The Urbanist Case for Nuclear Power Part 2: From Micro to Macro

The coolest thing about physics, in my opinion, is how it unites so many different concepts. Mainly, energy is energy is energy, and even mass is energy! The forces binding an atom together seem so different from those that power a steam engine, but as I’ll demonstrate, using the former to do the latter is a straightforward and well-understood process.

In Part 1, I covered the basics of nuclear fission and lightly touched on the idea that we might want to do something with all of the energy produced. Something to the benefit of humanity, preferably. So far, electricity generation is the primary application, although there are others. Let’s focus on power for now.

Talkin’ ’bout My Generation

There are four generations of development of nuclear power plants as defined by the World Nuclear Association. I’m focusing on those in use or development in the United States to stay relevant to our primarily U.S.-based audience.

Generation I is mostly experimental reactors from the 1940s to 1960s. Purposes range from scientific reactors to prove the principles of nuclear energy to the first commercial reactors with varying designs. The last Generation I reactor was closed in 2015.

Generation II consists of the first standardized reactors, built primarily from the 1970s into the 1990s, with the last one completed in 2016. Most operating plants today are Generation II designs, including the Monticello and Prairie Island plants in Minnesota.

Generation III built upon the Gen. II designs, but with additional safety features and efficiency gains as computerized design created advances in sensing, modeling, material science, and manufacturing. There are also Generation II+/III+ designs, which incorporate safety features adopted after the Fukushima disaster. Many existing plants have been upgraded to the “plus” standard. Apart from a few experimental and research reactors, they all share the same basic technologies.

Boiling Water Reactor (BWR)

Does exactly what it says on the tin; uses the energy released by fission to boil water. The neutrons released by fission bump around inside the pressure vessel, transferring their kinetic/thermal energy (which are the same thing) to the water before they hit more fissile material and continue the cycle. This process, called “neutron moderation,” slows down or “moderates” the speed of the neutrons. These are the second-most common type in use, including the Monticello plant. The pressure inside the system is kept at around 75 atmospheres to increase the temperature of the steam and therefore the efficiency.

This brings us back to the Second Law of Thermodynamics, specifically Carnot’s Theorem, which gives an upper limit to the efficiency of heat engines like steam turbines:

where η_max (eta) is the theoretical maximum efficiency, T_H represents the hot reservoir (steam), and T_C represents the cold reservoir (ambient air temperature). In practice, the actual efficiency – measured as the ratio of thermal energy released to electrical energy generated – is usually around half the theoretical maximum. There’s no such thing as a perfect insulator/conductor, or a frictionless system, so much of the heat is lost.

Even with steam heated to 285C, BWRs are still among the least efficient heat engines in common use today, with a Carnot limit of about 50%. Most fossil fuel plants heat steam to somewhere around 500C, increasing the Carnot limit to 63%. For reference, the theoretical maximum for a gas-powered car is about 37%.

In order to get the steam back down to ambient temperature, a condenser is used, which cools the steam and condenses it back to water. This creates something of a positive feedback loop, as this pulls a vacuum on the system, which helps pull more steam through the turbine. Once condensed, the water is fed back through the system.

BWRs are usually larger than other types of reactors and fossil fuel plants with the same power output, due to their lack of efficiency. Furthermore, having the phase change within the reactor core creates complex stresses that require additional bolstering. As the basic design dates back to the 1950s, eight decades of refinement plus their relative simplicity have made them the most standardized and among the safest. Some versions operate completely passively, using the thermodynamics of the system to move water and steam around instead of pumps. This lowers the efficiency but improves safety by eliminating moving parts and potential failure points.

All Gen II/III reactors use control rods to regulate the release of neutrons. These work because certain stable elemental isotopes — like Boron 10 or most Hafnium isotopes — have a much higher likelihood of capturing neutrons than others, transmuting them into a different stable isotope. Since no fission occurs, this reduces the number of neutrons available to start new fission events, reducing the overall energy of the system. Control rods are continuously modulated to keep the number of free neutrons the same, except when the reactor is shut down. Then, rods are completely inserted to keep the amount of decay as low as possible.

