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Nuclear Fusion Part 1: Theory

Two basic forms of nuclear reactions have been identified by physicists: nuclear fission, which we are all surely somewhat familiar with (even if we don't know it), and nuclear fusion, her less understood sister. Between 6th and 8th grade, I constructed a small nuclear fusion device. On this page, I've detailed the theory and construction of the device, to provide readers with some background. A thorough understanding of some not-so-complicated physics is essential for understanding the principles of fusion, the reaction that produced the atoms in your body and everything else around you. So let's get to the basics! 


Part 1 of Part 1: Plasma

In normal, everyday life, we're pretty familiar with the states of matter. Your laptop is a solid, your coffee is a liquid, and the air you're breathing is a gas. But the fourth state of matter is much less well known (although it's pretty common). Plasma is the high energy form of a gas and the form of matter in which fusion occurs (some common plasmas: welding arcs, lightning, plasma tv cells, the sun and other stars, and fire can be considered a very weak plasma). 







Now we just talked about energy, but what really is energy? Where does it come from? Physics is a lot of names that you put together to make more names. The most basic quantities in physics are mass (amount of matter inside of something), distance/length, and time (There are some others, see below). You can come up with most other quantities just from these: speed (distance over time), velocity (speed with direction), acceleration (velocity over time), and force (mass times acceleration).


Forces are the next step to understanding energy, and therefore understanding plasma. Forces are acting on us all the time: the force of gravity, pulling you down, the force of the ground, pushing you up, and the force of friction, stopping your car. The next quantity we can derive is work, the force times the distance over which it is applied, and from there we get to energy, a measure of the amount of work done/the capacity to do work. In the image below, the cosine just means that the direction the object moves has to be the same direction the force is applied for work to be done.



The two most basic kinds of energy are kinetic and potential. Kinetic is energy in motion (think about a car driving down a highway), and potential is the energy of position (think about a ball at the top of a hill). So a plasma has what kind of energy? The kinetic energy of the particles making it up (the name for the average kinetic energy of all of the particles should be pretty familiar: temperature).





So this plasma has particles moving around really fast, but so do gases, so why is it different? This has to do with the atomic structure. Electrons orbit the nucleus of the atom at (roughly) set distances depending on the amount of energy they have, the higher the energy, the farther out they move. In a plasma, the individual atoms and the electrons in these atoms have received so much energy that their electrons aren't even bound in their orbits around the nucleus anymore, so it's just a really hot slush of electrons and nuclei. This is still a bit simplified though; not all of the electrons may have been liberated, so the atoms might, instead of having no electrons, have less than normal, meaning that they are ions, not just nuclei. The images below show the difference between gas and plasma (black = gas atoms or molecules, red = ions, blue = electrons. Not to scale at all.)





From this arises another form of energy: electric potential. The nuclei (or ions), dense positive charges, are completely (or partially) exposed and moving really fast. So now, like opposite poles of a magnet, these individual nuclei repel each other whenever they get close. So our final definition of plasma (which is still pretty simplified) is: a super-heated gas made into a soup of nuclei/ ions and electrons that are moving really fast, and the nuclei repel each other. So if the nuclei repel each other, and if we need to get them close together to fuse, HOW DOES FUSION HAPPEN???


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Part 2 of Part 1: Fusion

Now it's time to get to the more interesting stuff. Armed with a rough understanding of plasma, we can begin to see a vague idea of fusion reactions. We've got a bunch of nuclei, and we need to get them to fuse. The problem we're finding is that they're all positively charged, so they repel each other. This brings up another good question. If the nuclei of atoms are made up of positive protons and neutral neutrons, how do the protons stay together? They're all positive, so by logic they should fly apart. The answer is the strong nuclear force.




Physicists have isolated four fundamental forces of nature: gravity, electromagnetism, strong nuclear force, and weak nuclear force. Gravity and electromagnetism (electricity and magnetism) are pretty well known and understood, but the other two are less so. Gravity is the attraction between masses. Electromagnetism is the attraction and repulsion of positive and negative charges. The weak force is responsible for forms of radioactive decay, and the strong force holds nuclei together.











So far, all of the forces we observe can be traced back down to these four forces, in fact, one of the biggest quests of modern physics is to find a grand unifying theory or GUT to reconcile the four into one working description of the universe. The forces we're interested in to begin with are the electromagnetic and strong forces.


(A fun take on the bosons, or force carrying particles, of the fundamental forces.)

The electromagnetic force is causing the repulsion (positive charge repels positive charge, via Coulomb's Law. See below). The strong force is joining the repulsive nuclei. Both forces are mediated by force-carrying particles called bosons. The E/M force is mediated by photons and has an infinite range. The strong force is mediated by gluons and has a range of 0.000000000000001 meters (10^-15 meters). The strong force may be extremely strong (137 times stronger than E/M), but the dilemma is bringing the nuclei so close together that the strong force can take over. 


(Past that barrier, the strong nuclear force takes over, but up until that point, the E/M force is repelling, so the nucleon needs a lot of energy.)

The best way to address this problem is by examining how fusion happens in the sun. The sun began as a large cloud of hydrogen gas. By large, I mean 1.3 million times the volume of Earth and 333 thousand times the mass. With such large masses, the force of gravity is extremely strong. The large mass becomes compacted into a ball because of the gravitational attraction of all of the hydrogen. The force of gravity is so strong, that the pressure and temperature become immense in the center due to all of the mass pressing in on the core. With so much energy being supplied from the heat, the gas becomes ionized (a plasma). Then, with the immense pressure, nuclei are pressed close enough together for the strong force to take over, and fusion occurs.

