, we can retain criticality down to some lower diameter. Let's say, just for the sake of argument, that a plutonium cylinder can retain criticality down to around 85 mm.

bare cylinder 2.png
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For our purposes, the exact length isn't important -- it's just going to be on the order of 3 times as long as its diameter, long enough that the diameter is the real limiting factor on criticality.

So we have an ~85 mm 239Pu cylinder which is just barely critical. If we now surround the cylinder with a neutron-reflective tamper like tungsten carbide or depleted uranium, we will transform the pit to a superprompt-critical state. Phyisicist Harry Daghlian was killed by the 89-mm demon core in 1945 when he accidentally dropped a final tungsten carbide brick onto it in an uneven configuration; it went superprompt-critical immediately. Based on this, then, we can speculate that completely even reflection would have also been able to produce superprompt criticality even if the core had been even smaller -- in the range of 80 mm or so.

This is the part where I don't have nearly enough information about criticality geometry to draw any certain conclusions, but if we compare the surface area of an 80 mm core to the 99 mm of a perfectly critical bare core, we find that a hypothetical superprompt-critical totally-reflected 80 mm core has just 53% the surface area of a critical bare sphere. So if we reduce the reflection-subjected surface area of our cylinder by the same proportion, we hypothesize that we could reduce the size of our reflected cylinder to just 62 mm while still retaining superprompt criticality.

reflective tamper 1.png
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We now have a very small plutonium cylinder -- less than the diameter of a soda can -- which is in a superprompt critical state. Of course, we don't want it to be in a superprompt critical state, because it won't stay there long enough to be useful to us. So let's remove some of the plutonium in order to reduce it from superprompt criticality to supercriticality. I'll also extend the reflective tamper. The cross-section will look like this:

retooling 1.png
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We now have something a little more refined. It's still a cylinder, but it's slightly tapered toward the ends as well as on the outer faces, and there are narrow voids missing at the ends and in the center. If we've done it right, it should still be supercritical, but no longer superprompt-critical.

To bring it to subcriticality, let's jam a couple of lightweight boron control rods into the ends.

with control rods.png
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You're probably wondering why the control rods look vaguely like golf pegs. That will become apparent soon enough. The boron control rods should absorb plenty of neutrons, making our pit safely subcritical.

Let's close the ends of the casing, then add a spaced uranium tamper, a spaced aluminum pusher plate, and some high explosive on either side:

with spacing.png


It's not quite done -- not yet -- but it's starting to take shape. Upon detonation, the high explosive will drive the pusher plate into the floating tamper, which will then begin linear implosion of the fissile mass. This will not only compress the plutonium, but will also push it inward and away from the control rods. At the same time, the lip on the outside of each control rod will "catch" a small portion of the force from the explosive. The pressure differential will serve to rapidly eject the control rods at the precise moment that the floating tamper reaches maximum momentum, thus impinging the tamper upon an already-supercritical fissile mass.

Let's go ahead and add a lithium-7 deuteride pellet at the center to increase our yield, surrounded by a couple of polonium-beryllium hemispheres as dual initiators (with the beryllium on the inside to prevent neutrons from hitting the lithium-7 too early):

core added.png


There's still a problem, though. This design will almost certainly blow out the sides of the casing before sufficient fission has taken place. Now, we can try to remedy this by making the casing as dense and high-tensile-strength as possible, using something like a depleted-uranium/titanium alloy (the high tensile strength won't help once fission begins but it will hold in the conventional explosive pressure quite well). And that might work. But we need to be able to control the deformation and implosion of the fissile mass to maintain superprompt criticality for as long as possible.

We can accomplish this by using multiple pieces of plutonium-gallium alloy in different phases. The α-phase of plutonium-gallium alloy is 25% denser and less malleable than the δ-phase plutonium-gallium alloy typically used, but implosion of δ-phase Pu will cause it to rapidly transition into the α-phase. We'll use this to our advantage by machining a portion of the pit out of α-phase Plutonium and casting the remainder in δ-phase:

sections.png
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We'll have to make four separate sections: the two cylindrical δ-phase hemispheres, a single α-phase "inner ring", and a single tapering δ-phase "outer ring".

