There are a number of stories in the news the last few days that hinge on issues of just how much uranium you need to build a weapon. I’ll get to addressing those items in subsequent posts. I just thought I’d lay out some general discussion first.
Most people are familiar with the phrase "critical mass", as a colloquial term rather than a technical term. Recall that “fissile material” is material that can be used as the fissioning material in a weapon; for present purposes, that is mainly highly enriched uranium (HEU) though plutonium is also used in other contexts. Critical mass is, broadly speaking, the amount of fissile material that, if brought together, will result in a nuclear chain reaction and explosion.
There are a lot of different caveats and dangers hiding in that one sentence, and I want to bring out two of them:
1. Once the explosion gets underway, the hot expanding fireball tends to blow apart all that fissile material you were just trying to put together
2. How much material you need for the chain reaction depends on the exact configuration of the materials
Let's take a look at the first one. The "Little Boy" bomb over Hiroshima contained 64 kilograms of uranium. It was a gun-type assembly. It is easiest to imagine (though it's not quite exactly how it was actually designed) a "bullet" of uranium being shot into a form-fitting hollowed-out core, so that at the moment the bullet slid into and filled up the core, a sphere of uranium--of above critical mass--was formed. One can see that if each of the masses is just below critical mass, a total mass of just under twice critical mass could be acheived, allowing considerable engineering margin.
Of that 64 kg, only about 1 kg actually underwent fission. The other 63 kg of uranium were vaporized and sent spewing into the atmosphere over Hiroshima. And of that 1 kg that fissioned, only about 0.6 g--roughly the mass of a penny--was actually converted into energy. The other 999.4 g were fission products, again spewed out in the massive fireball created by a penny's worth of E=mc2.
The fraction of Uranium that actually gets fissioned (in this case, 1/64 or about 1.5%) is known as the "efficiency" of the weapon. The total energy release in a weapon is directly proportional to the efficiency. If you double the efficiency, you double the explosive power of the weapon. But higher efficiency does not lower the needed critical mass.
One way to increase the efficiency of a weapon is to surround the fissile material by a significant quantity of dense, nonfissile material, which will serve to slow down the expansion of the internal fissioning fireball--giving a few more microseconds of time for fissioning to continue before the core is blown apart.
Now let's look at the second of the issues: the amount of material you need depends on the exact confguration of the materials inside the weapon. The phrase "critical mass", in general refers to the critical mass of material needed, at standard density, in a spherical shape, bare, without being surrounded by any other materials. For pure U-235, that is 52 kg; for Pu-239, it is 10 kg.
There are various ways to decrease the "critical mass". Surrounding the material with neutron-reflecting material is one way to decrease the critical mass.
Another is to increase the density. This latter is acheived by shaped explosive charges, which are fired together all at once around the ball of fissile material. By doing this, the density increases, so the material quantity that was originally less than critical mass, is now more than critical mass, since the critical mass has been lowered. All plutonium weapons are implosion-types.
Weapons design generally has two goals: (a) how can I make a weapon critical with as little fissile material as possible, and (b) how can I make the fissioning as efficient as possible once that critical mass is assembled?
The Bottom Line: How Much HEU?
So one may ask, OK, OK, bottom line, how much fissile material do I need to build a bomb? Let's ask this question focussing on uranium, since the Iranian nuclear program is based on uranium.
The "dumbest" thing one could do is to build a gun-type device without surrounding it with reflecting material. This would require 52 kg of uranium.
The next best thing is to build a gun-type device and surround it with a very thick neutron reflector. FAS reports that enough of it might reduce the needed mass to 15 kg (http://www.fas.org/nuke/intro/nuke/design.htm), though that seems quite a low number to me—probably because it is pure U-235.
There are a few other things I can imagine one might do to shave a few more kg.
From reverse-engineering numbers in publicly available documents on Little Boy, I'd guess that the critical mass was reduced by various methods to around 25 kg.
