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Saturday, September 21, 2013

Nuclear Reactors - How they work (part 1)

I've always been fascinated by nuclear reactors.  Even as a child, I was mystified by the blue glowing water I would see in the National Geographic Magazine.  The whole notion of releasing enormous amounts of energy by gathering certain materials together in a small area is a bit mind-boggling.

So how does a reactor work?  First, a little chemistry, then a little physics. 

As an example of how nuclear energy is created, we can look at an atom of Helium-4, which contains 2 protons, 2 neutrons, and 2 electrons. 
Neutrons (blue) have no electrical charge.  Protons (red) have a +1 charge.  Electrons (yellow) orbit the atom at a pretty far distance and have a -1 charge.  Electrons and protons (and therefore charge) are balanced in typical atoms.

Because protons have a +1 charge, they repel each other. The repulsive electrostatic force is squared every time the distance is cut in half.  The closer these protons get to each other, the more they want to fly apart!  This is similar to pushing powerful magnets together with both north poles together.  However nature provides a way to hold these repelling protons together in spite of themselves :)

Back now to our physics...

The atomic mass of each component:

proton = 1.007766612
neutron = 1.00864160
electron = .000548892490

OK, funky numbers with lots of decimal places.  Bear with me here.  This is important.

Mass of all these individual components added together in a Helium Atom = 4.03391420898
Yet the actual measured mass of a Helium Atom is only = 4.002602  What the HECK!!!!???  
These numbers should be the same!

There is a difference in the atomic mass of 0.03131220898 between the individal components and the assembled atom.

This difference in the calculated mass and the actual mass is called the "mass defect".   Holding two positively-charged protons very close together requires a great deal of energy.  It also requires an incredibly powerful short-range force, called the nuclear force.  The nuclear force is so strong that it can overcome the repulsion of particles with like charges.  However, it requires so much energy to bind a nucleus together against the repulsive electrostatic force that there is a noticable change in the mass of the atom and its components.

Here is where we get to Einstein's awesome realization: Mass and energy are equivalent and interchangeble.

The difference in mass of an assembled Helium atom and its components is due to the large amount of energy required to hold that atom's nucleus together against the repulsive force of those positively charge protons that are trying to repel each other.  E=mc^2 is the equation that explains how much energy was needed to assemble the Helium atom from its components.  It's also how much energy would be released if they were taken apart again.  This energy is called Binding Energy.

Binding energy is the same exact thing as the mass defect, only from the viewpoint of energy, rather than mass.  E=mc^2 is the mathematical conversion between the two states (matter and energy).

To better understand how much energy, E we are talking about, we need to look on the right side of the equation.  The m (or mass) is a very tiny number, 0.03131220898.  However c is the speed of light, and that number is squared.  So the speed of light times the speed of light is a very, very, large number.  The energy that would be released if we break apart one helium nucleus into its components would be 28.3 Million Electron Volts.  To put this in perspective, an X-ray has energy at 40-60 thousand Electron volts, while visible light has energy at 2-6 electron volts. 

Unfortunately for our energy needs, Helium atoms are notoriously stable, and almost impossible to break apart.  However, nature has provided us with certain atoms that will split apart quite readily under the correct conditions. 

It turns out that certain high-mass atomic nuclei will split into two smaller fragments after absorbing (or capturing) a neutron.  More importantly, when these atoms split, they release many more neutrons, allowing a continuous reaction (or chain reaction) to be sustained.  Neutrons are the best subatomic particle to create large numbers of fissions, because they have no charge, and readily interact with the nucleus of an atom.  Protons have a positive charge, and therefore are repelled by the positively charged nuclei of atoms.

Below to the left, a neutron is absorbed by a fissionable nucleus. The nucleus splits into two smaller fragments, three additional neutrons, and a gamma ray. This is a pretty typical result of fission.

Atoms that will split (or fission) after capturing a neutron are called "fissionable".  There are a large number of atoms that will fission.   However not just any fissionable material will work in a reactor. 

To assemble a reactor core we need to find fissionable material with some specific properties: 
  • Some atoms which are fissionable don't readily absorb neutrons, so they won't work.  
  • There needs to be a sufficient supply.  If the fissionable material is rare, it cannot be used.
  • The fissionable atom must produce 2 neutrons when spit, or a reaction cannot be maintained. 
  • The fissionable atoms must have a long half-life, and not decay to some other element while in the reactor.
There is one other property that has to be met in our fissionable material.  It must also be "fissile". 

To understand the difference between fissionable and fissile, we need to understand about neutron temperature.  When a neutron is ejected from a split atom, it has enormous energy, about 2 Million Electron Volts (or 2 MeV). 

Physically, this is the speed of the neutron.  A 2 MeV neutron is traveling at about 45 million miles/hr.  Neutrons moving this fast don't often linger to induce fission in other atoms.  Statistically they are likely to leave the reactor core before an interaction occurs.  For this reason it is desirable to slow them down.  Neutrons are slowed by allowing them to bounce off lighter atoms and transfer their kinetic energy to the atoms.  This process is called "moderation", and slows the neutrons down to what is called "thermal" energy, .025 eV, or about 4900 miles/hr.  Depending on the mass of the moderating material, it may take from 10-2500 impacts to reduce the speed of a fast neutron from fission to thermal equillibrium.

