A Mass of Incandescent Gas

[Title from They Might Be Giants.]

This week, I got a question from my father Steve: We're able to identify the source of nuclear materials used in reactors and weapons from their isotope ratios. Could we do the same thing to figure out which star material that hits Earth came from?

First, let's talk about isotopes: Atoms are made up of a nucleus or protons and neutrons, surrounded by a cloud of electrons. The number of protons tells you what element the atom is – one for hydrogen, two for helium, and on down the periodic table. The number of electrons tells you the charge of the atom – neutral if it's equal to the number of protons, negative or positive for more or fewer electrons. Finally, the number of neutrons tells you the isotope – These are variations on the same element. For example, most carbon on Earth is called carbon-12, which has 6 protons and 6 neutrons for a total atomic mass of 12. However, some is carbon-14, which has 6 protons (since it's still carbon), but 8 neutrons. This configuration is unstable, and gradually decays to carbon-12. The mixture of carbon-14 and carbon-12 leads to radiocarbon dating, which is used in archeology to measure the age of excavations.

Natural uranium is almost all U-238, with small amounts of U-235 and a few other isotopes. Putting it in a nuclear reactor though will change those ratios. As the U-238 decays, it loses neutrons, raising the amount of U-235 present. The amount of U-235 in a sample can be further increased through enrichment, which uses various methods (often advanced centrifuges, which come up in nuclear policy) to separate the lighter U-235 from the heavier U-238. There can also be other isotopes of other elements mixed in depending on the exact process a reactor was using.

Now to stellar compositions: Stars are mostly made up of hydrogen, but the star's mass causes the hydrogen to fuse into helium, releasing energy that helps keep the star from collapsing. Helium can fuse too, and that can continue a few steps down the periodic table, but it's limited, typically petering out near iron:

Wikipedia (Click to enlarge)

The elements in yellow may be present in an active star, and will be spread around the universe when the star eventually explodes. We can find which are in a given star by looking at their absorption spectra:

Wikipedia

The star emits light in a black-body spectrum due to its heat, but the elements it contains will absorb some of that light, leading to dark bands on the spectrum. The frequencies (colors) of those bands correspond to different elements that let us determine the composition of the star.

Now to Steve's suggestion: When massive particles hit the Earth, could we use their makeup to associate them with a particular star? To my understanding, the answer is no, the particles that hit us are typically single protons or neutrons, not entire atoms, and certainly not the collection of atoms that would be needed to find a concentration of certain isotopes. There's another problem too: Uranium and other elements typically associated with isotopic signatures aren't present in active stars – If you look at the table above, you see those need neutron star collisions to form.

So it seems this idea won't work for distant stars, but if we screw things up badly enough on Earth, future scientists will be able to figure out where things went wrong, and curse that we ever trusted Mr. Clevver.

Fusebox

I've been stuck for several weeks on an idea for a post, as well as doing some family visiting, so I've haven't been here for a while, but during one of those visits, I got another great question from Papou (paraphrased): I've been reading about plans for fusion power plants. How do they work?

Fusion is a type of nuclear power, but unlike the typical fission plants in use today, does not require radioactive elements such as uranium. In a fission reaction, the fuel naturally releases particles which heat the surrounding material, as well as knocking more particles off other parts of the fuel. Fission power relies on the natural release of neutrons from the fuel to spur further reactions. However, fission results in nuclear waste – radioactive materials not strong enough to supply power, but still dangerous to living things.

Fusion works along the opposite path: Forcing two atoms together until they bond, which releases energy. This is made difficult by the structure of an atom: protons and neutrons are bound together by the strong nuclear force in the atom's nucleus, which is surrounded by a cloud of electrons held by the electric Coulomb force. When we try to force two atoms together, initially the Coulomb force between their electrons will resist, until they get close enough for the strong nuclear force to pull the nuclei together.

