Science For Everyone - Atomic Fusion

Copyright © Karl Dahlke, 2022

Democritus believed that atoms were immutable and eternal, and he was almost right. Atoms rearrange and recombine during a chemical reaction, but they don't change. By analogy, you might take your lego house apart, and build a lego car, but the lego bricks used for construction are the same. In the previous chapter, we presented an exception to this rule, wherein a radioactive atom might decay into a different atom, or perhaps split into two smaller atoms, in ironic contradiction to the word atom, which means indivisible in Greek.

The energy released by atomic fission is three million times that of a chemical reaction, but unstable atoms are rare in nature, and must be gathered together in high concentrations to generate usable power, or even a little bit of heat and light. This "enrichment" process is not trivial. The United States spent several years, in the 1940's, learning how to separate uranium isotopes, in order to synthesize a couple pounds of enriched uranium for its first nuclear bombs. Massive chemical factories were built in Oakridge Tennessee, also called the Secret City, for this purpose. Needless to say, we have streamlined the enrichment process since then.

Along with fission, and radioactive decay, there is another mechanism whereby atoms can change - and it only happens in the center of stars. Start with a box of standard lego bricks, each 2 dots by 4 dots. These are the first lego pieces to come out of the factory in the early 60's, and a mainstay of lego construction. These pieces are all white, they aren't unusual, and they aren't radioactive. They are eternal, as Democritus anticipated. Now compress them under a force of 250 billion atmospheres, and heat them to 15 million degrees. Once in a while, and it's still a rare event even under these conditions, two lego blocks will merge into one, creating a 2 by 8 block. Two blocks fuse together, thus the word fusion.

As you might surmise, my lego analogy represents atoms in the center of a star. Our sun is a mid-sized star, and its core is hot enough, and dense enough, to force hydrogen atoms together, to make helium. We sometimes say it "burns" hydrogen, to make helium.

Hydrogen is the lightest gas on earth, lighter than air, and if one could heat it to 15 million degrees, it would spread out, as discussed in an earlier chapter, and become lighter still. However, the unimaginable weight of the sun compresses the hydrogen in the core, until it is 150 times as dense as water. The high pressure, and high temperature, increases the chances that some hydrogen atoms, here and there, will collide with enough energy to fuse into helium.

The super-compressed hydrogen isn't technically a liquid, it is much too hot for that. Particles still fly about as though it were a gas, but they can't fly very far, without colliding with their neighbors. At this high density, thicker than water, it can almost be modelled as a fluid. Imagine a cup of this fluid on your kitchen table; it weighs almost as much as you do.

In the hydrogen → helium reaction, the resulting helium atom is 0.7% lighter than the hydrogen atoms that comprise it. If we could fuse a kilogram of hydrogen, and that's not really how it works, scarce atoms of hydrogen fuse together, not the entire mass, but if we could fuse a kilogram of hydrogen, the resulting helium would weigh 0.993 kilograms, i.e. 7 grams lighter. Those 7 grams are converted into energy. That doesn't sound like much, but it's a lot! Recall the equivalence between mass and energy, as discovered by Einstein. The currency exchange is the speed of light squared, so a little mass produces a lot of energy. Hydrogen fusion releases several times more energy, per kilogram, than uranium fission, which is in turn 3 million times more energetic that burning wood or coal or oil.

Other fusion reactions are possible. Three heliums combine to make carbon, carbon and helium combine to make oxygen, and so on. All of these release tremendous amounts of energy, however, the sun is only hot enough, and dense enough, to convert hydrogen into helium. A larger and heavier star burns more of its fuel, and burns it faster, sometimes ending in an explosion that can be seen throughout the galaxy. We call this a nova, from the Latin for new; as it is a new star in the sky. If our sun were larger, and heavier, it would burn hotter, perhaps bluish white, and it would have run out of fuel long ago, perhaps ending in a bang, and we would not be here to talk about it. At the other end of the scale, a small star, known as a red dwarf, burns its hydrogen very slowly, and can shine for 10 trillion years, a thousand times as long as our sun. This small star is called a red dwarf because it only gets red hot, not white hot like our sun. Objects begin to glow red at approximately 500 degrees c, or 900 degrees f, whereas our sun radiates a full white spectrum at 5,500 degrees c, or 10,000 degrees f.

