Nuclear Fusion – The Promise of Sustainable Energy

Transformer by Victoria Catterson

The prospect of fusion energy as a clean, renewable, and cost efficient power source has tantalized scientists, investors, and businesses for years. A sustained focus on decreased dependence on hydrocarbon fuels, public concern regarding the environmental impact of increased emission of greenhouse gases, and the relative expense and limitations of other clean energy implementations such as solar, wind, and geothermal have drawn many to the promise of nuclear fusion as a potential solution. The concept of fusion power is easy enough – atomically combine renewable, readily available elements into other environmentally friendly elements and harvest the power output. So why is it taking so long?

Practical Considerations

There are some practical conditions that need to be met with any solution. First, the amount of energy harvested from any solution must be significantly greater than the amount of energy that was required to generate that output. This is called the Net Energy Gain, and it is important when it comes to nuclear fusion because initiating a reaction requires a significant amount of input energy, and there are additional energy losses incurred from power collection, radiation emission, and transmission.

The other consideration is economic. The cost to generate fusion power needs to be comparable to existing energy sources to gain traction. Some existing clean power sources that have higher generation costs like solar and wind power have experienced growth due to government subsidies and laws, but if the goal is to achieve widespread replacement of existing power generation methods with nuclear fusion, its costs need to be significantly lower than conventional systems to ease adoption.

IER Estimated Energy Generation Costs

So now that the goal is clear: leverage nuclear fusion technology to produce a net energy gain at a cost lower than existing conventional methods, we can turn to the science of how fusion works.

Achieving Fusion

It turns out fusion devices have been constructed for more than 50 years. In fact, hobbyists have been building Farnsworth-Hirsch fusion reactors (also known as “fusors” or “star-in-a-jar”) at home for years that can combine deuterium (a form, or isotope of hydrogen) into other elements using easily obtainable parts.1

Photo: Learn How To Build a Nuclear Fusor

These devices achieve nuclear fusion (which can be proven using a neutron detector) but so far no homemade fusors have been created that produce a commercially viable net energy gain. However, this approach (known as “inertial electrostatic confinement”) is not the only method to initiate fusion, so let’s consider how fusion works and dive into the different methods being developed to generate fusion power.

Fusion Primer

Nuclear fusion is a reaction that combines two or more atomic nuclei into a new set of nuclei. When combining lighter elements, surplus energy is released from the reaction because the total energy required to hold together the new larger elements (its “binding energy”) is less than the binding energy of the input components. Fusing larger elements that are heavier than iron absorb energy because the resulting heavier element requires the input of additional energy to bind itself together. The reverse process (fission), breaking up large elements into smaller ones, releases energy, and this is what powers existing nuclear fission reactors. But the fission process also generates radioactive waste that is difficult and dangerous to handle, so alternatives like fusion are very attractive.

So how do we combine two smaller elements and get some energy? Let’s combine two hydrogen atoms in a fusion reaction. Atoms are composed of various subatomic particles, and a ¹H hydrogen atom contains one proton and one electron, commonly represented in diagrams like a moon orbiting around a planet:

Hydrogen Atom
Common representation of a hydrogen atom.

There are a couple problems with this representation. The first is one of scale. As of the most recent measurements, protons have a diameter of 1.666 femtometers (0.000000000000001666 meters). The Bohr radius, the most probable distance of the electron from the proton (more on what that means later), is about 52,917 femtometers. If we draw a proton as a 1 millimeter dot so that it is visible on a diagram, we would need to place the electron 31.76 meters away to represent this value to scale.

The second problem is that electrons don’t orbit around protons the way the Moon circles around the Earth. Celestial bodies orbit each other due to the forces of gravity, which scales multiplicatively with mass, and because these bodies have large mass, gravitational models are best used to describe their behavior. If you hold two basketballs close to each other, there are tiny gravitational forces between them, but the effects are too small to notice and insignificant compared to the gravitational force the Earth is exerting on both of the basketballs. When understanding subatomic particles that have very little mass, gravitational forces become extremely weak compared to the other fundamental forces at work within the atom, and instead the field of quantum mechanics is used to better describe subatomic behavior.

