Reactor Control

Reactor Dynamics

Changing Power Level

To change the power level we need the ability to change the core conditions to our liking, making it critical, sub-critical, or super-critical; in other words, changing the environment so that the neutron populations are stable, declining, or growing. The control rods are neutron killers and moving them in and out of the core allows us to control the neutron population. For the MMR, temperature can also be used as the primary population control mechanism.

To increase the power, we want to increase the number of neutrons available for fissions. The core is made super-critical by withdrawing the control rods, which allows more neutrons to survive and propagate. The neutrons will continue to multiply, and their population exponentially increases unless we put the control rods partially back in and make the reactor critical again. Once critical, the reactor power level will remain constant. To shut it down, we must reinsert the control rods, making the reactor sub-critical and exterminating neutrons in the core.

Prompt and delayed neutrons

We’ve mentioned that the super-critical configuration is an exponential growth environment. So you might ask, why doesn’t a reactor just produce exponentially more power and blow up or behave like a nuclear weapon?

And fast things are generally hard to control. The lifetime of a neutron from birth to fission can range from a few microseconds to milliseconds depending on the moderator. When a fission reaction occurs, most of the resulting neutrons are released very quickly, on the order of 10-14 seconds. These are the prompt neutrons. This short timescale implies that neutrons breed really fast. It's like a rabbit species that reproduces every few milliseconds. There’s little you can do to control it or apply active feedback mechanisms to slow things down. You certainly can’t move the control rods quickly enough to make a difference. The dynamics are too quick for active control.

Fortunately, a small fraction of the fission neutrons, typically around 0.1%, are released more than 0.1 seconds later. These neutrons breed slowly enough to be observed and can be controlled with mechanical actuators. So reactors try to operate in the regime where these delayed neutrons are driving the criticality. The fraction of neutons that are delayed is higher for thermal spectrum reactors as they have more U-238, which produces 4x more delayed neutrons per fission than U-235.

It should be noted, that some reactors like MMR don’t particularly need delayed neutrons because the control is accomplished primarily by temperature feedback mechanisms which happen very quickly.

Feedback Mechanisms

A nuclear reactor can operate at whatever power level desired as long as criticality can be maintained. But there are many mechanisms that reduce criticality as power increases. These are based on the materials in the core (control rods), the temperatures, and the geometry of the core. Power can be increased as long as heat can be removed from the reactor core and temperatures remain safe and stable. If the power generation exceeds the limitations of the fuel and reactor, various physical mechanisms will cause the reactions to stop. It’s just a matter of how calmly or violently the negative feedback takes place. The fundamental idea is that super-critical conditions are not sustainable for long because they will lead to higher temperatures, the destruction of the reactor, and will ultimately achieve equilibrium with the environment.

For reactors with high power density, conditions can arise by which the only way the reactor can reach equilibrium is by melting or exploding. For low power density reactors, reaching equilibrium and subcritical conditions is a subdued affair.

While the control rods appear to be the main mechanism for controlling the reactor there can be stronger mechanisms that overpower the control rods.

Control Rods 

Control rods are usually neutron killers. So putting them into the core will kill neutrons, while taking them out of the core will allow more neutrons to live. For this reason, control rods are usually designed to fail by falling into the core with the help of gravity, thereby shutting down the nuclear reactions. 

The main exceptions are boiling water reactors like BWRX-300 and ABR, in which control rods are placed below the reactor core because they wouldn't survive the hot steam conditions on top of the reactor – not ideal. The other exceptions are control drum reactors which can be configured for a gravity driven automatic shutdown.

A core design has to consider the effects of accidental control rod ejection as well as the replacement of that empty space with water which will provide extra moderation and criticality. Failure to account for these effects is responsible for the power spikes and explosion at Cernobyl.

Most nuclear reactor designs only consider accidents with a handful of control rod ejections and would probably not be able to cope with the ejection of a majority or all the control rods. Ideally, reactors would be able to tolerate ejection of all the control rods with a simultaneous loss of coolant.