This “absorption cross section” works much like transparency with electromagnetic radiation. A glass pane lets light through easily, while a brick wall blocks it. In the same way, certain materials are better at absorbing or reflecting wavelengths outside of visible light — like radio and gamma rays — than others. This is true for other forms of radiation, like electrons and neutrons. Boron and hafnium can be considered opaque to neutrons, while materials like zirconium are more transparent. These properties are used not just in the control rods, but throughout the construction of the reactor, auxiliary equipment, surrounding buildings and the design of the fuel itself.

Pressurized Water Reactor (PWR)

These are the most common type of reactor in use today and is the design used at Prairie Island. Similar to a BWR, PWRs keep the water under even more pressure —about 150 atm. — to raise temperatures higher and prevent the water from boiling. Instead, the superheated water is fed into a secondary loop, which then boils water, powering the turbine, turning the generator, and generating electricity.

While not 100% of the energy is transferred from the superheated water to the steam generator, a PWR still create hotter steam than a BWR, resulting in an increase in efficiency. The higher temperatures and pressures, along with the extra mechanics of a second loop, add their own complexity and therefore risk.

Pressurized Heavy Water Reactor (PHWR)

Not used in the US, but it makes a good segway into some important topics when discussing future reactor designs. For example:

What Even Is Heavy Water?

Actually, no, let’s back up a bit.

Why Do We Use Water in Nuclear Reactors?

Other than its neutron slowing and heat transfer properties, we use water for the same reason most industrial chemicals are used: its cheap and plentiful. Is it the best thing to use? Actually, probably not!

Regular water — known as “light water” in the industry — has a high affinity for absorbing neutrons. In light water, the hydrogen atoms are all ¹H, which just has a single proton in the nucleus, so there is nothing bound to it and therefore no binding energy. As such, the hydrogen atoms in light water have a high affinity for neutrons and are about 600 times more likely to capture one than their resultant product, ²H. This product, called deuterium, is made of two nucleons: one proton, and one neutron. Water with deuterium instead of normal hydrogen is called heavy water, as it is noticeably heavier than light water. A heavy water ice cube will actually sink in a glass of light water.

If the ²H in heavy water absorbs a neutron, the resultant product, ³H, is radioactive, with a half life of about 12 years, meaning there’s a chance any absorbed neutrons will get sent back into the system and cause fission.

Only about 0.0156% of all hydrogen on Earth is deuterium, so almost all of the water in the world is light water. This rarity, combined with how challenging separation is (I’ll cover enrichment in the next part) makes heavy water an expensive commodity. Furthermore, PHWRs have a larger footprint than PWRs. As heavy water isn’t as good at moderating neutrons, they need more space between fuel bundles to sufficiently slow down. However, the properties of heavy water mean PHWRs usually extract more energy out of a single uranium atom, burn a higher percentage of the uranium, and can use a variety of fuels, including natural (unenriched) uranium and even spent fuel from LWRs.

Other than that, PHWRs operated using the same principles of PWRs; use superheated, pressurized heavy water to boil water in a different coolant loop, and send that steam to a turbine to generate electricity.

Historically, the price of mining and enriching uranium has been cheap enough that LWRs are still the preferred technology, but political factors, such as the desire to minimize waste and the use of non-enriched fuels, mean PHWRs are a sizable minority, making up the majority of reactors in Canada and India.

Small Modular Reactors (SMRs)

Of all the technologies on this list, this is probably the one you’ve heard the most about. SMRs aren’t a unique reactor type, but scaled-down versions of other kinds of reactors. They can utilize either Gen III+ or Gen IV technologies, but, as Gen IV is only getting off the ground, domestic SMRs are mostly Gen III+ designs. Smaller components are both easier to build and transport. These smaller components can be chained together to equal the power output of larger plants, theoretically resulting in cost savings for the same power output.

I say theoretically as this principle hasn’t yet been tested. At the moment, only one station using this design is connected to the grid. It started operation in China in 2021. There are several projects underway in the United States, including one right next door in La Crosse, Wisconsin. So far, these projects are still riddled with cost overruns and delays. Personally, I’m not convinced having several small reactors will prove to be cheaper and easier than one large one.

There’s an innate safety advantage to SMRs, though. The square-cube law dictates that an object’s volume grows, or in this case shrinks, much faster than the surface area. This proportional reduction in volume means each reactor generates less heat and can release heat more easily. Therefore, they are more forgiving to operate, as they take longer to reach critical temperatures. If an incident does occur, it will be proportionally smaller. SMRs can start and stop power production much faster, as the heat they generate gets sent through the system faster, and the smaller turbine and generator have less inertia. The downside being the increased surface area allows more heat and more neutrons to escape when compared to standard reactors, affecting the overall efficiency.