When the floating tamper impinges upon the fissile mass, it will compress the lighter δ-phase inner cylinders more readily than the denser α-phase ring around them. As the control rods are ejected and criticality builds, the denser α-phase ring will impede the radial expansion of the inner fissile mass until the inner mass has transitioned into α-phase. Finally, as the whole superprompt-critical α-phase inner mass begins to expand, it will squeeze the outer δ-phase tapering against the strong fixed-tamper casing. This outer ring will tend to expand outward along the z-axis of the whole device due to its taper; it will thus take a minutely longer amount of time before transitioning to α-phase and completely filling the open space. In this way, the chain reaction will be well underway before the outer casing is breached, allowing secondary fission of the lithium-7, rapid D-T fusion, and subsequent yield-boosting of the plutonium pit.

Anyway, that's the idea. Any thoughts on workability or failure modes?

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Sizik
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Re: Smallest possible plutonium implosion device

Postby Sizik » Mon Apr 06, 2015 10:43 pm UTC

I think you broke the forum.

Or it might be the filters messing with the BBCode tags.
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Re: Smallest possible plutonium implosion device

Postby BlitzGirl » Mon Apr 06, 2015 11:51 pm UTC

It's because you have more than a trio of attachments, and attachment modules look like [attachment=#]. The modules [attachment=0], [attachment=1], and [attachment=2] are fine, but the next few numbers after that are currently affected by forumfilters, until you get to [attachment=6] which is fine again.
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sevenperforce
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Re: Smallest possible plutonium implosion device

Postby sevenperforce » Tue Apr 07, 2015 2:44 am UTC

Yay forumfilters.

It will get better eventually, I suppose.

In the meantime, here's a detailed schematic with all the labels all in one place.

Complete with labels.png


You could, I suppose, pump the open spaces full of D-T gas for all manner of fun and exciting effects, but I doubt it would make much of a difference in yield.

EDIT:

If these dimensions work, then we'd be looking at 1.33 kg for the two inner cylinders, 4.16 kg for the inner ring, and 1.53 kg for the outer ring, for a total fissile mass of 8.35 kg. More than the Gadget/Fat Man/Demon Core cores, but still less than a bare-sphere critical mass. The plutonium cost would be around $33 million. With the tampers, casing, and various other parts it would weigh around 14 kg or just 31 pounds, in a package roughly the size of a Pringles can.

Yield could be as high as 4-5 kilotons if fusion boosting could be achieved. Otherwise it would probably be in the sub-kiloton range, a fizzle by most nuclear weapons standards, but devastating for a package small enough to carry in one hand.

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Re: Smallest possible plutonium implosion device

Postby Autolykos » Wed Apr 08, 2015 9:50 am UTC

Yield could be as high as 4-5 kilotons if fusion boosting could be achieved. Otherwise it would probably be in the sub-kiloton range, a fizzle by most nuclear weapons standards, but devastating for a package wee enough to carry in one hand.

This design is likely to fizzle, even by its own standards (next to no yield, but some nasty fallout). We'd need a simulation to be sure, but Pu-239 requires a quite spectacular amount of pressure to make most of it fission before the vaporized metal disperses your fuel in the surrounding area. A gun-type design will work just fine with U-235, but not with Pu-239 - and your schematics look a like a hybrid between gun-type and implosion. Most importantly, you lack the explosion lenses of different-velocity HE that make sure your fuel will get compressed from all sides at once, and not just "squish" out the sides. From what I gathered, this step is critical enough that small variations in shape and timing are used as "launch codes". Without knowing when to start the priming charges, all you can do with a stolen nuke is scrap it and melt it down for the raw materials.

