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Thursday, September 26, 2013

Unusual Reactors - A reactor in nature!

So far, I've discussed BWRs and PWRs fueled with Low-Enrichment U-235 (typically 5% enrichment)

Lets talk about some other reactors.  How about a naturally occurring reactor that once occured in nature in a seam of Uranium?

I will simply copy and paste bits from the Wikipedia article linked above, since I cannot improve on it in any way.

From Wiki:

A natural nuclear fission reactor is a uranium deposit where self-sustaining nuclear chain reactions have occurred. This can be examined by analysis of isotope ratios. The existence of this phenomenon was discovered in 1972 at Oklo in Gabon, Africa, by French physicist Francis Perrin. The conditions under which a natural nuclear reactor could exist had been predicted in 1956 by Paul Kazuo Kuroda.

The conditions found were very similar to what was predicted.

Oklo is the only known location for this in the world and consists of 16 sites at which self-sustaining nuclear fission reactions took place approximately 1.7 billion years ago, and ran for a few hundred thousand years, averaging 100 kW of power output during that time 

My aside:  This enought to power about 1000 light bulbs of 100 Watts each.

In May 1972 at the Pierrelatte uranium enrichment facility in France, routine mass spectrometry comparing UF6 samples from the Oklo Mine, located in Gabon, Central Africa, showed a discrepancy in the amount of the U-235 isotope. Normally the concentration is 0.720% while these samples had only 0.717%, a significant difference.

This discrepancy required explanation, as all uranium handling facilities must meticulously account for all fissionable isotopes to assure that none are diverted for weapons purposes. Thus the French Commissariat à l'énergie atomique (CEA) began an investigation. A series of measurements of the relative abundances of the two most significant isotopes of the uranium mined at Oklo showed anomalous results compared to those obtained for uranium from other mines. Further investigations into this uranium deposit discovered uranium ore with a U-235 concentration as low as 0.440%.

This loss in U-235 is exactly what happens in a nuclear reactor. A possible explanation therefore was that the uranium ore had operated as a natural fission reactor. Other observations led to the same conclusion, and on September 25, 1972, the CEA announced their finding that self-sustaining nuclear chain reactions had occurred on Earth about 2 billion years ago. Later, other natural nuclear fission reactors were discovered in the region.

Geological Situation in Gabon leading to natural nuclear fission reactors
1. Nuclear reactor zones
2. Sandstone
3. Ore layer
4. Granite
My aside:  Here is where the reactor physics gets interesting!
 
The natural nuclear reactor formed when a uranium-rich mineral deposit became inundated with groundwater that acted as a neutron moderator, and a nuclear chain reaction took place. The heat generated from the nuclear fission caused the groundwater to boil away, which slowed or stopped the reaction. After cooling of the mineral deposit, the water returned and the reaction started again. These fission reactions were sustained for hundreds of thousands of years, until a chain reaction could no longer be supported.

Fission of uranium normally produces five known isotopes of the fission-product gas xenon; all five have been found trapped in the remnants of the natural reactor, in varying concentrations. The concentrations of xenon isotopes, found trapped in mineral formations 2 billion years later, make it possible to calculate the specific time intervals of reactor operation: approximately 30 minutes of criticality followed by 2 hours and 30 minutes of cooling down to complete a 3-hour cycle.

A key factor that made the reaction possible was that, at the time the reactor went critical 1.7 billion years ago, the fissile isotope U-235 made up about 3.1% of the natural uranium, which is comparable to the amount used in some of today's reactors. (The remaining 97% was non-fissile U-238.) Because U-235 has a shorter half life than U-238, and thus decays more rapidly, the current abundance of U-235 in natural uranium is about 0.7%. A natural nuclear reactor is therefore no longer possible on Earth without moderation using heavy water or graphite.

The Oklo uranium ore deposits are the only known sites in which natural nuclear reactors existed. Other rich uranium ore bodies would also have had sufficient uranium to support nuclear reactions at that time, but the combination of uranium, water and physical conditions needed to support the chain reaction was unique to the Oklo ore bodies.

Here are a couple of pictures I found on the web of the Oklo reactors.




10,000 pageviews

Just sayin'.  Probably most of them are mine :)

Wednesday, September 25, 2013

Moderators, Neutrons, and Enrichment, oh my!

I want to discuss a few other reactor designs besides the typical US power reactors, the PWR and BWR types.  Before I do that, it's important to understand a few things that force us down certain paths in designing reactor cores. 

We need to understand the relative abundances of U-235 and U-238, why we use neutrons to split atoms, and also how a moderator works, in a physical sense.

