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.
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.
Don't neutrons lose some energy as they transit through the material? That would make this bounded in some respect anyway.
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).
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.
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.
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.
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.
Excluding collisions, it does not. As far as the neutron is considered, it's traveling through empty space, just as if it was in vacuum.
> I suppose the probability of splitting the collidee nucleus decreases.
In this regime, probability of splitting a nucleus goes up as energy decreases.
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.
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".
You might be conflating that condition with prompt criticality.