Why a nuclear reactor can never turn into a nuclear bomb

Edit: Karl Withakay has pointed out a couple of omissions and a small factual error in this post. I have indicated this in the footnotes. Please do read his illuminating comments, especially if you are interested in the more technical aspects of nuclear technology.

The news from the Fukushima Daiichi nuclear plant continues to be horribly depressing. For me, nothing mitigates this kind of discouragement more than being overly technical about it, so let's do that.

As bad as the situation is, there's been lots of really just stupidly over-the-top fear-mongering, and other websites have done a good job addressing that. One thing I've noticed has been omitted, though, is that while there are many resources out there reassuring people that a nuclear explosion is not possible in this case, because a nuclear reactor and a nuclear bomb are two completely different things, I haven't seen anyone offering a lay explanation of why that is the case. So I will attempt to do so here.

Say you've got a lump of Uranium-235, the fuel used in most nuclear reactors. Really, you'd have a lump of rock that contained some amount of U-235, which you would have attempted to purify as much as possible, but this is all beside the point¹. This lump of U-235 can be subcritical, critical, or supercritical.

To understand what these terms mean we need to briefly revisit the basics of a nuclear fission reaction. I'll leave the detailed explanation to the Wikipedia article, but for our purposes, the important point is that when a U-235 atom splits into two pieces, along with the energy that is released, it also ejects three stray neutrons. It turns out that what induces the U-235 atom to split in the first place is being struck by a stray neutron. So you fission one atom, which causes three more atoms to split, which in turn trigger nine more fission reactions, then 27, then 81, and so on exponentially until you get a whole heapin' load of energy.

Except not quite. The stray neutrons don't always hit a U-235 atom. Sometimes they miss, and just go shooting off into the distance. Actually, since all the matter around us is mostly empty space, they usually miss.

And here's the key point: The more dense your lump of U-235 is -- the closer together the atoms are -- the more likely it is for an ejected neutron to bump into one of the atoms. I'm sure this makes good intuitive sense, since obviously it's easier to hit one of a whole bunch of targets clustered close together than it is to hit a one of a few targets scattered far apart.

If the odds of a neutron hitting a U-235 atom are less than 1 in 3, i.e. on average, each time an atom splits and ejects three neutrons the average number that go on to trigger another fission reaction is less than one, then we say the mass is subcritical. You will get some energy released, but the reaction will rapidly peter out as you run out of neutrons.

If the odds of a neutron hitting a U-235 atom are exactly 1 in 3, i.e. on average, each time an atom splits and ejects three neutrons an average of one of them connects, then we say the mass is critical. You will get a fairly constant release of energy until all of the fuel is used up. This is how you want to run a nuclear reactor.

If the odds of a neutron hitting a U-235 atom are more than 1 in 3, i.e. on average each split atom causes more than one other atom to split, then your mass is supercritical. All other things being equal (which they aren't; more on this in a second) fission will continue in a chain reaction style, releasing energy faster and faster, until you get a mind-numbingly large explosion.

This is how you want to build your nuclear bomb. But the thing is, just being supercritical isn't enough. Your mass has to be really supercritical to get a bomb of any serious yield. This is because supercriticality tends to be self-limiting. To see why this is, let's examine what (probably) happened with North Korea's unsuccessful atomic bomb test: Fizzle.

The North Korean bomb test managed to create a pretty supercritical mass of U-235². The chain reaction starts, and, as intended, a really impressive amount of energy is delivered in a really short period of time, causing an explosion. But in that unsuccessful bomb test, the resulting (relatively small) explosion blew the mass of uranium apart before most of the U-235 had a chance to fission. So there was an explosion, but not nearly as big as they were looking for.

It turns out it's really hard to get around this problem. The North Korean engineers had to work pretty damn hard even just to get the result they did. If you tried to just slowly squeeze some U-235 together to make a supercritical mass, you'd never get there, because as soon as you got very slightly supercritical, you'd either burn up enough uranium that you weren't supercritical anymore, or you'd heat it up and the density would go down enough to take you out of the supercritical zone.

And that's what makes it so damn hard to build a nuclear bomb. Your bomb contains some amount of subcritical material, and you need to smash or squeeze it together so that it becomes not just a little supercritical, but hugely amazingly supercritical, and it does it so fast that the bomb doesn't blow itself apart when you are only halfway there. Even successful nuclear bombs of the type described so far have a fairly low percentage yield, which is why engineers have designed all sorts of clever ways to mitigate this problem.

(For a moment, I must digress because I noticed my enthusiasm is showing through here. I find the technology behind nuclear weapons to be absolutely awe-inspiring; it is just such a remarkable feat of pure engineering. But from a human perspective they are also terrible terrible things, and I am confident the world would be better off without them. Just to be clear. My fascination with the technology does not in any way diminish my opposition to the horror that these devices can wreak upon humankind.)

So what does all this have to do with nuclear power plants? Well, as mentioned before, you want the fuel for your nuclear power plant to be right around (actually just under) the critical mass. That means it's not even close to exploding. (The explosions at Fukushima Daiichi were hydrogen combustion explosions, not nuclear explosions, and other blogs have already explained how that happened far better than I ever could)

Even if somehow the fuel got compressed so that it became supercritical, it would rapidly self-correct down to the critical level, by heating, melting, or (if somehow it got really supercritical, which it wouldn't) blowing apart. It's just so damn hard to get uranium to the level where you'd have a legitimate atomic bomb explosion, there's just no way it could possibly happen by accident.

We might have intuitively expected this, since the first artificial nuclear reactor was built by Enrico Fermi and a handful of grad students on a freakin' abandoned tennis court (and in fact it even occurs naturally in at least one place in the world), whereas the first successful nuclear bomb test required scores of the world's top physicists, a massive industrial support operation, and god knows how much money and resources. But it's worth understanding the reasons anyhow.

This doesn't mean that the situation at Fukushima Daiichi couldn't get really bad. The worst case scenario for a nuclear power plant is more akin to a dirty bomb, which is not exactly super happy fun time either. And, I struggle how to say this tactfully, but the real tragedy may be that this torpedoes our last best shot at a politically tenable solution to (at least temporarily) dodge the problem of global warming. It is only a little bit hyperbolic to say that this tsunami may in the end kill billions. More about that in a future post, perhaps.

¹Turns out this is not so much "beside the point" as I thought. Karl Withakay tells us that while the fuel used in commercial nuclear reactors is enriched to contain about 3-5% U-235, the minimum purity requirement for a bomb is around 20%, and in practical devices it is much much higher. So not only is it impossible for even highly-enriched uranium to "accidentally" become supercritical enough to create a significant explosion, you couldn't even do it on purpose with the fuel used in nuclear reactors.

²Karl also points out that the North Korean test used plutonium rather than uranium. For the purposes of this explanation, the concept is similar enough to suffice. But please do read Karl's comments, which provide some additional technical background and clarify a few minor errors I made in trying to whip off this post using top-of-my-head knowledge rather than actually doing the research.