What do Sheldon, zebras, and nuclear power all have in common?

In my last post, I tried to give you a little technical insight into how a nuclear power plant can be made passively safe.  These safety systems are not the coolest passive safety systms incorporated into modern day plants though.  Some of you had your ear caught by the idea of a nuclear power plant that was stable, even when all cooling systems were removed during operation.  This is by far the worst case scenario that a nuclear reactor could face.  Designing a reactor that will not allow itself to heat up enough to meltdown despite the loss of all cooling is kind of like genetically breeding a cat to clean its own litterbox and feed itself.  It fixes a lot of the problems of having one.

Any reactor that could be built in the United States now has to have what is known as a negative feedback coefficient.  I am sure that nuclear engineers refer to this as a NFC to go along with the other 10,000 acronyms that they have...ok, I made that up.  Anyway, the negative feedback coefficient means that any kind of power increase in the reactor (which is responsible for the reactor getting hotter) causes the reactor to automatically begin to shut itself down until it obtains the original power level.  Old reactors, and many research reactors do not do this.  Many of them actually have positive feedback coefficients, meaning that the power level in the reactor increases as a result of a power increase.  This is not good when it comes to the safety of a commercial reactor.

So how do we design a reactor to have a negative feedback coefficient?  Well, there are several mechanisms that cause negative feedback in the reactor, but I want to talk about my favorite one.  It is something known as doppler broadening.  Yes, it is related to doppler effect that you all know and love, especially if you watch the Big Bang Theory.

The doppler broadening effect in nuclear engineering has nothing to do with a shift in frequency though.  The effect is actually quite complicated as I found out when I wanted to do a presentation on it for an undergraduate nuclear physics class.  I wish I knew of another place to point you to learn more about the subject, but all I can point you to is engineering textbooks for more information.  Sorry about that!  On the other hand, you are about to get a lesson in something that few outside of nuclear engineers know much about.  Don't worry, I don't claim to know that much about it either, but I never the less will tell you what I have deciphered.

In nuclear engineering, a quantity known as the microscopic cross section is one of the most important properties for nuclear materials.  It is basically telling us the probability of a neutron interacting with our nuclear fuel.  For fissile materials, it is this quantity that tells us the liklihood of a fission reaction occuring given a certain neutron.  It is kind of like playing darts.  The microscopic cross section gives us the probability of hitting the dart board.  The bigger the dart board, the more likely I will be to hit it (believe me, I need a big dart board).  In other words, the microscopic cross sectin is kind of like the area of the dart board.  The bigger the cross section, the more likely a neutron will interact with the fuel.

Nuclear materials have what are known as resonances when it comes to reacting with neutrons.  You see, not all the neutrons in a nuclear reactor are the same energy.  In fact, there is pretty much a continuous distribution of neutron energies in the reactor core.  The microscopic cross section though is energy dependent, meaning that it changes depeding on how much energy the neutrong has (how fast the neutron is moving).  The nuclear material is more likely to react with neutrons of some energies than others, meaning that the microscopic cross section is higher for neutrons of certain energies than they are for most.  This gives rise to resonances in the cross section that look like the graph.  At a certain energy, there is a peak in the cross section.

Fissile material is not the only type of material that reacts with neutrons although.  U-238 captures neutrons of certain energies to become Pu-239, which happens to be fissile.  My point is that U-238 also has a cross section for neutrons in a reactor, not just U-235.  Under operating conditions, the resonant peaks for which U-235 and U-238 react with neutrons occur a different neutron energies.  In other words, normally they are not stealing each others neutrons.  U-235 has a high affinity for neutrons of one energy, while U-238 reacts with neutrons of another energy.  They are like two kids that have their own set of toys.  They are off in their own little corners playing their own game.  They are not concerned with what the other is doing.

But the story doesn't remain so friendly.  You see, as it turns out the microscopic cross section is also temperature dependent.  This means that changes in temperature in the reactor affect the cross section, and it does so in a very intriguing way.  It causes the resonant peaks, like the one in the picture above, to kind of melt.  Thus, at the resonant neutron energy, the cross section actually becomes smaller.  This is not what induces the negative feedback though.  Here is a picture that depicts what is going on as the temperature in the core increases.

This is the reaction cross section at a resonance peak for three different temperatures.  The tallest peak is at the lowest temperature.  That thing that is more of a hill than a peak is what the cross section resonance looks like when the temperature gets significantly higher.  I already noted that the height of the peak will shrink, and it does.  The interesting part though is that the peak gets fatter.  It widens to cover more neutrons energies.  Hence the term "doppler broadening."  As temperature rises, the resonant peaks which describe what energy neutrons the nuclear material will react with becomes wider.  This means that as the temperature increases, the nuclear material will actually react with more energies of neutrons.  There are now more "fish in the sea" to borrow a popular cliche.

You are probably thinking, "Aaron, you are nuts...this will cause the reactor to increase in power because there will now be more fissions occurring in the fuel!"  Well, actually quite the opposite happens.  You see, the resonant peaks at which U-238 and U-235 react with neutrons are not that far apart from each other in terms of energy.  As the resonant peaks get fatter due to doppler broadening, the resonant peaks of the two materials begin to overlap.  Now, they are starting to play with eachother's toys.  They are no longer the two kids in opposite corners contently playing with their own toys.  Now one has become a bully and has come over to steal the toys from the other kid.

Fortunately for us, remember that U-238 makes up most of the fuel in a reactor.  U-238 does not undergo fission when it absorbs a neutron, unlike U-235.  Thus, U-238 does not release heat when it captures a neutron.  But because it makes up about 97% of the reactor core, it can absorb much more neutrons than the fissile U-235.  Thus, when the reactor begins to heat up, the U-238 begins to infringe on the U-235 and begins to stifle the U-235.  U-238 absorbs more of the neutrons in the range that the U-235 is reacting with neutrons, meaning that there is less neutrons available for fission reactions.  This is directly related to the power of the reactor.  Thus, as the temperature of the reactor gets hotter, fission in the reactor actually begins to shut itself down!

This is one part of the negative feedback coefficient in modern reactors.  You see what I mean when I say that modern reactors can be inherently safe?  We can take advantage of such mechanisms to make reactors inherently safe!  I don't know about you, but this just makes me get hot all over!  Just kidding...