Inside The Atom

Instead of spinning around a proton like a moon, electrons behave like a wave that is vibrating at a certain frequency, modeled by a mathematical formula called a wave function. This function describes the electron’s position as a probability distribution, which means that there are any number of locations where the electron could be, and the distribution tells us the probability that it is at a particular location. This is difficult to visualize, but recent advances in microscopy scanned the orbital structure of a hydrogen atom, giving us a real “picture” that is actually pretty descriptive.

“Quantum Microscope” Peers Into the Hydrogen Atom

There’s only one electron in the hydrogen atom, but it appears to be in multiple places at once in a definite pattern, and that pattern is what hydrogen’s wave function describes in mathematical terms. Because of this, it is sometimes easier to visualize atomic structures by plotting the areas that the electron could occupy, known as its atomic orbital. However, the shape of orbitals is not the same for all atoms because orbitals take different shapes depending on the state of the atom.

This what is known as the electron’s quantum state. This is is simply a set of numbers defining certain features about the electron; the reason the word “quantum” is used is because these features can only have certain specific values, called quantum numbers. Our hydrogen atom at its lowest energy level (the “ground state”), has an energy level (a “principal quantum number”) of 1. If you add enough energy to the atom, the electron will jump to energy level 2. It cannot be a value in between, such as 1.5. It takes 10.2 eV (electronvolts) to energize an electron from level 1 to level 2, and until enough energy is provided to jump to level 2, it will stay at level 1, not in between.

The electron has other quantum numbers to describe its state besides its energy: the magnetic, angular momentum, and spin quantum numbers. With these values, we can determine how the electron behaves. A simple hydrogen atom can have all sorts of configurations based on its quantum state:

Understanding quantum state is useful for us to be able to combine two of these hydrogen atoms together and achieve nuclear fusion.

Chemical Fusion

Let’s say two hydrogen atoms bump into each other or are otherwise pushed together. Remember when we said that gravitational force at the atomic level is weak, but other forces are stronger? Electromagnetic force is one of those. Some subatomic particles have an electric charge that is either positive or negative, and just like magnets, opposite charges attract each other, and charges that are alike repel each other. Protons have a positive charge and electrons have a negative charge, and their electromagnetic attraction keeps the hydrogen atom’s electron attached to its proton nucleus instead of flying away. (The electron’s kinetic energy is what keeps it from being absorbed by the proton.)

Our two hydrogen atoms each have a zero net charge, because they each have one positive charge from the proton and one negative charge from the electron. So the atoms as individual units are not attracted or repelled from each other by electrostatic forces. But when they come close enough together to interact, if the two atoms are compatible with each other, they will form a chemical bond with each other, because their combined form (dihydrogen, or H²) is a more stable arrangement that requires less energy to bind together, and atoms tend to combine into their lowest energy state. Because the new dihydrogen molecule requires less binding energy, this combination releases energy.

One of the possible sigma bond orbital configurations of H2 – Molecular Orbital Theory

But wait a second, this isn’t nuclear fusion, all we made was a dihydrogen molecule with two atoms! That’s because the interaction between the two atoms as they came closer caused the formation of a stable chemical relationship that now would require energy to break apart. So how do we achieve fusion and not just end up with a bunch of hydrogen molecules?

May The Force Be With You

In order to fuse these two hydrogen atoms, we must overcome the electrostatic force holding together this dihydrogen molecule and push the two atoms even closer together. The two protons, which are positively charged, have a repulsive electromagnetic force toward each other, so as we push them closer and closer to each other, their electric charge resists us more and more. So if we can overcome that and keep pushing them closer and closer together, how do the protons fuse together?