Another route is, instead of a gun-type design, to implode uranium, increasing the density. I have yet to find any good statement on how low the critical mass can be pushed for uranium implosion devices. I'd speculate an acheivable number around 15 kg, perhaps a hair lower.
Now, let's take a moment to look at the strategic implication of good design. The main impact is not on means of delivery, but on the number of weapons a state can build with limited fissile stock. To me it seems that there is only a very short time period in the life of a nuclear power in which quality of nuclear design actually matters. (See Update for more commentary on this). When you have no material, design isn't an issue--you have no weapons. When you have plenty of material, the strategic impact of good design is relatively less; there comes a point where there's not much difference between having 100 weapons and 300; either will serve as an effective deterrent.
But when first "turning on" as a nuclear power, good design is the difference between having enough material to simply test a weapon, and enough material to test a weapon and announce you have two more ready to retaliate with if anyone tries to strike you.
A state that is considering going nuclear will likely not perform any test until it has sufficient material to make several weapons, for precisely the above reason. Good design shortens the breakout time, from the time needed to enrich 52*3 kg of U, to the time needed to enrich 15*3 kg.
Nb that the various means to decrease the critical mass of fissile material needed generally tend to increase the mass of the complete weapon. That is because reflectors, tampers, etc are generally heavier than the number of kg they save. However, because these other materials are abundant, while fissile material scarce, it is a worthwhile tradeoff. But in general, lowering the critical mass through good design does not make the weapon more easily deliverable, for instance by means of a missile.
If anything, I’d speculate that for delivery purposes, high-critical-mass designs may be superior.
So a new nuclear power probably has to choose a balance between raw weapons count, and delivery capability, to maximize the deterrent it can achieve with limited fissile material.
Finally, improved efficiency weapons, at least for the new nuclear state, does not have significant strategic implications.
How Much LEU?
Above we give a discussion of the amount of highly enriched uranium (HEU) needed to make a weapon. Iran is not currently known to possess any HEU; nor is it simple to see how it could come into possession of any while under the NPT regime.
Recall that natural uranium consists of 99.3% U-238, and 0.7% U-235. Only U-235 is usable in a (simple) weapon. Uranium in a weapon is generally above 90% U-235, though 80% is usable and considered HEU.
However, Iran is certainly enriching LEU (for argument, let us say 4% U-235). How much LEU would Iran need to stockpile, in order to eventually turn it into enough HEU material for a weapon?
In principle, the answer is simply the critical mass, multiplied by 80% divided by 4%. That gives a number somewhere between 300 and 750 kg. However, this is “the slow road”. If there is only this bare minimum amount, it will take considerable time to enrich to HEU.
By raising the tail enrichment, one can enrich to HEU with less enrichment capacity, but at the cost of needing more LEU as input. That is to say, given fixed enrichment capacity, it’s faster and easier to enrich 2000 kg of LEU to 50 kg of HEU, than it is to enrich 750 kg of LEU to 50 kg of HEU. (http://www.wise-uranium.org/nfcue.html)
For a nation with access to much LEU (as Iran does have under IAEA safeguards) and limited enrichment capacity, the fastest breakout capability is achieved by enriching as much LEU as possible, combined with “good” weapons design.
So how much LEU is needed to build a weapon? Actually “needed” is 350-700 kg. But given Iran’s limited enrichment capacity, considerably more would be desired before committing to enrich to HEU. There really is no red line in LEU quantities.
Updated: CKR rightly points out that good weapons design can have a strategic impact for a longer time than I had supposed, due to improved "weight engineering" for delivery, esp. by missile. Contrary to what I had first thought, the point is well taken, especially in light of today's ACW post about the North Korean weapon test; such designs drive down the fissile mass needed.
Update II: Figure 2 on page 16 of Cochrane & Paine has a good summary of how design quality impacts yield. A 10 kt yield would be a very reasonable one to demonstrate a deterrent capability. If I were a project manager, I would be focussed on the low-tech designs for a first weapon, just to be absolutely sure it went BANG. However, there's some evidence North Korea and Pakistan both tried to start out in the medium technology range.