First off, about Uranium.  According to Wikipedia, naturally occuring Uranium consists of three major isotopes: U-239 (99.28%), U-235 (0.71%), and U-234 (0.0054%).  The stuff we need for fission (U-235) is less than 1% of naturally occuring Uranium.

There is an entire industry based around the enrichment of Uranium.  The process of enrichment is as fascinating as it is tedious.  I might do a post on that process at some point, but for now it will suffice to point out that it is very, very difficult to create fission with naturally occuring Uranium.  For this reason, in most reactors, the concentration of U-235 vs U-238 is increased, or enriched.

And we always accomplish large numbers of fissions by using neutrons.  Why neutrons?  A couple of reasons.  Since neutrons have no charge, they can wander at will through any part of an atom, and through many materials other than Uranium, as if that material weren't there.  Also, since fission produces more neutrons than it uses, they are ideal for initiating more fissions!

When a fission occurs, 2-3 neutrons are ejected, but they are moving at 2MeV, which is about 20% of light speed.  At this speed, they CAN interact with another Uranium nucleus and cause a fission, but it is unlikely.  In order to improve the likelihood of a fission, there are two things we can do:  Increase the number of U-235 atoms in the core, or moderate (slow down) the neutrons.

In practice, both methods are usually used.  Reactors using no moderator, and containing a core of highly enriched U-235 have been built and operated.  Since there is no moderator slowing the neutrons down, these type of reactors are called "Fast Neutron Reactors". 

The vast majority of reactors are "Thermal Neutron Reactors".  The reasons most reactors use thermal neutrons are two-fold.  Fast Reactors require fuel enriched above 20%, which can potentially be diverted and used for a nuclear weapon.  Additionally Fast Reactors have poor safety characteristics from a reactor physics standpoint, and thus very poor safety record.  Of the handful of Fast Reactors built, several  have suffered meltdowns.

More on moderators though.  The purpose is to slow neutrons down to the point where they are at thermal equillibrium with the surrounding material.  The way to accomplish this is by allowing them to impact (or "scatter") against atoms with low mass.  Think of the neutron as a ping-pong ball fired from a cannon.  To remove the most energy by collision, ideally it should run into another ping-pong ball, which will recoil and remove some speed.  If it collides with a heavy nucleus, like steel, it would be like our ping pong ball bounced off a boulder.  It would not lose as much energy to the boulder. 

Water is a decent, but not great, moderator.  It has two hydrogen atoms for neutrons to scatter against, and it is dense.  The oxygen molecule has the ability to scatter a neutron, but it due to its mass (16) it would take many more oxygen atom collisions to accomplish the task.  Water is also plentiful and cheap.  This is why in most applications, water is used as a moderator.

Water though, is not an ideal neutron moderator, and here is why:  Both the hydrogen and oxygen atoms have a small, but noticable possibility of absorbing a neutron, thus removing it from the process and making it unavailable to cause a fission. 

There are other moderators that are superior to light water from the standpoint of neutron absorption.  Even though a Fast neutron may require a larger number of collisions to reach thermal equillibrium, the lower likelihood of being absorbed make other materials better moderators.

Moderator         Number of collisions      Likelihood of neutron absorption
Hydrogen                   18                                             0.3326
Dueterium                  25                                             0.000519
Beryllium                   86                                             0.0076
Carbon                       114                                           0.0035
Oxygen                      150                                           0.00019
Uranium                    2152                                         7.57

Dueterium (in the form of heavy water) is probably the best moderator known.  This is water with hydrogen atoms that already have one neutron and one proton.  Normal hydrogen atoms have just one proton, and occasionally capture one, taking it out of use for the reactor.  Dueterium hydrogen atoms have already absorbed a neutron, and are unlikely to absorb a second one.

Dueterium is found in nature, but like U-235, is not abundant.  It also needs to be enriched at great difficulty and expense, to be available in sufficient quantities to be used as a moderator.

Beryllium is another excellent moderator, with very little likelihood of absorbing a neutron.  Its disadvantages are expense and high toxicity.

Carbon is an excellent moderator, evenwith the large number of collisions required, its low neutron absorption, and low cost make it a practical moderator, even if it is not a good material to remove heat.

The other two items on the list, Oxygen and Uranium are not moderators at all.  They just show how increasing the mass of the target atom increases the number of collisions required to moderate a neutron.  However on the right hand column, notice the likelihood of absorption for Naturally Occuring Uranium.  It does love to vacuum up neutrons :)

In the next post, using what we have learned here, I will describe a few unusual reactors that have been built, either for testing purposes, or for breeding additional nuclear fuel, for nuclear weapons production, and how a nuclear weapon itself works.