It turns out protons are composed of multiple sub-particles called quarks, held together by another force that is even stronger than gravity or electromagnetism, called the strong nuclear force. And like electrons, these quarks vibrate according to their own wave functions and interact with other quarks. If you bring two protons close enough together (less than one femtometer), the quarks in both protons start to interact with each other and the forces holding each proton together also begin to exert a residual nuclear force on each other. The strong force is more than ten times more powerful than electromagnetic force. So if we can manage to push together two protons that close, this strong force will take over and fuse our two protons into a helium nucleus, releasing energy. Easy enough, right?

The quarks composing a proton – by Jacek rybak

The Need For Speed

It turns out that energy it takes to push two protons that close together (1.25 MeV) and overcome their electromagnetic barrier is pretty high, because the closer the two protons get, the more electrostatic resistance we encounter from their positive charges.

One way is to accelerate the two protons and make them move faster, giving them enough kinetic energy to smash together. This can be done by applying an external electromagnetic force to them using an electric potential difference, which is how many particle accelerators work. Let’s say you had a chamber full of hydrogen atoms, and on one side of it you had a plate that was positively charged (the anode), and on the other side was a plate that was negatively charged (the cathode). The hydrogen atoms, having both a proton and electron, have zero net charge and are not particularly attracted to one plate or another. But as you increase the voltage difference between the terminals, an electric field is created between the two with a large electric potential difference. Increase the voltage enough, and the electrons get pulled away from the protons in a process called ionization. This is because the electric potential force from the field overcomes the electromagnetic force binding the electrons to the atoms, and the electron gains enough energy to escape its proton. If dihydrogen molecules have both their electrons stripped from them, no negative charge is left and the two remaining protons will repel each other since they are of the same charge. What you’re left with is a soup of protons and free high energy electrons called plasma, and the hydrogen atoms remaining that had their electron ripped away are now just a bunch of bare protons. Any atom that has a non-zero charge (positive or negative) is called an ion.

Plasma Globe
Plasma globes are examples of ionization

So now that we have these ions, we need to smash them together with enough speed for them to get close enough for the strong force to take over and bind them together. Because they are positively charged, we can use electromagnetism to speed them up by using a positively charged terminal to repel and push them in a certain direction, making a particle accelerator. But firing such tiny particles at each other and getting them to fuse is like trying to fire two bullets at each other from two different guns and getting them to strike each other. Sure, if we fire enough of these ions at each other, eventually we will get lucky and smash two protons together, where the strong force will bind the two together and make a new atom, a helium-2 ion with +2 charge. Fusion, right?

Shortest Relationship Ever

Just like electrons and other subatomic particles, protons have their own quantum state that define their existence, and the strong force has its own set of rules that determine how protons interact with each other. When we combined our two protons into a new atomic nucleus, they became subject to these rules. One well-known rule is the Pauli exclusion principle, which states that for certain particles (such as protons or electrons), within a quantum system there cannot exist two of the same particle with identical quantum states. This principle explains why identical electrons do not occupy the same orbital, and it also means that identical protons cannot be too close to each other in an atomic nucleus. Like electrons, protons have a “spin” quantum number (although they’re not actually rotating), and there are two possible values for each proton’s spin.

So now we have a dilemma. The strong nuclear force is stronger when it is holding together particles that have the same spin values. But the Pauli exclusion principle causes two protons with the same spin to repel each other. And protons, both with a positive charge, still have repulsive electromagnetic force pushing each other apart. On top of that, the strong force is weaker in higher energy states, and we just slammed these two protons together with an enormous amount of kinetic energy. So our strong force holding these protons together is fighting against multiple forces driving them apart, and our nucleus becomes unstable.

Almost always, the unstable diproton nucleus decays back into two separate protons, our recent accomplishment of nuclear fusion crumbling apart. Wait, almost always?

