physics, science

The Moment a Nuke Goes Off

Nuclear weapons give me mixed feelings. On the one hand, I really like explosions and physics and crazy shit. But on the other hand, I don’t like that somebody thought “You know what the world needs? A bomb capable of ruining the shit of everybody in an entire city. And you know what we need? Like fifty thousand of the bastards, all in the hands of angry buggers that all have beef with each other.”

That aside, though, the physics of a nuclear explosion is pretty amazing. Especially when you consider that nuclear bombs were developed at a time when: there was no vaccine for polio, commercial airliners hadn’t been invented, the big brains in Framingham hadn’t even started to work out just what causes heart disease, and a computer needed one room for all the vacuum tubes and another for its air conditioning system.

There’s an absolutely awesome 1977 paper by Glasstone & Dolan that describes, in great detail, and from beginning to end, the things that happen when a nuke goes off. The paper’s also surprisingly readable. Even if you’re a little rusty on your physics, you can still learn a hell of a lot just by skimming it. That’s the mark of a good paper.

To me, the most shocking thing in that paper is just how quickly the actual nuclear explosion happens. But first, a little background. This is what the inside of an implosion-type fission bomb looks like (This is the type that was dropped on Nagasaki, and seems to be the fission device used in modern arsenals. Correct me if I’m wrong.)

Fat_Man_Internal_Components (1)

(Source.)

It looks complicated, but it’s really not. The red thing at the center is the plutonium-239 that actually does the exploding. The dark-gray thing surrounding it is a hollow sphere of uranium-238 (I’ll explain what that’s for in a second). The light-gray thing is an aluminum pusher (I’ll explain that in a second, too). And the peach-colored stuff is the explosive that sets the whole thing off. The yellow things it’s studded with are the detonators.

When the bomb is triggered, the detonators go off. Spherical detonation waves spread through the dark-peach explosives on the outside. When they hit the light-peach cones, the shape of those cones forms the thirty-two separate waves into one smooth, contracting sphere. That spherical implosion wave then passes into the dark-peach charges surrounding the aluminum pusher. So far, the process has taken roughly 30 microseconds.

When the implosion wave hits the pusher, it crushes the aluminum inward, generating remarkable pressures. This takes something like 10 microseconds.  The pusher’s job is to evenly transfer the implosion force to the core.

The imploding pusher then crushes the uranium tamper in roughly 15 microseconds. The tamper serves two purposes: it helps reflect the neutrons generated by the plutonium-238, and, being such a dense, heavy metal, its inertia keeps the core from blowing itself apart too quickly, so more of it can fission.

Speaking of the core, a whole bunch of crazy shit is about to happen in there. Normally, I don’t think of metals as the sort of thing you can compress. But when you’ve got hundreds of kilos of high explosives all pointing inwards, you can compress anything. The core is a whopping 6.4 kilos of plutonium (14 pounds). That’s how much plutonium it takes to wreck an entire city. But just having 6.4 kilos of plutonium lying around isn’t that dangerous. (Relatively speaking.) 6.4 kilos is below plutonium’s critical mass. At least, it is at normal densities. That implosion wave, though, crushes the plutonium down much smaller, until it passes the critical limit by density alone. (There’s also a fancy polonium-210 initiator in the center, to make sure the core goes off when it’s supposed to, but this post is already getting too rambly…)

Once the plutonium passes its critical limit, things happen very quickly. Inevitably, a neutron will be emitted from an atom. That neutron will strike a Pu-238 nucleus and cause it to fission and release a couple more neutrons. Each of these neutrons sets off another Pu-238 nucleus, and bam! We’ve got the right conditions for an exponential chain reaction.

Still, from the outside, it doesn’t look like much has happened. It’s been approximately a hundred microseconds since the detonators detonated, but next to none of the plutonium’s fission energy has been released. Here’s a graph to explain why:

Nuclear Explosion

(Generated using the excellent fooplot.com)

Here, the x-axis represents time in nanoseconds. The y-axis represents the number of neutrons, expressed as a percentage of the number needed to release 21 kilotons-TNT of energy (the amount of energy released by the Fat Man bomb that destroyed Nagasaki). At time-zero, the neutron that initiates the chain reaction is released. And by time 240, all of the energy has been released. But the thing to notice is that it takes all of 50 nanoseconds for the vast, vast majority of the fissions to happen. That is to say, the plutonium core does all the fissioning it’s going to do–releases all of its energy–within 50 nanoseconds.

21 kilotons-TNT released over 50 nanoseconds is equivalent to a power of 1.757e21 Watts. That’s ten thousand times more power than the Earth receives from the sun. That’s roughly 5 millionths of a solar luminosity, which sounds small, until you realize that, for those 50 nanoseconds, a 14-pound lump of gray metal is producing 0.0005% as much power as an entire star.