So How much Energy can you get from a Cup of Plasma?

It's a hot summer day in July, and as you look for shade, or duck into an air conditioned building, It's hard to believe the source of all that heat is 93 million miles away. What would it be like to approach the sun's surface, a blazing 10 thousand degrees, or swim in its center, at 15 million degrees? Protons and electrons fly about in a frenetic subatomic dance that is the hallmark of heat. Yet they soon crash into one another and bounce off in different directions, as the immense weight of the sun packs them into a fluid 150 times as dense as water. Within this high energy soup, protons will occasionally come together at high speed and form a helium nucleus. Thus hydrogen fuses into helium, and energy is released. Heat accumulates in the center, travels to the surface, radiates into space, and gives life to you and me.

How efficient is this process? How much energy is released? In other words, what is the power output per unit volume? If you have a cup of hydrogen plasma in your living room, at high temperature and pressure, with a very tight lid keeping it all inside, could you use it to power a city? A building? Your house? The answer is none of the above. Energy production per cubic centimeter is very low, about the same as that of a resting salamander. A warm blooded animal such as yourself liberates more energy per unit volume than the sun. And yet the sun produces, and releases, huge amounts of heat. How is this possible?

The secret is its size. Each cubic meter only generates 276 watts, but there are a lot of cubic meters in there! Heat builds up inside until the center is 15 million degrees, while the surface radiates heat out into space. Everything is in equilibrium.

If it were not so, if the sun produced energy rapidly, as happens in a larger, heavier star, it would never last for 5 billion years, and life would not evolve on earth. Once again the physical constants of the universe are fine-tuned to support life. The sun's paltry energy production per cubic centimeter has to be so, or we would not be here to talk about it.

Controlled Fusion Energy

Fusion releases even more energy than fission, and you don't need rare radioactive isotopes of uranium, and there is no dangerous radioactive waste to besmirch the land for a hundred thousand years, and there is no danger of a meltdown, rendering an entire city, or state, uninhabitable. It is literally the power of the sun come to earth. So isn't this the way to go?

Although the laws of physics make life possible, by slowing down the fusion process, they conspire against us as we try to harness the power of the sun here on earth. In the 70's I read optimistic articles in Scientific American about controlled fusion, and the dream of low cost power with virtually no environmental impact, especially when compared to coal fired power plants and nuclear reactors. That was before global warming; the need for fusion power is even greater today. So how about it - compress some hydrogen under 250 billion atmospheres to 150 times the density of water, and heat it to 15 million degrees c, and you're on your way, right? Well here we are, 50 years later, and 100 billion dollars later, with almost nothing to show for it.

Unfortunately, recreating these stellar conditions in the lab, even for a millisecond, is an enormous technological challenge, and after all that it's still not enough. Nobody can power a city with a fuel that releases energy like a salamander sitting on a rock, looking in your direction and blinking once or twice. Yes, we have a few tricks up our sleeve, like using other nuclei that fuse at lower temperatures and pressures, but the task remains daunting at best, far more difficult than sending humans to Mars. Still, if commercial fusion power could be achieved, the economic, environmental, and social benefits would be enormous.

When Science Contradicts Itself

By the 19th century, science faced an irreconcilable contradiction. Geologists and archaeologists and cartographers amassed a trove of data that suggested the earth was very old, perhaps a million years old. I will give one example; there are many others.

Sailors had finally drawn accurate maps of the earth: it's continents, its islands, its seas and rivers, and its mountains. It was clear at a glance that Africa fit into South and Central America, like two pieces of a puzzle. Indeed, it looked like the Americas and Africa were one land mass, and a crack developed, and these continents pulled apart, leaving the Atlantic ocean in between.