Below is a table showing neutron energy (or straight line speed) of a neutron with its description.
Neutron energyEnergy range
0.0 eV-0.025 eVCold neutrons
0.025 eVThermal neutrons
0.025 eV-0.4 eVEpithermal neutrons
0.4 eV-0.6 eVCadmium neutrons
0.6 eV-1 eVEpiCadmium neutrons
1 eV-10 eVSlow neutrons
10 eV-300 eVResonance neutrons
300 eV-1 MeVIntermediate neutrons
1 MeV-20 MeVFast neutrons
> 20 MeVRelativistic neutrons

It is at thermal energy, speed, or temperature (pick one), that neutrons will more readily be absorbed by a nucleus and lead to another fission.

Now that we understand the process of neutron moderation, we can return to our need for Fissile atoms.  Fissile atoms are a small subset of fissionable atoms, that will readily split after absorbing a thermal neutron.  The list of candidates of fissile materials is small.  Uranium 233 and 235, Plutonium 239, and 241.  Only Uranium 235 is naturally occuring, while the others must be produced by excess neutrons from other materials inside a breeder reactor.

In another post I will describe other types of reactors, but for now we will stay with the basic thermal reactor, which is fueled with 5% U-235, both cooled and moderated by normal (light) water.

When an atom splits, it creates two highly radioactive atoms that must be contained, and not allowed to get into the coolant/moderator.  Otherwise that water will become very contaminated with radwaste.  For this reason, the uranium fuel is surrounded by zircaloy cladding.  Below is a photo of people inspecting new fuel assemblies for defects in the cladding.

The energy of a single split U-235 atom is about 10MeV, most of which is in the form of kinetic energy of the two new atoms.  They are moving at high speed, but due to their mass and charge, they quickly come to rest among other atoms of fuel.  The energy these atom fragments lose as they come to rest is converted to heat.

Back to the reactor core.  Water surrounds an array of these fuel assemblies, which is called the "core".  It takes a certain amount of fissile U-235 packed closely together, and moderated  neurtons for a continuous reaction to take place.  Below is a top-down view of a generic reactor core.

The reaction is started by withdrawing control rods.  Control rods contain strong absorbers of thermal neutrons.  These neutron absorbers are also known as "poisons", in that they slow or stop the nuclear fission process.  Typically a control rod contains cadmium, boron (or a borated alloy) for neutron control.

"Keff" is the number reactor physicists use to determine whether the reactor core is shutdown, steady-state, or starting up.  It's the neutron multiplier.  Keff is the likelihood that a single neutron will make it from birth to cause a fission in another Uranium atom.  Some of the other possibilities are that a neutron will escape from the reactor core, be absorbed in some material other than Uranium, or be absorbed by a Uranium atom, but not cause a fission.

If Keff is < 1.0 the reactor is "subcritical".  If Keff is = 1.0 the reactor is "critical", and if the Keff is >1.0 the reactor is "supercritical".  Nothing in any of these terms should be fear-inducing, they just describe a core reactivity condition for sustaining (or changing) the neutron population.

So... what happens when the control rods are removed?  I will skip the mathematics this time and give a simple description.  Neutrons are always present in U-235, because one of the natural decay modes for U-235 is spontaneous fission.  However reactors contain a strong artificial neutron source to ensure there are plenty of neutrons to get things going.  Think of the installed neutron source as sort of a pilot light for a gas furnace.

When the control rods are removed partially, neutron population begins to increase for two reasons.  The neutrons are no longer being absorbed in the poison, and so they begin splitting U-235 atoms, which generates even more neutrons.  The neutron population increases, even if Keff is less than 1, for the above reasons. 

Eventually though, if the control rods have been removed far enough, neutrons from new fissions will equal the losses, and Keff will be 1.  The reactor will then be critical.  However it won't be generating any heat.  Reactors typically are critical at an output of about 5 watts.  About the power required by a single "night light" bulb.  Power must be increased by a factor of 10^8 to get to 500 Megawatts.

After the reactor is critical, the neutron population must increase a great deal before any noticeable heat is generated.  So the rods are pulled out a little more, and each generation of neutrons has a few million more than the previous generation.  With this small increase in reactivity, there is no further need to withdraw the control rods.  Neutron multiplication will increase on its own.

Eventually the reactor reaches a point at which heat is generated, and this is where things get interesting.  The moderator (cooling water surrounding the fuel assemblies) heats up, and becomes less dense.  It is therefore less effective at slowing down neutrons. 

Because the moderator is less effective as temperature increases, more neutrons escape the core, which reduces neutron population, and reactor power stops rising.  We therefore have a heat-induced dampening effect on reactor power.  Its technical term is "negative temperature coefficient of reactivity".  Basically, more heating tends to reduce reactor power.  This is a desirable thing, because it prevents a runaway nuclear reaction.  Unfortunately not all reactors have this characteristic :(

So far, so good.  We have a critical nuclear reactor (Keff = 1.0) which is adding heat to the coolant!

I think that now is a good place to stop and think about the next post.  My brain hurts :)

Part 2 is here.


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Anonymous said...

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