Boiling Water Reactors

Boiling Water Reactors (BWRs) are a fairly common design in electrical generation.  The advantage a BWR has over a Pressurized Water Reactor (PWR) is mainly the up-front cost.

The primary coolant loop in a PWR is kept at about 2200 psig (155 bar) to prevent boiling in the core.  This means the reactor vessel, pressurizer, and steam generators as well as all primary loop components, must be very robust.  In addition, they must be made from (or lined with) corrosion resistant materials, due to the addition of boric acid for reactivity control.

With a Boiling Water reactor, the primary coolant loop is also the steam loop.  There are no steam generators or pressurizer.  The operating pressure is about half that of a PWR, and no boric acid is used.  Thus a boiling water reactor can be built with less cost.  A BWR also has higher thermal efficiency than a PWR.

Below is a diagram of a BWR vessel.  While less expensive to build than a PWR, these are still pretty complex reactors. 


Below is a simplified overall diagram of an entire BWR steam/water circuit.


A few things you will notice that are different from a pressurized water reactor: 
  • The top of the reactor vessel is used as a steam drum, to separate water and steam.
  • Because the top of the reactor is a steam drum, control rods are moved to the bottom.
  • Inside the reactor vessel are circulation pumps (#4).  More on these later.
  • Steam directly from the reactor core flows through the entire steam system.
  • Not shown in the above image are the feedwater and steam shutoff valves.  In the event of a steam line rupture, it is important to keep water in the core, and also to prevent the release of radioactive steam outside of the containment structure.
  • Note the shielding required around the entire steam system. 
Some of the disadvantages of a BWR with respect to a pressurized and segregated reactor coolant loop become apparent. 
  • The control rods and circulating pumps penetrate the bottom of the reactor vessel.  Should a leak develop there, it can drain all the water from the reactor vessel.  Since the fuel must be kept submerged in water (even for several years after use), this is a potential hazard.
  • Water circulating in a power plant always contains minor levels of corrosion - flecks of iron from valves and pumps, and magnetite that falls from the inside of piping as temperatures expand and contract the pipe.  These corrosion particles can be carried through the reactor core and absorb a neutron.  They can become very radioactive, and then settle outside the reactor core.  This material is called CRUD, and is only detectable with a radiation detector.
  • In a PWR, CRUD is all contained within the primary loop and inside the containment structure.  In a BWR, CRUD is everywhere within the steam system - the steam and drain lines, the turbine, the condenser, the condensate pumps, and feedwater pumps.
  • There is an important nuclear reaction that occurs that involves the Oxygen in water molecules, H2O.  Oxygen-16, when hit with a high energy neutron, can absorb the neutron and eject\ a proton.  It then becomes radioactive Nitrogen-16.  This is a nasty isotope of nitrogen, mainly because it decays by emitting a gamma of 10 MeV.  That's a VERY hot gamma ray.  Nitrogen-16 has a half-life of 7.1 seconds, so that means it will be emitting these hot gamma rays while it is passing through the steam turbine, condenser, and settling in the hotwell.  Therefore massive shielding is required from all steam and feedwater systems during operation. 
  • Due to the short half-life of Nitrogen-16, it quickly decays away.  Shortly after the reactor is shutdown, the only serious radiological hazard in the steam system is due to CRUD, which is composed of metals that have longer half-lives.
 Below is the generator for a BWR.  Note the tan-colored radiation shield blocking the view of the steam turbine.  This is to protect personnel on the operating floor from Nitrogen-16 gamma radiation.
.
BWRs are a little more complex than PWRs from a reactor control standpoint.  A BWR, by its very description, has significant in-core boiling - primarily in the upper portion.  However a BWR, like the PWR, uses water as a moderator.  When water changes to steam, its neutron moderating properties change drastically - 1/1000 drop in density equates to about 1/1000 drop in moderating ability. 

With the phase change from water to steam there is an ongoing change in moderation and thermal neutron population, and therefore in the fission process.  It is therefore important to monitor neutron levels (flux) at many more points than would be necessary in a BWR, to ensure even power distribution.  Fuel burn-up (both axial and radial) is also difficult to calculate for the top end of a BWR, due to the dynamic two-phase activity in the core.

Interestingly, like the PWR, the BWR control rods are out of the core at full power, and reactivity is controlled by using the circulation pumps.  When the pumps are run at high speed, boiling occurs higher up in the core, and so more moderator is present, and more neutrons are available to create fissions.  Similarly, if reactor power needs to be reduced, the recirculation pumps can be slowed down, and boiling occurs lower in the core.  More steam in the core means less neutrons will be thermalized, and so fewer neutrons will be available to cause fission.