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Even though it looked compelling on a map, this was an extraordinary claim, that required, in the words of Carl Sagan, extraordinary evidence. Over the decades, evidence began to mount. Geologists confirmed that the rocks on the two coasts, eastern South America and western Africa, were chemically similar, as though they were once part of one region. Furthermore, there were similarities in the ancient fossils, left behind by the animals who lived at that time. Several lines of evidence converged, and suggested that one land mass split in two, and pulled apart over time.

Thanks to our modern global positioning system, we can now measure the continental drift with high accuracy. South America and Africa are moving apart at one inch, or 2.5 centimeters, per year - making the Atlantic Ocean that much wider. Our ancestors couldn't possibly make these precise measurements, but they knew that drift, if it existed at all, had to proceed very slowly. A rapid expansion of the Atlantic Ocean, e.g. one or two kilometers per year, would have been apparent to the sailors of the day - and what force could possibly move entire continents at that speed? No - continents move at an almost imperceptibly slow pace, requiring at least a million years to create the Atlantic Ocean as we see it today. Therefore, the earth is at least a million years old.

This is good science, but at the same time, we have the chemists and the physicists and the astronomers who concluded the sun is no more than a few thousand years old. We are fairly certain the earth was formed at the same time as the sun, or soon thereafter, so the earth can't be a million years old, while the sun is only a few thousand years old. This is a startling contradiction.

How did the scientists of the day measure the age of the sun, which we can't even touch? Astronomers had measured its size, and thus its volume. At the same time, chemists knew how much energy was released from burning coal, which was the most energetic reaction of the day. In fact, that reaction was used to power the industrial revolution. If the sun was a giant ball of burning coal, it would run out of fuel in a few thousand years. The math was inescapable. The sun could not be older than that.

The resolution had to wait until the beginning of the 20th century, when atomic fission and fusion were discovered, reactions that release millions of times more energy than a traditional fire. Now the sun has plenty of fuel, in the form of hydrogen, to last billions of years, and the contradiction goes away. Both the sun, and the earth, are old - 4.5 billion years old as it turns out.

Sometimes science doesn't have all the answers, and sometimes there are apparent contradictions in the journals we read. It is important to keep the faith however. Science is self-correcting, and eventually, the answers will come. We already understand our world, and our place in the world, to a degree that our ancestors could never have imagined. For half a million years, humans looked up in the night sky and wondered what those twinkling lights might be. Today we know they are suns, incredibly far away, and we even understand what makes them shine. You are truly privileged to possess this knowledge, which is only a century old. Yes, science brings us indoor plumbing, and cars, and smart phones, but it also brings us a wonderful understanding of our universe.

A Chain of Energy

Recall, in an earlier chapter, we followed the energy all the way from the sun, to winding up a grandfather clock. Energy is never created or destroyed, it merely changes form. Let's follow the chain of events again, this time in more detail.

The energy begins as mass, embodied in hydrogen in the center of the sun. Under extreme pressure and temperature, some of these atoms fuse, and become helium. The resulting helium weighs 0.7% less than the aforementioned hydrogen. Mass has been transformed into energy, in particular, high speed subatomic particles and heat.

The heat keeps the interior of the sun at 15 million degrees. By conduction, convection, and radiation, this heat flows out to the surface, just as an apple pie might be piping hot inside, even though the crust is pleasantly warm to the touch. Of course the sun constantly generates its own heat internally, so it's not exactly like an apple pie.

The surface of the sun, which we see from earth, radiates exactly as much heat, per second, as the sun generates inside. If the surface didn't generate enough heat, the core would get hotter, and the sun would get hotter throughout, and the surface would get hotter, and brighter, and radiate more energy into space. Conversely, if the surface radiated more energy than the sun was producing inside, the sun would gradually cool, thus sending less energy out into space. Since the sun has been shining for a very long time, it is in equilibrium, and the energy generated inside equals the energy radiated into space. We don't have to guess, or run computer simulations, to determine exactly how much heat is generated inside - simply multiply the radiation that we see by the sun's surface area. In fact, if we run a computer simulation of the core, and get a different answer, then there is something wrong with our simulation.