Weakest Lottery Every

Very, very, very rarely (1 out of 1028, or 1 in every ten octillion times), when you fuse two protons, something unexpected happens. When the two protons were individuals, their composite quarks were held together in a stable arrangement, held together tightly by the strong interaction. But when the two protons came together, all of the quarks from both protons began to interact, and from that interaction there is a tiny possibility that a new force comes into play, the weak nuclear force. Among other things, the weak force is responsible for the decay of unstable atoms, for example the radioactive decay of unstable elements. But unstable nuclear decay over time has a probability component to it and doesn’t occur all at once. If it did, we wouldn’t have radioactive waste that takes years to break down.

So in the tiny amount of time where our helium-2 atom exists and its two protons have a chance to interact with each other at the nuclear level before forces pull them back apart, there is a tiny probability that the weak interaction between them hits the jackpot and causes a beta-plus decay. This interaction starts an interesting chain reaction. In one of the two protons, one of the quarks (an “up quark”) changes into a “down quark” in a process called flavor change. This change turns the proton (which had two “up” quarks and one “down” quark) into a neutron (which has 1 “up” quark and two “down” quarks). A particle called the W+ boson is emitted, which carries away the positive charge from the proton, leaving the neutron with no charge. That W+ boson quickly decays itself into a positron and a neutrino, which speed away from the nucleus. The positron, which is the positively charged antimatter form of en electron, flies off until it collides with another electron, which causes both particles to annihilate each other and produce two photons (electromagnetic waves). Neutrinos interact very weakly with other particles and have very little mass and will ride off into the sunset. And because our atomic nucleus now has one proton and one neutron, it is no longer helium, but now is an isotope of hydrogen called deuterium.

Feynman diagram describing the beta-plus decay of a proton into a neutron, releasing a positron and a neutrino

But we can’t build a power plant around an event that only happens rarely! And technically all we did was create a heavier hydrogen atom, we didn’t fuse two hydrogen atoms into helium.

The Nuclear Moderators

It turns out deuterium can be reliably fused with another proton and result in a stable helium-3 atom. That’s because neutrons, although they have no electromagnetic charge, are composed of quarks just like protons, which makes them subject to the strong interaction with other particles. This means within an atomic nucleus, they contribute binding energy to help hold it together, and because they have no positive charge, they don’t exert a repelling electromagnetic force on other protons. The extra binding energy contributed by the neutron is enough to overcome the electrostatic repulsion between two protons and hold the deuterium atom together in a stable configuration.

With this knowledge about neutrons, it turns out there are multiple options when it comes to selecting an appropriate fuel for fusion. Deuterium can also be combined with tritium (another hydrogen isotope with two neutrons in its nucleus) to make helium-4. Deuterium can be combined with lithium to make two helium molecules. Boron can be fused with a proton to make 3 helium atoms. All of these combinations release more energy than it takes to combine them, but some are more challenging to achieve than others, because as the number of protons increase in the choice of fuel, the energy required to overcome the electrostatic repulsion and push the two atoms together also increases. For example, fusion between boron and hydrogen only occurs at temperatures above 2 billion degrees Kelvin, and making an oven that hot is an engineering challenge.

What about using neutrons to achieve fusion? Since neutrons have no net charge, neutrons can easily get close to the nucleus of an atom without an electrostatic barrier to overcome, close enough for the strong force to interact with the neutron in a process called neutron capture, releasing energy in the process. Unfortunately, there are two unsolved challenges with this method. The first is that it takes a lot of energy to make a neutron, and the energy that you would gain from the neutron capture is not enough to make another neutron, so the net energy gain in a sustained reaction is negative. The second is that free neutrons (not attached to a nucleus) are unstable, and they decay into protons in about 10 minutes if not within a nucleus, so they must be generated and cannot be stored as a stable fuel.