Lastly, BWR cores have to be somewhat larger than PWR cores for a given output, and that is mainly due to the fact that the upper part of a BWR core isn't generating much power, because steam is a poor moderator.

Sunday, September 22, 2013

Nuclear Reactors - How they work (part 2)

Previously we had a Pressurized Water Reactor (PWR) which was critical and adding heat to the coolant/moderator.  After the reactor reaches the point where it is generating heat, and the moderator becomes less effective, it becomes neccessary to withdraw the control rods again to increase power output.

Since this is a PWR, we are not supposed to have large-scale boiling in the core.  Steam doesn't transfer heat as readily as water does, and in a PWR, in-core boiling is a bad, bad thing.  For this reason the pressure in the primary coolant loop must be kept well above the boiling point of water for the temperature found in the core.  How do we do that?  We have a pressurizer!

The pressurizer is a dual-purpose vessel that does two things:  It acts as a surge volume for the primary coolant system, by having a compressible steam-filled void space.  Secondly, it keeps the system pressure high, so that boiling cannot occur in the core.  This is done by keeping a vessel half full of water and adding enough electrical heaters that the temperature in the pressurizer is maintained higher than that of the core.  All boiling will occur in the pressurizer, not in the core.

Below is a simplified diagram of the primary and secondary systems of a PWR.  The radioactive primary coolant (Red) is contained in a closed loop.  The reactor core is the heat source, the control rod drive mechanism positions the control rods to increase/decrease reactor power, the primary pump circulates the primary coolant, and pressurizer serves as a static surge volume.

The steam generator segregates the radioactive primary coolant from the steam/water system, but  allows heat to be transferred out of the primary coolant loop and generate steam for the turbine.  


Pressure in the primary system is increased by energizing submerged electrical heaters in the pressurizer, and reduced by spraying a small slip-stream of primary coolant from the reactor coolant pump through a spray head at the top of the pressurizer. This cools and condenses some of the steam in the pressurizer, reducing system pressure.

Temperature is gradually increased by withdrawing the control rods.  Remember in the previous post that the neutron population would increase with no control rod movement if the reactor were slightly supercritical?  That is no longer the case when power level is high enough for the reactor to generate heat.  After the core begins heating and the "negative temperature coefficient of reactivity" kicks in, withdrawing the control rods increases power, followed by a smaller drop in power as the primary coolant heats up.  So control rods are withdrawn in a series bumps, and the coolant temperature is slowly increased.

The primary coolant pump circulates primary coolant (very pure water) between the reactor core and the steam generator.  The reactor core adds heat created by fission.  The steam generator removes heat by boiling secondary water in a heat exchanger.  Thus, primary coolant is radioactive, but does not boil.  Secondary water is non-radioactive, and does boil.

In a PWR, excess fuel is loaded, more than what is required to bring the reactor up to power.  This is done so that the reactor can continue to run as the U-235 is expended, and fission products build up.  Many of the atoms that are created by fission are strong neutron absorbers (poisons), and eventually result in the inability of the reactor to maintain full power.  This is in spite of excess U-235 added at during refueling.  Only about 3% of the U-235 is used up before the accumulation of poison halts reactor operation.  This is why fuel recycling is so desirable from an industry standpoint.

Commercial PWRs are unique in that they add boric acid to the primary coolant.  Boron is a neutron absorber.  With the addition of boron to the coolant, the control rods may be entirely withdrawn from the core, using only boron to control neutron population.  This is desirable because in the vicinity of control rods, neutron population, and fissions will be depressed.  This forces other regions of the core to run hotter for a given power level.  With control rods out of the core, neutron distribution is more consistent and hot spots due to uneven neutron flux are less likely to develop.

At a certain point, on the secondary side of the steam generator, steam is at an adequate pressure to begin warming up the steam turbine.  This also has an interesting impact on reactor power.  As we create steam on the secondary side of the steam generator, we are also removing heat from the primary coolant.  This slightly cooler primary coolant returns to the reactor.  Since it is now more dense, it is a better moderator, and more neutrons stay in the core to cause fissions.  Reactor power now increases along with steam demand.  This is a very desirable feedback loop, because now there is little need to adjust the control rods.  We allow the steam turbine load to determine what power level the reactor will operate at.

The remainder of the steam plant operates in a very similar manner to a fossil-fueled plant.  One difference:  Since it is not possible to superheat the steam with this process, steam dryers are added between different stages on the steam turbine, to prevent mist from damaging the lower pressure sections.

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.