The nuclear explosion happens so fast, in fact, that by the time it’s finished, the x-ray light released just as the chain reaction took off has only traveled 15 meters (about 49 feet). Everything happens so rapidly that the bomb’s components might as well be stationary. The casing might be starting to bulge outward from the detonation of the implosion device, and the bomb, while still bomb-shaped, is rapidly evaporating into plasma as hot as the core of the fucking sun. But even at those temperatures, the atoms in the bomb haven’t had time to move more than a couple centimeters. So, by the time the nuclear detonation has finished, the bomb and the surrounding air look something like this:

Fat Man End of Detonation.png

But perhaps the wildest thing of all is that we’re not limited to hypothetical renderings here. We actually know, thanks to the incomparable Harold Edgerton, exactly what those first moments of a nuclear explosion look like. Doc Edgerton developed the rapatronic camera, whose clever magneto-optic shutter is capable of opening and closing with an exposure time of as little as 10 nanoseconds. The results of Mr. Edgerton’s work speak for themselves:

Glowing Shot Cab

The thing above is the “shot cab” for a nuclear test. It’s a little shack on top of a tower, with a nuclear bomb inside. In this picture, the bomb has already gone off. Those white rectangles are actually the cab’s wall panels, being made to glow brightly by the scream of X-rays bombarding them. And those ominous-looking mushroom-shaped puffs are where the X-rays have just started to escape into the air and make a nuclear fireball. A moment (probably measured in nanoseconds) later, the fireball looks like this:

Very Early Fireball

I take my hat off to Mr. Edgerton for having the guts to say “Oh? You need a photograph of the first microsecond of a nuclear explosion? Yeah. I can probably make that happen.” (Incidentally, both those photos are taken from the paper “Photography of Early Stages of Nuclear Explosions”, by Edgerton himself, which is, regrettably, behind a fucking paywall. Grumble grumble.)

And, thanks to sonicbomb.com, we can see the evolution of one of these nightmare fireballs:

Hardtack_II

Progressing from left to right and top to bottom, we can see the shot cab glowing a little. Then glowing a lot. Then erupting in x-ray hellfire. And after that, just sort of turning into plasma, which things that close to a nuclear explosion tend to do.

Soon enough, this baby fireball evolves into a nightmarish jellyfish from the deepest pit in Hell:

Tumbler_Snapper_rope_tricks.jpg

(Source.)

The horrifying spikes emerging from the bottom of the fireball are caused by the so-called “rope-trick effect”: they’re the guy wires supporting the shot tower vaporizing and exploding under the onslaught of radiation from the explosion.

And soon enough (after about 16 milliseconds), the fireball swells into a monster like this:

Trinity_Test_Fireball_16ms.jpg

(Source. Note, this is the fireball from the Trinity test, humanity’s first-ever nuclear explosion.)

It’s worth noting that, at this point, 16 milliseconds after the bomb goes off, your retinas have barely had time to respond to the flash. In the roughly 75 to 100 milliseconds it takes the retinal signal to travel down the optic nerves and reach your brain, you are already being exposed to maximum thermal radiation. And after a typical human reaction time (something like 150 to 250 milliseconds), about the time it takes to consciously register something, you’re probably already on fire.

So nuclear explosions are cool, and they’re awe-inspiring, but I must pose the question once again: who the hell saw the plans for these hell-bombs and thought “Yeah. That’s a thing that needs to exist. We need to have that nightmare hanging over humanity’s head forever! Let’s build one!”

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Exploding rabbits.

(Courtesy of Wikipedia.)

I have a thing against rabbits. I don’t like them. They fill me with contempt. There’s absolutely no reason for this. It’s an utterly irrational hatred. Because of this particular neurosis, during a conversation with a friend, I happened to say something about vaporizing a rabbit. That sent my loony swamp-bog brain spinning off on another of its tangents, and I started to wonder What would happen if you vaporized a rabbit?

For the sake of this thought experiment, I’m going to start off assuming that a rabbit weighs 1 kilogram. That’s within the mass range listed by Wikipedia, but Wikipedia can’t always be trusted. But by virtue of the fact that they exist, we know that rabbits weigh more than 0 kilograms, and by virtue of the fact that we don’t inhale rabbits and get horrible nibbling-rabbit pneumonia, we know that they probably weigh more than 0.000 000 000 000 001 kilograms (1 picogram, which is about the mass of a bacterium). And from this oft-referenced report from the BBC, of Ralph the Unthinkably Large Bunny (who I must admit is kinda cute), we know that rabbits can reach 7.7 kilograms. So 1 kilogram is not unreasonable.

Now that we’ve got that bit of pedantic obsessiveness out of the way, we can proceed.