The Next Generation

Generation IV represents the first shift in reactor design in almost 60 years, although some proposed designs borrow ideas from some of the Gen I prototypes with modern refinements. Currently, there are two Gen IV designs nearing commercial development in the United States, with several others abroad and plenty more proposed.

Some readers may have noticed that I didn’t completely answer the question, “Why do we use water as a moderator/coolant?” I gave an example of one possible alternative, but that was just a different kind of water, leaving the implication that there’s something else we could use. If Gen IV reactors can be characterized by one difference, it’s their use of alternative coolants. While they tend to be more expensive and harder to work with than water, their respective material properties create a number of advantages.

High-Temperature Gas-Cooled Reactor (HTGR)

Instead of using water for both roles, HTGRs use graphite as a moderator and helium gas as the coolant. Graphite isn’t as good of a moderator as water, but it’s better than most other materials and has an extremely high melting point. Helium is used as it is the least reactive element, doesn’t absorb neutrons, and also doesn’t change phases as it’s already a gas. As such, HTGRs can operate at much higher temperatures while maintaining lower pressures, at 700-950 C and 30-90 Atm. respectively, depending on the exact design. These reactors are sometimes called Very-High Temperature Reactors (VHTR), but I feel like that describes all Gen IV designs.

There have been a couple of experimental HTGRs in the U.S., including one at Ft. St. Vrain that operated commercially for a short time, but there were issues in keeping water out of the coolant system and thus was plagued by corrosion issues. Nevertheless, the Department of Energy and the Nuclear Regulatory Commission chose the technology for their Next Generation Nuclear Plant in the early 2000s. While they made progress in material science and the regulation of Gen IV designs, the project was culled before a definitive design arose. Framatome, which is majority owned by the French government, also developed an HTGR design that has failed to reach the market.

X-Energy is the latest entity to take a crack at HTGRs, recently landing a deal with Amazon to build four SMRs in Washington state using the technology.

Most HTGRs use a different fuel design known as a pebble bed. This is a different shape of fuel that has requires handling techniques, although the moderator makes up part of the fuel pebble as well. The design of the pebbles makes them self-passivating, so that, even in the event of a loss-of-coolant incident, the pebbles will not reach criticality and will not melt down. Controls rods are still used, both as an additional safety feature and to shut down the reactor for maintenance or refueling.

The main benefit of this technology over existing reactors is increased efficiency from the higher temperature steam, at the cost of greater design complexity and higher material costs. There are also some safety and material-handling trade-offs, but I’ll talk about those in a later installment of this series.

Sodium-Cooled Fast Reactor (SFR)

Alright, it’s time to challenge another basic assumption: why do we slow the neutrons down in a reactor? Ostensibly it’s to extract the heat, but what if there’s another way to go about it? In certain cases, fast (i.e. high-energy) neutrons are much more likely to collide with and cause fission in certain isotopes that would not traditionally make for good fissionable material.

Isotope	Thermal fission cross section	Thermal fission %	Fast fission cross section	Fast fission %
Th-232	53.71 microbarn	1 n	79.94 millibarn	3 n
U-232	76.52 barn	59	2.063 barn	95
U-233	531.3 barn	89	1.908 barn	93
U-235	585.1 barn	81	1.218 barn	80
U-238	16.8 microbarn	1 n	306.4 millibarn	11
Np-237	20.19 millibarn	3 n	1.336 barn	27
Pu-238	17.77 barn	7	1.968 barn	70
Pu-239	747.4 barn	63	1.802 barn	85
Pu-240	36.21 millibarn	1 n	1.328 barn	55
Pu-241	1012 barn	75	1.626 barn	87
Pu-242	2.436 millibarn	1 n	1.151 barn	53
Am-241	3.122 barn	1 n	1.395 barn	21
Am-242m	6401 barn	75	1.834 barn	94
Am-243	81.58 millibarn	1 n	1.081 barn	23
Cm-242	4.665 barn	1 n	1.775 barn	10
Cm-243	587.4 barn	78	2.432 barn	94
Cm-244	1.022 barn	4 n	1.733 barn	33
n=non-fissile. Bold indicates isotopes that have higher cross sections in the fast spectrum.

