Susan X-Plains Prompt Critical

Kickass scientist Susan Beaver–who’s also the former associate director of the Reed Research Reactor–joined us in Episode 114 – Meltdown to talk about the actual science of nuclear reactors. Unfortunately, the downside of talking about complex science on a comics podcast is that there’s never enough time to go into as much depth as we’d like. Luckily for us–and you–Susan was kind enough to write a follow-up, discussing some of the terms and concepts we had to gloss over in the episode proper. -Jay

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Let’s talk about nuclear fission.

As I got to say in the episode, the fourteen-page rundown of basic nuclear fission and the Chernobyl disaster that starts of Havok and Wolverine: Meltdown is surprisingly accurate, aside from attributing the human errors to a nefarious conspiracy rather than a combination of bad design and bad judgment. But one thing that the artistic overview doesn’t explain is a term that comes up a couple times in the comic, and that’s the term “prompt critical”.

It surprised me to see that term come up in the comic, since most of the time when people in entertainment industries throw around concepts regarding nuclear reactors they’re getting them wrong. (If you’ve ever had a career that gets depicted in movies and television shows–I’m looking at you, CSI techs and nurses–you know exactly what I mean.) So to see the comic getting a lot right was a welcome surprise. Radiation signs posted the correct way up instead of rotated 30 degrees! Neutron moderation! Control rods! And, of course, the sinister-sounding (not Sinister-sounding, though in this comic you have to be careful) phrase “prompt critical.”

So what happens when a nuclear reactor goes prompt critical?

In order to explain a prompt critical reactor, I’ll need to talk about a few things that happen during a fission chain reaction. I’m going to go step by step through all the things that happen in bringing a reactor to power, and I’ll have a section at the end where I actually go through the math for those who are curious. But don’t worry, calculators can stay in your desks, we don’t need to talk about hard numbers in order to understand the concepts.

Dr. Neutron talks us through the basics. Uranium 235, which is the less-common but more easily fissioned natural isotope of Uranium[1], absorbs a neutron and breaks into pieces. Strontium and Cesium are indeed two of the more common fragments that fly off our broken Uranium nucleus, but fission fragments come in many shapes and sizes. Including, of course, more neutrons.

Now, Uranium-235 only wants to absorb neutrons at a lower energy than they come out of a fission event. This is where the graphite moderator in the Chernobyl reactor comes in. The only way to slow neutrons down is to bounce them off other atoms, like billiard balls bouncing against each other and the sides of the table. Once these neutrons slow down enough, they can get absorbed by the fuel and cause another fission event. The time between these fission events is called the *prompt neutron lifetime*.

Why prompt? Well, *prompt* in neutron terms refers to neutrons that come directly out of fission events. There is another source of neutrons in the reactor core, though. Remember how I said that the pieces of uranium atoms after fission come in all shapes and sizes? Well, some of those pieces also have extra neutrons that they spit out. These fission fragment neutrons come out up to a minute after the original fission event, so they’re called delayed neutrons. There aren’t very many of them compared to prompt neutrons, but they’re less energetic, so they get absorbed more easily. Delayed neutrons have an important drag effect on reactor power. Because of them, power goes up and down more slowly, which is very important when you’re trying to control a nuclear reactor.

So now we know what prompt neutrons are. What does *critical* mean?

Critical is another one of those reactor words that gets used a lot because it sounds impressive and kind of scary, but it’s actually one of the least scary words you hear working at a nuclear reactor. When a reactor is critical, that means that the fuel is producing and absorbing just enough neutrons–prompt and delayed–to keep a steady state of power. Fission always produces more neutrons than the one absorbed by the uranium, so those extra neutrons get absorbed by the control rods. (Or they bounce out of the core or get absorbed by other things in the core, like the coolant or the xenon that Dr. Neutron talked about, but it’s the control rods that the operator moves to change how many neutrons are being absorbed.)

If a reactor isn’t creating enough neutrons to sustain a chain reaction, if too many are being absorbed by the control rods and the power is decreasing, the reactor is *subcritical.* And if the reactor is increasing in power, it’s *supercritical*. I don’t have first-hand experience with a Soviet-style power reactor, but the research reactor that I ran (with a maximum power of 250 kW, several thousand times smaller than Chernobyl which had a normal power of 3200 MW (or 3,200,000 kW)) would go from 0.025 kW to 250 kW over a couple minutes under the eye of a watchful operator.

However! Remember how I said that delayed neutrons act like a drag on reactor power? Without them, reactor power would increase exponentially faster. Reactor operators wouldn’t be able to control the reaction, because the tiniest shift in control rods or core conditions would cause the power to start increasing or decreasing thousands of megawatts per second. And that’s what happens in a prompt critical reactor. Being prompt critical means that the reactor is generating enough neutrons to be critical on prompt neutrons alone. That means that all the delayed neutrons go into accellerating the increase of power.

So what does a prompt critical reactor look like? Well, for the Soviet Union’s reactor design, it looked like a complete disaster. The positive temperature feedback design, which meant that as the reactor increased in power it got more efficient, meant that there was no natural brake on the power increase. The massive amounts of heat generated caused a steam explosion which broke open the containment vessel and vaporized the remaining coolant, and the fuel itself melted through the floor and into the basement. The graphite fire was really adding insult to injury at that point.