Also, firing particles at each other is not an efficient way to achieve fusion. Particle accelerators fire a a stream of individual particles at each other to achieve small scale collisions for research, but are not suitable to initiate sustained reactions for power generation. If you accelerate a large volume of positively charged particles toward each other, their electromagnetic repulsion would be cumulative. All those protons resist each other and so the amount of energy required to push them together would grow exponentially, and ultimately, the particles just scatter instead of fuse.

Turn Up The Heat

There is another way to achieve fusion, the thermonuclear method. You may have heard this term used in the context of nuclear weapons, but its actual meaning is that we can initiate a fusion reaction if we apply enough heat to the particles while maintaining their proximity. If we can keep the particles close enough together, increasing the heat energizes them, which in turn increases the probability that they will fuse. But the heat requirement is very high, more than 100 million degrees Kelvin to fuse deuterium atoms. And maintaining particle density is also challenging, because as particles become subject to increased heat, they gain more energy, which causes them to be more excited and more difficult to contain. Just as an electric field ionizes atoms and turns them into plasma if the field is strong enough, when you apply enough heat to a collection of atoms, it also turns into highly energized plasma.

Plasma containment is an engineering challenge, because plasma is so energetic that it strongly resists confinement, and to sustain fusion the density of the plasma must be maintained. Some solutions use high powered magnetic fields to contain the plasma and keep particles together. Another method employs a system called a zeta pinch, which uses an electrical current to generate a magnetic force that compresses the hot plasma so that fusion can occur.

ITER Tokamak
ITER Tokamak and Plant Systems, a magnetic containment fusion design

There are still other approaches, such as compressing fusion fuel into tiny pellets and using very powerful lasers to induce an implosion of the fuel quickly enough to heat the fuel, compress the plasma, and initiate a fusion reaction. Certainly there are concepts and ideas that have not yet been tested or not yet been discovered, and is no shortage of speculation on which method will be the most promising. When a process is finally developed and tested that creates and sustains a reaction that produces a sufficient net energy gain, commercial fusion power will be soon to follow.

Other Methods

As tends to occur with any emerging technology, there have been all sorts of claims made in the fusion industry. Some have a limited scientific basis, others are made to attract investment, and others still have been made to garner publicity. One of the most famous was made in 1989, when a claim was published by two scientists that they had developed a method for cold fusion, fusion at temperatures typically encountered on Earth versus the extreme temperatures needed to achieve thermonuclear fusion. Most physicists were skeptical based on then-current understanding of the conditions required to initiate fusion (which you also now understand from reading this article). Ultimately, after millions of dollars of research and a lack of reproducible results, most efforts to pursue cold fusion have been abandoned.

There has been research into other methods, such as using uncommon subatomic particles such as muons or the annihilation of antimatter to generate energy. Particle physics and quantum mechanics are themselves rapidly developing areas of research, as more discoveries are made there, more theories of nuclear power will be developed and tested. Until there is evidence to support any conclusions, it is not possible to establish the credibility of any given theory. After all, history is filled with examples of humanity believing one thing to be true, only to discover evidence that proves otherwise.

30 Years Away

There’s a joke among fusion researchers that fusion power is always “30 years away.” While its difficult to pinpoint exactly when we will have our first commercial fusion plant, multiple teams have been making steady progress toward implementing sustainable fusion power. Clearly, as we’ve covered some of the scientific and engineering challenges involved with implementing a working solution, producing fusion power is not a simple process. And once you achieve a net energy gain, you still need to make it economically efficient enough to replace existing conventional methods.

Electricity was discovered in an experiment in 1752, and over the next hundred years, researchers works on various ways to harness that power. A working, reliable light bulb was not produced until 1879, 127 years later. For the next ten years after that, utility power began to reach cities, but only within small areas. As innovation and research continued, eventually the modern power grid was developed, which is able to distribute electricity to our homes and businesses across the world. As more funding, more people, and more time is spent researching and experimenting with fusion power, it’s only a matter of time before we can harness the power of the atom to produce the next generation of clean power.

References

  1. https://fusor.net/files/fusor_schematic.jpg