I'm no "science popularizer", but I can't resist a good chance to explain a tough concept.
Hmm. My (admittedly layman's) understanding of nuclear physics is that...
Yes, you have a layman's understanding. But unless you're also a string-theory physicist who fools an adulterous ex-politician "anchor" that he knows what he's talking about, then you still have credibility.
... in the absence of a neutron "brake" (eg., the control rods), the reaction will occur uncontrollably.
It can. What usually happens a few microseconds afterward, though, is that the resulting rise in power overheats the system until things boil & melt. The components (including the uranium fuel) tend to fly apart from this pressure/heat, which spreads out the fuel. The geometry becomes once again a sub-critical mass. There are still plenty of neutrons and fission products, but the nuclear reaction is no longer critical.
In fact, even with the "brake" fully applied (the control rods fully inserted, absorbing a large percentage of stray neutrons), the nuclear fuel still generates an enormous amount of decay heat (7-10% of full capacity). So much so that they still need to be cooled by being completely immersed in water. And that water gets so hot that if it were not in a sealed pressure vessel, it would be boiling. In fact, in cases where the water level dropped and the water did in fact boil, even the tiny "voids" in the water (the bubbles) were enough to compromise the cooling effect of the water, and overheating occurred.
True.
"Nucleate" boiling (water phase-transforming into small steam bubbles forming on the metal surfaces and quickly detaching) is an extremely efficient way to transfer heat. It'd be great if we could control it. Unfortunately it usually mutates into "departure from nucleate boiling" where the water heats up and transforms into sheets of bubbles that grow into steam blankets around the metal surfaces, greatly reducing heat transfer and allowing the decay heat to melt the metals. We can't reliably keep NB from turning into DNB so we try to avoid both of them. Usually the only way to get things back under control is to raise the pressure to collapse the bubbles back into really hot (but not quite boiling) water. If the pressure vessel has holes (or if all the high-pressure pumps are out of service) then you can't keep pressure high enough to control/avoid boiling. Nukes get really upset about losing pressure control because the DNB means heat can no longer be effectively removed from the core.
My point is that even with the control rods fully inserted, the reaction is still occurring. If the cooling agent (water) drops below the tops of the fuel rods, they overheat and melt, even when only producing "decay" heat. Thus, the reaction is "sustained," even after the geometry of the fuel rods disintegrates into a puddle of molten uranium.
Semantics issue. The fission chain reaction has stopped and quickly subsides. The decay of the fission fragments continues, which is still a heat-removal problem, but that's not fission. That's just decay.
As I understand it (and again, I'm no physicist), the only requirements for a sustained fission reaction is proximity/density of fuel, and absence of a neutron absorber.
Incorrect. Proximity/density is one requirement, and absence of a neutron absorber is another. But the uranium's fission neutrons usually fly out of a nucleus with too much energy to be absorbed by nearby uranium nuclei. The neutrons zip out of the fuel mass and don't sustain the chain reaction. The trick is to slow the fission neutrons down enough to allow nearby uranium nuclei to absorb them. This is done by letting the neutrons ricochet around enough to lose some energy. The best ricochet material is hydrogen atoms, and there are two of them in every water molecule. So the fission neutrons zip out, bang around in the water molecules until they lose enough energy to slow down, and then smack into another uranium nucleus with just the perfect amount of energy to be absorbed to cause a new fission.
The proximity and number of hydrogen atoms is critical. Just messing with their density will disrupt their ability to slow down the fission neutrons. If the core heats up the surrounding water, the water molecules try to spread out and they let too many neutrons escape. So as a core's fission raises its power and heats the water, the water lets more neutrons escape and the fission reaction levels off. This negative-feedback loop in a pressurized-water reactor is what lets the nukes control the core's power.
In a molten state, at the bottom of the reactor chamber, I would expect that both of these conditions would be met, and the reaction would indeed be sustained indefinitely.
Nope. Definitely not enough water around to slow down the fission neutrons. Fission stopped as soon as the water boiled, but decay heat generation (and a lack of heat transfer) started the melting. Of course the melting leads to boiling off the water and the loss of even more heat transfer, so the molten mess gets hotter. Lots of decay fission products are gases, and if the mess stays hot then it keeps offgassing radioactive fission products which eventually leak out of the containment vessel. So even though there's no more fission, and even though decay heat is dropping off (eventually), nukes still have to get excited about cooling the molten mass to stop the offgassing.
