PingPongReactor

The video may be a tad long for some; if you want to get to the good part, it’s at 4:55m which is the normal speed shot, followed by the 500 fps slo-mo.

One can model the process in a reactor, though this is more like a bomb. In reality one would distinguish between the effects of “fast” neutrons (i.e. ones with significant kinetic energy) and thermal neutrons, which are generally of such low energy that the KE’s contribution to the reaction is negligible, but I’ll ignore that here for simplicity and because the analogies don’t really hold up.

If we consider what happens to a ping-pong ball, we can model the behavior. Once you have a ball in motion, it can physically escape from the region, or “leak” out. The probability it does not leak out — the non-leakage probability — is L. Since the walls are not of infinite height and there is a hole in the surface, L < 1.

If a neutron does not leak out, it might hit a trap and cause it to snap. The probability that this happens is f, which we will call the utilization fraction. This depends on the ratio of the probability that the ball hits a loaded trap and causes it to snap, to the probability of just hitting a trap — in this model we would have to count a ball that lost all of its energy before hitting any trap as one that has leaked. (edit: and also include the probability that a ball could cause more than one trap to trigger)

In this example, a snapped trap gives us two new balls, but in general we can model this reproduction factor as some value n. In real fissions, n depends on which fission products you get.

So we have K = Lfn

If K = 1 the system is critical and the population remains constant. If K > 1 the system is supercritical and the ball population increases, and similarly if K < 1 (subcritical) the population drops. Obviously, at the outset of the video K is significantly greater than 1 since we see a rapid rise in ping-pong-ball population, but as the traps "deplete" f drops, because the number of loaded traps is getting smaller. This rapid change in K makes this more like a bomb, where you are trying to get a lot of interactions in a very short time, while in a reactor you'd like to get up to some reaction rate and maintain K = 1 for a long time.

In a real reactor, the number of neutrons is much, much smaller than the number of fuel nuclei, so this depletion is at a much smaller rate. Imagine, though, if we could construct a system that lasted just a little longer. Since the initial rate of ball multiplication tends to be higher, you could "poison" the system by adding a sticky blob here and there that would grab and hold a ball if it struck, but these losses would diminish over time as you used up the blobs. Reactors do this with Boron-10, which quite happily absorbs neutrons, but only once — B-11 is much, much less likely to undergo this "capture" reaction.

Another effect would be to initially lower the wall(s) and let more balls escape, and raise them over time, meaning that your non-leakiage factor is compensating for the drop in the utilization fraction. The changing wall in this case would be the effect of changing the height of the control rods, though in a real reactor this exposes more fuel, making the reactor effectively bigger, but also harder for neutrons to leak out. Real reactors are often designed so that as the reaction rate drops, the water that thermalizes (slows/moderates) the neutrons undergoes a drop in temperature and becomes more dense, which traps more neutrons in the core — another effect which reduces the neutron leakage.