In the sun, the immense force of gravity pulling an extremely large mass together drives the reaction, providing the perfect conditions for fusion. That seems pretty hard to replicate on Earth. But before we get into replicating the reaction, there are a couple more advanced things I want to take a look at. First off: how does fusion produce energy?


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Part 3 of Part 1: Quantum

Right now, it seems like fusion takes a ton of energy, but we're not really seeing how any energy would be released. The answer actually comes from chemistry. It's called binding energy. Binding energy is the energy that is released to stabilize the nucleus. It's the energy that holds the nucleus together.

On the periodic table, the light elements have low binding energies because they don't have that many protons to hold together. And the heavy elements have lower binding energies too because they have so many protons that they're very unstable (most of them are radioactive to try to remedy this instability). The middle ground though has elements with higher binding energies. So, if you take two small, low binding energy atoms and fuse them, then the resulting nucleus will have a higher binding energy.


This higher binding energy will be released to stabilize the new nucleus, and that energy is the product of fusion that we're interested in. Nuclear fission, the inverse, occurs by splitting a heavy nucleus into two or more higher binding energy products. The energy, in either case, is a product of the famous  E=mc .    Part of the mass of the nucleus is converted into binding energy, which is released as kinetic energy of the products and possibly light/other electromagnetic radiation, like gamma rays.


The final step to understanding the theory behind fusion is the realm of quantum mechanics. There are two basic principles in quantum mechanics. Basically, the idea is that physics at the subatomic, or quantum level is different in behavior than the macroscopic world and cannot be explained by our classical notion of physics. Instead of concrete laws, the two main principles are based around probabilities: particle-wave duality and the uncertainty principle.



Particle-wave duality defines subatomic particles as behaving as both particles and waves, not one or the other (subatomic particles exhibit properties of both). The uncertainty principle states that you can't know both the position and momentum of a particle certainly (if you know one with certainty, the other is very uncertain).




Particle-wave duality arises from actual observations of the properties of subatomic particles. The uncertainty principle arises from something called conjugate variables. This can best be understood from considering the example of time and frequency of a musical note. Let's say you're playing the flute and you play a note and hold it out for a while. That produces a sound wave that looks something like this: 




Now, this wave has a pretty well-defined frequency, but what would you say if I asked at what point in time does this wave occur? Clearly, it doesn't have a well-defined location in time. But what if you play a super short note, like a nearly infinitely short note? Let's say we zoom in a lot and it looks something like this:

Now we have a well-defined location in time, but the note is so short that it doesn't really have a well-defined concept of frequency. An early statement of quantum mechanics was that position and momentum are conjugate variables, like time and frequency in the example, lending an inherent, probabilistic nature to subatomic particles. 

Now let's apply this to fusion. Let's imagine that our nuclei are made of paint on a canvas. Rather than being dots, like we would expect, they're more like streaks, and the thicker areas of the streaks are where the nucleus most probably is. Now we'll make the repulsive electromagnetic barrier (the Coulomb Barrier) a wall. If the nucleus was ball like, it would hit the wall and bounce back. But let's say it's like our canvas streak. The streak comes at the wall, and we'd expect it to stop and bounce back, but what if one of those thinner areas on the end makes it through the wall. Maybe it's so thin, that it was just able to pass through. This means that the tiny piece that passed through represents a tiny probability that the nucleus passes through the repulsive Coulomb barrier and fuses. 





This example is to bring light to the reality: many nuclei that participate in fusion reactions don't have sufficient energy to do so. What actually happens is that due to their probabilistic nature, they are able to "tunnel" through the electromagnetic barrier, and the strong force takes over.

This was a pretty intense look at the theory. Now we're gonna look at how a fusion reaction is made on Earth.

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Nuclear Fusion Part 2: Fusor

Alright, the theory wasn't so bad. Now we have a pretty good idea of what to do, but how do we go about doing it? This next section is going to look into the practical concepts. I've detailed the construction of my device, and some other designs.

Part 0 of Part 2: The History

The history of practical fusion starts with the proposition of fusion reactions in stars, after Einstein's groundbreaking publications on relativity. British astrophysicist Arthur Eddington suggested that stars produce energy turning hydrogen into helium in his 1926 paper, Internal Constitution of the Stars  (further work on nucleosynthesis in stars was done by Hans Bethe, who won a Nobel Prize for his work). Using particle accelerators (see my particle accelerator page for more info about accelerators) designed by John D. Cockroft and Ernest T.S. Walton (early pioneers of particle physics research) Ernest Rutherford (widely considered the father of nuclear physics, having discovered the proton/nucleus, and theorized the existence of the neutron) performed early fusion experiments in the thirties, shooting protons at a deuterium target, and creating deuterium to helium fusion reactions. His assistant, Mark Oliphant, further developed early fusion reactions, discovering tritium (the third isotope of hydrogen, consisting of a proton and two neutrons) and helium-3 (an isotope of helium), demonstrating the fusion of heavy-hydrogens. Accelerator fusion devices produced reactions, but on a very small scale. With the rise of fission devices (particularly nuclear weapons), physicists like Enrico Fermi explored the idea of fission-driven fusion reactions (theoretically). Intrigued by Fermi's ideas, Edward Teller tried to apply them experimentally, succeeding with the creation of a thermonuclear weapon design in the early fifties, which would be used extensively to develop new weapons. Meanwhile, other researchers, chiefly in the Soviet Union and the U.S.A. explored practical fusion reactions for an energy source.