A million years ago, some hydrogen fused into helium, and released heat. That heat has finally made its way to the sun's surface, keeping it at roughly ten thousand degrees f, six thousand degrees c. This glowing plasma sends its heat and light through space, and a tiny fraction falls upon the earth.

In our example, the sunlight lands on a wheat field in Kansas. The leaves of a wheat plant, or any plant for that matter, are green, due to a green compound called chlorophyll. Under a microscope, a plant cell contains small green spheres called chloroplasts, which in turn contain the chlorophyll. The word chlorophyll is Greek for green leaf. You may remember the description of chlorine, in an earlier chapter, as a light green gas; its name is also derived from the Greek word for green. Indeed, chlorophyll includes some chlorine, but that isn't the source of its green color. It also includes a magnesium atom, which is unusual for an organic molecule. Magnesium and chlorine work together to capture sunlight and convert it into chemical energy. This provides the "food" that the plant needs to grow, and develop, and reproduce. Some of this food energy is stored in starch, which we are (fortunately) able to consume and digest. Other animals, such as a goat, can eat leaves, stems, and all, but we are not so lucky.

There are many forms of chlorophyll, and many energy capturing processes. One reaction, which occurs across many steps, takes in 6 molecules of carbon dioxide from the air, and 6 molecules of water from the ground, and produces one sugar molecule, and 6 molecules of oxygen, which vent back into the air. Indeed, virtually all of the oxygen in our atmosphere comes from plants or algae, using the power of the sun.

6CO2 + 6H2O = C6H12O6 + 6O2

Notice that this equation balances, with the same atoms on each side. Once we leave the core of the sun, atoms become eternal again. They can be rearranged to store and release tiny dregs of energy, but that's enough energy to keep you and me alive.

Sometimes sugar is left as sugar, as in an apple, but sometimes sugars are chained together to make long starch molecules. The chemical energy in the sugar is the same either way, it is merely a matter of storage. The sugar contains energy of course, but so does the oxygen in the air. In both cases, the energy comes from the sun. When you metabolize sugar in your body, to exercise, or think, or keep yourself warm, you are running this process in reverse. The atoms revert back to water and carbon dioxide, ready for another plant to turn them back into sugar or wood or leaves, or anything that might serve the plant's needs. Fire also releases the captured energy of the sun, but much faster. A tree may spend 50 years turning sunlight into wood and oxygen, and when you burn that wood, in the presence of oxygen, all that energy is released in just a few hours.

From farm to silo to factory to store to your table, the wheat is processed into cereal, which you eat for breakfast. You digest the starch, and repackage its chemical energy in different compounds that are more appropriate for humans than for plants. Some energy is lost in translation; in fact some energy is lost at every step. Perhaps some of the energy was converted into heat, but that's not all bad, you're a warm blooded animal and you need to keep your body at 37 °C.

Next, the chemical energy is released in the muscles of your arm as you turn the key and raise the weights from the bottom of the clock up to the top. Chemical energy has been converted into potential energy, the energy of the weights high up off the floor. Some energy is lost; the sprockets clink as you turn the key, and the muscles of your arm are a bit warmer after the exertion. Over the next week, the weights descend, and potential energy is converted into sound and heat. You know the sounds of the clock, the gentle tick tock tick tock, and the strike and the chime. The heat is so tiny you can't even measure it, but it's there, primarily in the escapement. After a week, all the potential energy has been converted into heat, even the sound dissipates into heat, and the clock is in the same state it was before, waiting for someone to come and wind it up again. Where did this energy come from? The sun. Specifically, the hydrogen atoms in the center of the sun. The sun winds you up every day, through the food you eat, and you wind the clock up once a week.

It is fair to ask, who wound up the sun? More precisely, where did the hydrogen come from , the hydrogen that fuels the stars? The answer is, we don't know. It's ok to say we don't know, there are a lot of things we don't know, and some things we may never know.