I was also surprised. I thought you had to use an explosive to initiate the reaction. I never took the expression "critical mass" to such a literal expression, but it seems to be.
Criticality is simply the condition where on average a single neutron interacting with nucleii in the device will on average (through initiating fission) cause one or more additional neutrons to interact with nucleii.
Geometry and mass matters here because the "default" thing a neutron does is "misses all the nucleii and exits the device", unless the device is fairly big, simply because as electrically neutral particles neutrons do no interact with electrons and only interact with nucleii when very close, so most material looks mostly like empty space to them.
So in principle if you just form a large enough ball of Pu-239, it would go critical. The reason you need explosives is that in order to form that ball, you need to go from a state where there is not enough material together to go critical to a state where there is, and the criticality will immediately start releasing very large amounts of energy. This energy then heats things and drives them apart, preventing a chain reaction where the entire core goes up.
In the criticality accidents listed above, that is precisely what happened. In Slotin's case, the upper half of the core kept falling on the lower half and then pushed apart.
The reason you need explosives is that you want that release of energy to be as rapid as possible to make the contraption pass `bomb` object class duck typing.
If you kept criticality to a stable level and let energy of fuel release over e.g. 20 years, it's called a nuclear power plant. If you let it run away and let the material melt itself, it's called a meltdown situation. If you instead take highly purified fissile material and compressed it instantly into size of a peanut or however small you could, the material compressed experience nuclear chain reaction everywhere inside that peanut, and spontaneous release of that insane amount of energy resemble behaviors observed with conventional chemical explosive material exploding, and such a contraption that do this is somewhat metaphorically called an atomic "bomb".
They certainly can, see https://en.wikipedia.org/wiki/Resonance_escape_probability. The all-important number in nuclear reactions is "k", the average number of child neutrons a single neutron will produce. The neutron population follows an equation something like N = exp((k - 1) * t). For k<1, you get exponential decay, and for k>1, you get exponential growth (until everything becomes a plasma and k changes). Check out https://en.wikipedia.org/wiki/Six_factor_formula.
The energy of neutrons isn't really analogous to the energy of atoms in chemical reactions, but absolutely affects the reaction dynamics. The "cross section", or interaction probability, is a strong function of neutron speed. In bombs the neutrons don't get a chance to slow down, but in reactors you try to reduce them to "room temperature" speeds using collisions with light, inert nuclei (the moderator). Here's a diagram showing the interaction probability vs. neutron speed for a few isotopes of uranium: https://tinyurl.com/u235-cross-section
It changes very little because there’s nothing to receive their kinetic energy.
Neutrons lose energy by colliding with things of similar mass, such as hydrogen nuclei (often in water). If they collide with a heavy nucleus, such as plutonium, they just bounce off without losing speed. (Or fission or capture.)
Think of billiards. The cue ball may slow or stop after hitting another ball, since they have similar masses. But hit the rail and it just bounces off, at the same speed, because the table is so much heavier.
If there are no light nuclei in the environment, then the neutrons won’t slow down.
No, as in, as the average distance a neutron-hitting nucleus travels before the collision increases, the average energy of the neutron at collision time decreases. Or so I imagine, that's what I'm asking.
The scenario was that the size of the material can increase until you guarantee a sufficiently high rate of collision, and I'm asking whether neutrons really do not lose energy as they travel prior to collision (as the scenario seems to assume).
Why would the average distance a neutron has to travel to strike a nucleus increase?
I suppose it does eventually, as the number of undecayed nuclei falls, but that wouldn’t be a significant effect until the criticality reaction had very significantly progressed. In other words the reaction can’t go on forever.
> Why would the average distance a neutron has to travel to strike a nucleus increase?
Because if the problem is that neutrons are escaping the object before hitting a nucleus, and we are adding more nuclei so the likelihood that they hit something increases, the new collision candidates will be further away than the old ones.
In other words, adding material to the edge of the object does not affect the per distance probability of collision. It only affects the overall probability of collision. Since the per distance probability does not change while the overall probability does, the probability increase must lie outside of the average path length of a neutron through the original object.
In the case we are considering, it doesn’t, but it could with other materials.
Consider that the wavelength of the neutron is a function of its energy, and that the cross sections for interaction between nuclei and neutrons are strong and complex functions of energy.
If the cross section for the interaction of interest gets smaller with decreasing energy, then it would be the case that the neutrons mean free path length would increase as energy decreased.
> In the case we are considering, it doesn’t, but it could with other materials.
Sorry, I said something subtle and easy to miss and also made a confusing typo, writing too fast.
"average distance a [nucleus-hitting neutron]"
As in, as more material is added, the percent of neutrons that successfully collide and don't just fly out increases. But, for the class of nucleus-hitting neutrons, the average distance prior to collision increases.
If the neutron loses energy as it travels, then as the average distance increases I suppose the probability of splitting the collidee nucleus decreases. So as the class increases in size, its rate of nucleus splitting may fall below the threshold, which bounds the useful size increase.
Perhaps this doesn't occur until the object has grown in size way past the point of basically guaranteed criticality, I haven't done the math, just curious since GP's statement sounded as if neutrons do not lose energy across any distance and the object could therefore could be increased to an arbitrary size while maintaining the same qualitative per-iteration behavior, and I find that surprising.
In the regime that's interesting for pure fission devices, the opposite is true. The cross section increases as energy decreases. This is why moderators are a thing in nuclear reactors.
I may be misremembering, but it seems like I've read that the explosive variation is the "supercritical mass". Critical masses aren't anything to sneeze at though, unless you like the tickle of fast neutrons massaging your internal organs.
Criticality is what you get in a nuclear reactor and what killed Slotkin. Supercriticality requires explosives. One is a self-sustaining chain reaction, the other is a runaway chain reaction.