Most organisms contain quite a lot of water. The density of a human being is similar to the density of water. (If you can float in a pond or a swimming pool, your density is less than that of water, meaning less than 1,000 kilograms per cubic meter. If you have to tread water, your density is higher than 1,000. For the record, I float.) So, for the sake of simplicity, let’s pretend that our 1-kilogram bunny is made entirely of water, like a really disappointing version of those chocolate Easter bunnies. Let’s also assume that it starts out at typical rabbit body temperatures: 100 Fahrenheit, 38 Centigrade, or 311 Kelvin. In order to vaporize this all-water rabbit, we have to add enough heat-energy to it to raise its temperature to the boiling point, which is 212 Fahrenheit, 100 Centigrade, or 373 Kelvin (Have you noticed that we have way too many fucking temperature units? It’s a pain.) That’s a difference of 62 Kelvin. To find out how much energy we need to boil this rabbit (and make some extremely watery rabbit stew), we need water’s specific heat capacity, which happens to be about 4.18 Joules per gram Kelvin.

Specific heat capacity is one of those nice units that just makes sense. Newton’s gravitational constant is measured in units of (Newtons * square meters) / (square kilograms). What the fuck is a square kilogram? Well, the constant is one of those universal constants that tells you, in a vague way, just how weak a force gravity is. Specific heat capacity, though, makes intuitive sense. Water has a specific heat capacity of 4.18 Joules per gram Kelvin (Not to be confused with Jules per Graham Kevin, who is the president of the Earth in the alternate reality where Canada became a totalitarian superpower). That means that, to increase the temperature of one gram of water by one Kelvin, you have to add 4.18 Joules of heat energy to it. The units tell you exactly what they mean, which is nifty.

Anyway, in order to heat our rabbit-shaped mass of water to boiling temperature, we need to add 259,200 Joules of heat energy. But notice that I said “to heat our rabbit-shaped mass to boiling temperature.” That’s not the same as actually making it boil. For that, we need to add extra energy. This extra energy won’t increase the temperature at all, but it will get the water over the hump and vaporize it. This extra energy is quantified by another constant: the specific heat (or enthalpy) of vaporization. For water, this is 2,260,000 Joules per kilogram. That means we need 2,260,000 more Joules to turn our rabbit-shaped water balloon into a rabbit-shaped cloud of steam. So, all told, we’re concentrating 2,500,000 Joules into a volume on the order of 1,000 cubic centimeters. 2,500,000 Joules is about the energy released in the explosion of half a kilogram of TNT, which seems to me (citation needed) like a decent fraction of a stick of dynamite.

Unfortunately, energy alone isn’t going to get us the explosion we’re looking for. Just because we have the equivalent of a stick of dynamite doesn’t mean we’re going to have the same explosion as a stick of dynamite. That energy is all bound up in the rabbit-shaped cloud of steam.

What will get us the explosion we’re looking for, however, is the fact that we’ve got a cloud of hot gas compressed to the density of water and eager to expand. From the ideal gas law (and assuming a rabbit volume of 1,000 cubic centimeters), the cloud will begin at a pressure of 1,699 atmospheres (172.19 megapascals). That’s about half the pressure generated by the burning gunpowder in a .357 magnum cartridge. Maybe not enough to kill you, but certainly enough to make your ears ring. And enough to make you stand in the meadow blinking while a fine mist of rain falls around a little crater in the grass, asking yourself what the hell just happened.

But you know what? Rabbits aren’t just made of water. They’re made of all sorts of weird shit like water, tubulin, hemoglobin, cadherin, vitamin D, collagen, phospholipids, and more rabbit-semen than anybody wants to think about. And from cooking (and from that one scene in The Lord of the Rings) we know that heating a rabbit up to boiling won’t destroy all of its chemical bonds.

I want to make sure this rabbit is gone. I mean gone. Vaporized. I want to rip its fucking molecules apart, so that there’s no trace of fucking rabbit left. I should probably talk to my therapist about this. But for now, I’ll finish what I started.

As it turns out, I can still reasonably assume that the whole 1-kilogram rabbit is made of water, because the hydrogen-oxygen bonds in water are some of the strongest you’ll find in ordinary materials (carbon-hydrogen bonds are stronger, but not by much; nitrogen-nitrogen bonds are much stronger, but there’s not a lot of gaseous nitrogen floating around in a rabbit’s tissues, so we don’t need to worry about it). We’re looking at 55.56 moles of rabbit (NOT 55.56 moles of rabbits; disgusting shit happens when you try to assemble a mole of small mammals). The bond-dissociation energy for the hydrogen-oxygen bond in water is a shade under 500,000 Joules per mole, and there are two such bonds in every water molecule, so the total energy will be about 1,000,000 joules per mole. That means that completely vaporizing a rabbit will require something like 55,500,000 Joules, which is (roughly) equivalent to the detonation of 10 kilograms of TNT. 10 kilograms of TNT works out to just over 6 liters, so imagine two three-liter soda bottles (or six big liter-size beer steins, or a 1-gallon jug and a half-gallon jug) filled to the brim with TNT. That’s more explosives than you find in some artillery shells. You know what that means?

ExplodingRabbit

KAAAAA-BOOOOOOOOOM! 

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