Fuel Negative Temperature Feedback

In the fuel, raising the temperature causes doppler broadening which allows more neutrons to be absorbed by U-238, thereby reducing the reactivity. This effect is dominant and instantaneous as fuel temperatures rise. Higher temperatures indicate faster vibrating atoms and a higher velocity relative to incoming neutrons, which means a given reaction is accessible at more neutron energies. Visually, the high probability peaks are smeared.

Notice the peaks in the U-238 absorption probabilities. If a neutron has one of those energies, there is a very large chance of absorption. At lower temperatures, the U-238 resonance absorption peaks (the spikininess) are tight, and there is small chance of neutrons having those exact energies, allowing many neutrons to pass through unscathed. At higher temperatures, the peaks broaden and the probability of neutrons having energies susceptible to absorption increases, effectively culling the neutron population.

For this mechanism to work, the fuel cross sections must have significant spikiness or resonances. Comparing U-235 and U-238 probabilities reveals the importance of U-238. It contributes significant resonance absorption probabilities that ultimately give rise to negative temperature feedback. Keeping a low enrichment (high U-238 fraction) is needed to achieve a strong negative temperature feedback.

Another feature of the U-235 resonances is that they occur at lower neutron energies. So to access the negative feedback of these resonances, the core should significantly rely on slow neutron fissions (aka thermalized or moderated). This means that thermal reactors that use quite a bit of moderator have superior negative temperature feedback in the fuel compared to fast fission reactors.

Moderator Negative Temperature Feedback

Moderator feedback mechanisms tend to be delayed compared to fuel feedback mechanisms because the moderators take some time to heat up from the fuel's power changes. In general, moderators will expand with rising temperature, thereby reducing moderation and the number of slow neutrons available for fissions.

Geometric Changes: aka Meltdown and Explosions

If things get very bad, the reactor will achieve temperatures and conditions that lead to geometric changes. The reactor will eventually reach an equilibrium with its environment, and it's just a matter of how gently or violently it gets there. For example, there could be a sufficient build up of pressure and hydrogen (in water-cooled reactors) that leads to an explosive release of energy. This could spread out the core from a tidy, critical core into a spread out jumble that is sub-critical. Similarly, the core can melt itself, morphing from a compact cylinder into a flat puddle. 

Needless to say, this is not a great feedback mechanism to achieve a sub-critical system because the fuel has basically failed, releasing many fission products outside of the pressure boundary. At a minimum, the powerplant will be trashed with 10s of $B in losses and cleanup efforts. Worst case, the containment fails or leaks and there is a release of fission products into the atmosphere or ground.

Putting it all together

Once we have a collection of materials capable of sustaining nuclear reactions, we have to package the core into a reactor and extract its heat. The basic function of the reactor is to change the power level and extract heat from the core for use elsewhere, either in a turbine or for process heat applications.

We place the nuclear core into a pressure vessel that holds pressurized helium or other coolants. The helium flows to the core though a double walled pipe (aka concentric tube). The cold inlet flows on the outside to insulate the vessel walls. It then flows up the sides of the reactor and then down through the warm core, picking up heat. The hot outlet fluid then flows through the inside of the pipe to the end use.

For this type of high temperature gas-cooled reactor, we basically have just two controls on the reactor. The coolant flow rate and the position of the control rods. Together, these determine the criticality, the reactor power, and core temperatures. Control rods are moved in and out of the core to change the criticality which then allows the neutron population to grow or shrink. The neutron population is directly proportional to the power. The criticality is also affected by the core temperatures.

The temperature of the core remains constant as long as we remove heat at the same rate as it is being generated by the nuclear reactions. Temperatures rise if more heat is produced than removed. As temperatures rise, heat transfer becomes more efficient and more power is removed until the reactor reaches a new equilibrium. Also, as temperatures rise, the reactor produces less power due to the negative feedback mechanisms described above.