In the United States (and most countries since the Chernobyl disaster) reactors are designed with a negative temperature feedback. As reactors with this design heat up, they get less efficient, and control rods have to be pulled out further in order to keep the reaction going. A prompt critical reactor in the USA still has the potential to be a disaster–read the history of SL-1, the worst reactor accident in the USA, for an example–but a reactor is much less likely to get to that state because of the negative feedback.

In addition, some reactors are designed to take advantage of that state. Reactors with a very quick power response to temperature can perform what’s called a pulse, where a control rod is ejected from the core fast enough to briefly put the reactor in a prompt critical state. And thanks to the internet, some of these reactors have put videos of the process up on YouTube:

A nice HD recording of a pulse at JSI, with the lights on so you can see the core

A bit of background noise from the primary cooling system, but really nice color balance. UT Austin.

Here it is in slow-motion! 240 fps means it’s ten times slower than normal. The video doesn’t say which reactor this is, but there are only about 17 TRIGA Mk IIs active in the world, so with some sleuthing I’m sure we could figure it out.

Here’s another underwater camera without sound. I don’t know for sure what the bubbles are following the pulse, but they’re most likely nitrogen gas created by the absorbtion of neutrons by oxygen in the water in what’s called a p-n replacement reaction. The radioactive nitrogen decays back to oxygen by the time it reaches the surface of the pool.

So there you have it! Nuclear reactors are capable of great destruction, which is why they need to have careful oversight. But they can also be designed to be much safer than the reactors at Chernobyl, and can allow us to do a lot of cool things we’d be unable to do otherwise.

For more information about SL-1: accident recovery and accident description with a really good animation.

For more information about the blue glow.

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Addendum: Oh, you wanted math?

Every time a fission event happens, more neutrons are created than were absorbed by the fissile nucleus. The ratio of the neutrons produced in the new generation to the neutrons produced in the previous generation is called the multiplication factor, k. When talking about nuclear reactors in the real world, we use the term k_eff, or “k-effective”:

k_eff = number of neutrons produced by fission in a generation / number of neutrons produced by fission in the previous generation

So we can see that if k_eff is less than one, there are less neutrons in each generation and power is decreasing (the reactor is subcritical.) If k_eff is equal to one, the power is steady and the reactor is at critical. And if k_eff is greater than one, the power is increasing and the reactor is supercritical.

Moving the control rods in a reactor affects one of the factors that makes up k_eff. To increase power the rods are removed until the reactor power is increasing, the operator waits until the power is at the desired level, and then the rods are moved again to return k_eff to one. Of course, other factors can affect k_eff besides the control rods: the buildup of xenon is one, and the effect of heat on the core is another.

The ratio of k_eff doesn’t make any distinction between prompt neutrons and delayed neutrons, but the difference is very important. First, let’s define some more terms. The lifetime of a neutron generation–the time it takes for a neutron to go from creation to causing another fission–is called l. The lifetime of prompt neutrons only depends on the time it takes for the neutrons to slow down and diffuse through the fuel, and this is a very short time scale indeed, on the order of a hundredth to a ten thousandth of a second. (Water moderated reactors have a much shorter lifetime than graphite moderated reactors like Cheronbyl, because water slows down neutrons faster than graphite does.) For prompt neutrons, we call this lifetime l*.

Now, by performing some derivations which I will leave as an excercise as the reader, we can demonstrate that the rate of fission, which we’ll call n, is determined by how long the reaction has been supercritical and the size of the multiplication factor:

n(t) = n(0)e^((k_eff-1)t/l*)

This is ignoring delayed neutrons for the moment. Notice that as long as k_eff is greater than one, the number of fissions increases exponentially! This means that not only is power increasing, it’s accellerating.

The period of the reactor T, is the amount of time it takes for the power to increase by a factor of e. If we’re only considering prompt neutrons, then we can define T:

T = l*/(k_eff-1)

Now, for normal reactor operations, delayed neutrons are very important. The delayed neutron fraction, defined as beta, has a mean lifetime of about 12 seconds. The mean lifetime of all the neutrons will be:

(1-beta fraction)l* + (beta fraction)l(delayed)

For graphite reactors, this works out to around 9.4×10-2, which is six times longer than the prompt neutron lifetime of 1.6×10-2. In light-water reactors, this difference is even more dramatic, on the order of a hundred times longer!

This can change the period of the reactor drastically. A graphite reactor with a k_eff of 1.01 with only prompt neutrons will have a period of around 2 seconds, while with delayed neutrons, the period is up to ten seconds. That’s a big difference when you’re talking about increasing power in a power reactor!

Now, we can actually define numerically what prompt critical means. It is the state that occurs when k_eff = 1/(1-beta). This means k_eff is high enough that it overwhelms the delayed neutrons with prompt neutrons, and it takes a nuclear reactor from routine button-pushing to scrambling for the SCRAM bar. It’s even worse in a reactor like Chernobyl, where all that power keeps increasing k_eff in a cycle of increasing power.

[1]: Uranium-238, the most common form of uranium, is more than 99% of the naturally-occurring uranium in the world. It also can absorb neutrons and produce fission, but it absorbs much less readily than U-235. The process of increasing the proportion of U-235 in a sample of uranium is called enrichment, and involves huge centrifuges and lots of chemical processing. Bomb-grade uranium is enriched to as close to 100% U-235 as you can get, while nuclear reactor fuel is usually in the 2-20% range.