To borrow the analogy from part 1, breaking apart isotopes larger than ²³⁵U, like ²³⁸U, results in a stronger “kick” or “throw” down the binding energy curve, resulting in a larger release of energy. This still requires enriched fuels to kickstart this process, as the neutrons emitted from ²³⁸U do not have enough energy to sustain a chain reaction. The neutrons emitted can also transmute these “fertile” materials into fissionable ones, which is called “breeding.” Sticking with ²³⁸U, it can be transmuted to Plutonium 239, which is fissionable. It and other fissionable materials can then be refined and fed back into the reactor or into thermal (slow) neutron reactors, increasing the amount of energy extracted from the fuel, thereby increasing the overall supply of fuel, reducing the amount of waste and also reducing the amount of time the waste is radioactive.

So, what we need is a coolant that doesn’t easily absorb neutrons and can operate at extremely high temperatures, preferably without use of a pressure vessel. A number of materials are suitable, but liquid sodium is the material of choice in the US. It has a relatively low melting point but a high boiling point at standard atmospheric pressure. As such, there’s no internal pressure and no need for a pressure vessel. It just needs to be strong enough to hold the components inside. As sodium’s density is about the same as water’s, the containment vessel can be as thin as a water tower. While water often contributes to corrosion, sodium actually passivates the steel through galvanic corrosion, prolonging the lifespan of the vessel and other components.

A number of sodium reactor designs were proposed in the 1960s-70s as a solution to a predicted uranium shortage. The shortage, however, never materialized, and development since then has been limited, popping up occasionally as the solution to our waste storage problem. These reactors can be adapted purely to burn waste, as was proposed by GE-Hitachi in the early 2010s, and is a large motivating factor behind the current push. You may have heard of the SFR Terrapower and GE-Hitachi are currently building as the Bill Gates-funded project has recently broken ground.

The biggest downside is that it’s highly reactive. If the sodium does leak out, it’s almost guaranteed to ignite upon contact with air. If it comes in contact with water, it will react to form sodium hydroxide and hydrogen, the latter of which could also ignite. One solution is to replace the pure sodium with a salt. Terrapower is also currently developing a Molten Salt Fast Reactor (MSFR) that uses plain-old sodium chloride as a coolant, although other sodium, lithium or beryllium salts have been explored. There are some tradeoffs here. For example, NaCl’s extremely high melting point and the corrosiveness of chloride make vessel design challenging. ³⁵Cl also has a high neutron affinity, so any salt used can only contain ³⁷Cl.

Another alternative is to use a different metal with a low melting point, low neutron affinity and low reactivity. Lead is the leading choice here, with several Lead Cooled Fast Reactors (LFR) deployed abroad. The obvious downside is it uses lead. Not only is lead highly toxic, but its high density means all supporting structures, containment vessels and even fuel/control rod assemblies must be built to withstand the additional weight. Still, there’s no need for a traditional pressure vessel, and all three operate at much higher temperatures than LWRs, increasing efficiency and simplifying construction.

The most promising metal, in my opinion, is gallium. The density is about halfway between sodium and lead and has a higher neutron affinity than either of them. That said, it has a very low melting point, very high boiling point, is nontoxic and doesn’t react violently with air or water. It does tend to dissolve most metals, but material science problems are much easier to solve than changing the laws of nature. Still, use of gallium or alloys of it are only in the very early stages of research.

Gas-Cooled Fast Reactor (GFR)

Finally, there’s the Gas-Cooled Fast Reactor (GFR), which is sort of a cross between liquid metal designs and an HGTR, eliminating the graphite moderator and using high-temperature helium instead of liquid metal. This gas can also directly power a turbine instead of using a steam generator, making it one of the simplest designs out there. Operating principles are otherwise the same as liquid metal designs. Fast neutrons create a ton of heat, that heat goes into the helium and the change in temperature is used to spin a generator. There’s several designs in various stages of development around the world. General Atomics is just starting the certification process for theirs in the United States.

How Did I Get Here?

So now you know what fission is and how we use it to turn some sort of generator, but many questions still remain. Like, where does uranium come from? What do we do with it when it’s used up? And, wait, why do we use uranium to begin with? Some readers may have also noticed I’ve glossed over safety and nuclear weapons, for the most part. I’ll get to all of these topics in future parts of this series.