To put some numbers to this idea, we can look at the potential energies of the two forces involved. The Coulomb potential is given by

where the first term is some constants, the qs are the charges of the two particles, and r is the distance between them. The nuclear potential is a bit more complicated, and requires making some approximations. I used the Reid potential, which uses terms of the form exp(-m*r)/m*r. We can look at how these two potentials behave near the nucleus:

The x-axis is measured in femptometers, or 10^-15 m, about the size of a proton. Notice that the Reid energy has a large dip at around that size. This dip is enough to make up for the rising Coulomb energy, and it's what makes fusion power an attractive energy source. The trouble is that at larger distances, the Coulomb force pushes the atoms apart. We can look at the point where the forces cancel:

You can read a potential energy plot like an elevation map: Objects go downhill, faster for steeper slopes. Anywhere flat, an object will stay still, but if it's the top of a hill, like above, it's an unstable equilibrium and will fall one direction or the other with a slight disturbance. Here, you can see that the crossing point appears between 5 and 6 fm. Getting atoms that close is extremely difficult, and a major obstacle to fusion power.

One way to do it is by heating and compressing the material. This is how stars like our Sun achieve fusion: Gravity squeezes the hydrogen into a tight area, increasing both the temperature, and the chances of atoms hitting each other. The fusion then releases more heat, continuing the process. To scale that down to a power plant though, we need a different way to squeeze the atoms together.

The solution to that is to create a plasma. By heating the hydrogen to a little over 150,000 °C, we can make it ionize, or separate into individual protons and electrons. That makes it susceptible to electric and magnetic fields, which we can use to compress it. This is the method used by tokamak reactors, including the ITER, which is set to be the biggest such reactor beginning operation in 2025.

The problem such reactors need to overcome for power generation is that heating the hydrogen into the plasma state, and containing it with the electromagnetic fields requires a significant input of power. If everything works correctly, the output from the fusion can surpass that, but so far the best we've been able to do is generating 70% of the input power, a net loss. The plan for ITER predicts it will achieve a 10-fold increase in generated power over the input. It's exciting to see the progress being made in this field, but we should keep in mind the tangible results may still be a long way off. Thanks for another great question, Papou!

Gone Fission

This week, Marika and I watched HBO's Chernobyl series. In spite of the depressing topic, and the at times gruesome imagery, we found it extremely interesting. I was (of course) most drawn to the explanation of how the reactor operated, and then failed. I've never studied nuclear physics in detail, but I had a rudimentary understanding of how reactors work:

• Uranium atoms radiate particles which can hit other uranium and cause them to split
• When uranium splits, it releases energy, which heats the fuel
• The fuel is cooled by water, which drives a turbine to generate power
• Control rods block the radiated particles, slowing down the reaction

The final episode of the series shows the trial of the technicians in charge of the plant, and a scientist gives an excellent explanation of how their decisions and flaws in the design caused the disaster. There are a number of interconnected systems that control the behavior of the reactor, including the control rods and the cooling water, but also buildup of gasses and the power output of the reactor when any of these properties change.

I was curious if I could create a rudimentary simulation of these systems to see if I could cut it as a Soviet reactor tech. I decided to base my model on a boiling water reactor, which seemed to be nearest to my previous understanding of how these plants work. A bit of searching turned up this document describing exactly the type of setup I was imagining, intended for training power station operators!

I wasn't interested in reimplementing a product developed by the International Atomic Energy Agency, but their description was a good starting point to identify the variables, and pare down the complexity. The elements I chose were: Reactor power output P, which increases or decreases as the control rods are removed or inserted; the heat transferred to the water ΔQ, which corresponds to the electric power produced by the plant; the volume of water surrounding the fuel V; the rate water is pumped into the reactor F; and the temperature of the fuel T. These are related by some differential equations. The heat transferred from the fuel to the water is proportional to the temperature of the fuel, and how much water is in contact with it:

That heat is taken out of the fuel, which cools it, while the nuclear reactions I described above are heating it:

The heat is also causing water to evaporate, but we're pumping water in to compensate:

I've played a bit loose with the units here – There should be conversion factors to go from energy to temperature, and energy to volume. I just wanted to get a feel for how these parameters interact, and I did! Below, you'll find another HTML5 simulation, where you can control how far the control rods are inserted, and how much feed water is entering the reactor. If the reactor gets too hot, it will meltdown, and you'll need to reset. I don't think it's very realistic, so aspiring nuclear technicians should not include this on their resume, but you can see some interesting behavior. Have fun!