I'm not sure what you mean here - you seem to be saying the water helped facilitate the fission reaction. My understanding is that the water actually discourages the nuclear reaction (by absorbing stray neutrons, preventing them from perpetuating more reactions), in addition to providing a cooling effect to avoid meltdown.
Water does both. In the right core geometry, pressure, and temperature, it will help slow down fission neutrons to create more fissions.
In a big cooling tank, without the right core geometry ("critical mass"), the water slows down neutrons as always. However those neutrons don't find a nearby uranium nucleus in time to keep them from experiencing more water collisions and slowing down to the point where they can no longer cause a fission. Or the neutrons slow down enough to get captured by other materials (like the hafnium in control rods, or the boron in core poisons) before they get to uranium atoms.
Sure, but I believe that that "decay heat" is itself a fission reaction, and in the absence of a cooling agent, will generate enough heat to reduce the fuel to a molten state.
Another semantics issue. The fission products are still spewing off parts of themselves but it's usually in the form of neutrons, high-energy electrons, gamma rays, and alpha particles. Nothing like the big chunks that come from a fissioning uranium nucleus.
To be fair, we're talking about dramatically different amounts of nuclear fuel here. The amount of raw nuclear material in the Hiroshima and Nagasaki bombs were about the size of a softball. The nuclear reactors in question contain much, much more fuel than that. Also, the bombs were only able to fission about 10% of their material before being dissipated too broadly for the reaction to continue. Left undisturbed, the reactor core material will continue to fission to a much higher percentage, unless we can extract it and separate it from itself.
It's not just the "amount", but also the density of the U-235 atoms and their geometry.
In the 1930s everybody knew how to fission U-235. It just wasn't sustainable, the same way today's laboratory fusion reactors aren't sustainable. The problem was purifying enough of U-235 into a big enough ball to cause the fission chain reaction to be sustainable instead of a short-lived "fizzle". The only effective way to purify the 0.7% of U-235 from the uranium ore (mostly U-238) was by the centrifuging banks developed at the Oak Ridge labs (and duplicated all over the world today).
Commercial nuclear reactors can be built out of natural uranium. Geologists even discovered a formation in Africa where a rich uranium deposit was soaked in water in just the right conditions to cause a "natural" chain reaction-- but one that quickly melted the formation and ended the fission. Navy nuclear reactors use an unbelievably highly purified U-235 fuel in a very small space which, ironically, is that much more easily handled by the control rods and the surrounding water because of its small size.
So "left undisturbed", the core material will fission, but it usually produces enough heat (and pressure) to mess up its geometry. In effect it separates itself and can no longer maintain criticality. The big challenge for weapons designers is using unbelievably high pressures to keep the critical uranium together long enough to cause all of it to fission-- even a couple of microseconds makes a difference.
Again, I'm not a physicist, everything I just wrote could be completely wrong.
Like the physicist, it's enough correct information with enough comprehension errors to cause all sorts of confusion.
This stuff ain't easy. A fission chain reaction is a combination of physics and chemistry complicated by thermodynamic heat transfer. It happens so rapidly that even the math defies analysis and is dependent on statistics & probability.
The learning process is brutal and Darwinian. I graduated pretty high up in my USNA class and still got beat up by Admiral Rickover before he grudgingly admitted I might be worthy of the chance. My six months of nuke power school class lost 20% enroute graduation, and that was just classroom lectures & essay tests. By then I was middle of the pack. My six months of shore-based nuclear power plant training was in upstate New York (even back then we actively avoided M_Paquette's Idaho classroom) for more studying, essay exams, and watchstanding. By then I'd sunk down to the lower third of the pack and I actually failed a final exam. (Two of my classmates put themselves into psychiatric care during this period, and were no longer with us.) I managed to pull it all together by my final boards and graduate, but I was not among the sharper tools in the shed.
Confirmed masochists like Gumby tired of the Navy and entered the civilian nuclear power industry, where they were treated like nuclear newbies and made to suffer the training & qualification process all over again. Because those civilian designs have different physics, chemistry, and thermodynamics characteristics than the Navy plants-- let alone the different control systems and missions.