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sevenperforce
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Re: Smallest possible plutonium implosion device

Postby sevenperforce » Wed Apr 08, 2015 7:43 pm UTC

Autolykos wrote:thith design is likely to fizzle, even by its own standards (next to no yield, but some nasty fallout). We'd need a simulation to be sure, but Pu-239 requires a quite spectacular amount of pressure to make most of it fission before the vaporized metal disperses your fuel in the surrounding area. A gun-type design will work just fine with U-235, but not with Pu-239 - and your schematics look a like a hybrid between gun-type and implosion.

Simulations which require supercomputers and lotsa classified test results, no doubt.

There's already a hybrid design between gun-type and implosion: it's called linear implosion. With gun-type bombs (Little Boy, Thin Man) you're starting off with much more than a single critical bare-sphere mass but in a separated subcritical arrangement; the idea is to assemble the pieces together into a hyperprompt-critical mass as fast as possible to get the maximum fission before the mass blew itself to smithereens.

In a typical implosion weapon, like the kinds you're describing, there's inertial confinement of the fissile mass (either from a heavy tamper like in Fat Man or from the momentum of the collapsing hollow pit itself) and so it stays together a bit longer, achieving more fission. However, the minimum diameter for an ideal hollow-it two-point implosion weapon like Swan is about a foot. You can't get a hollow-pit device much smaller than that.

To achieve smaller diameters, as with the W54 and W48 warheads, linear implosion is employed. As in a gun-type weapon, you use much more than a single bare-sphere critical mass of fissile material, but in a single pit that is kept subcritical by its shape rather than by using separated pieces. There's some compression of the pit as the high explosive rapidly reshapes it into a hyperprompt-critical sphere, but there's no true inward momentum and thus no inertial confinement. It won't "bounce-fizzle" like the Thin Man would have, but without inertial confinement the yield will only be whatever fission takes place while the pit remains critical.
Spoiler:
Standard linear implosion.png
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The W48 nuclear artillery shell was only 6 inches in diameter. It may have used as much as 25 kg of plutonium-239, but had a yield of just 72 TNT-ton equivalent, meaning just 8.6% of the Pu would fission (compared to 17% of the Pu in Fat Man and 1.56% of the U in Little Boy).

Trying to come up with an even smaller package is a tremendous challenge, but that's what I wanted to try and accomplish.

By using circumferential neutron reflection around a cylindrical rather than ellipsoidal pit, it's possible to have a superprompt-critical fissile mass with a smaller diameter than even the W48. Traditional linear implosion designs will still produce sizeable yield merely because they reach superprompt criticality without any inertial confinement, but those start in a subcritical state and are reshaped into superprompt criticality. I wanted to try and go at it the opposite way: "start" with a supercritical fissile mass and then reduce to subcriticality using control rods which would be rapidly ejected at the point of detonation. Merely by ejecting the control rods, the subcritical mass is instantly transformed into a supercritical mass capable of producing a significant yield all on its own. Any compression by the HE only serves to increase the yield from that point.

The challenge is that with a cylindrical arrangement rather than a spherical one, you have to maintain that cylindrical shape and the neutron reflection in order to stay critical. That's why I propose the three-layer approach, where the inner δ-phase cylinder would deform first due to the higher density of the α-phase ring. Then, as the now-completely-α-phase center begins to fission and expand, it must compress the outer δ-phase ring into α-phase before it will be able to rupture the neutron-reflective casing. Hopefully, that will give enough time for the lithium deuteride booster charge to begin fusion and boost the plutonium with fast neutrons.
Spoiler:
stepbystep.png
The instant the control rods are ejected, the assembly is already in a prompt-critical configuration. As fission begins, the inner ring (either simply α-phase Plutonium-Gallium or even an α-phase Plutonium-Tungsten alloy) serves as an internal tamper, containing the pressure until the central cylinder has transitioned to α-phase. Because a sturdy U-W or U-Ti casing will easily withstand the pressures needed to force 239Pu from δ-phase to α-phase, it will continue to serve as a neutron reflector until the expansion of the rapidly-fissioning central column has compressed the outer ring.


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