### Pick Any Ion You Want, As Long As It's Noble

In writing Astronomical Returns (and teaching myself about space in general), the challenge I always come up against is learning and discussing the perfectly intermediate level of technical knowledge. As a lifelong space fan, I know way more than the average person, but with just my meager finance degree, I know nothing compared to an actual engineer or scientist. Fortunately for me, in the field of rocket fuel my problems were solved by a single book - Ignition: An Informal History of Liquid Rocket Propellants. I consider it the most informative book I've ever read, and I highly recommend it to you all!

 Originally published in the 1970s, they just released a new reprint! It used to be quite rare, I had to dig deep in the UT Austin library to find it

When people think of rocket fuel, the image that comes to mind is usually a big booster firing massive chemical engines on the launchpad. But while conventional rockets are both powerful and necessary to escape Earth's gravity, they have their limitations. The fuel they carry is heavy and quickly exhausted, so once in orbit most spacecraft simply coast onward with minimal further course corrections; there's no way to produce constant acceleration/deceleration, the way we drive our cars on the highway. For that, an entirely new form of propulsion has been developed in the past few decades: ion drives! These futuristic engines provide a minuscule yet super-efficient thrust by using electrical currents to accelerate ions out the back end of the spacecraft, and though it sounds like science fiction, ion engines have been used since the late 1990s!

 Looks like something straight out of your favorite science fiction movie!

Here's my best attempt at a 30-second ion engine crash course: rather than combusting fuel to produce exhaust and propel a spacecraft forward, an ion engine bombards a chamber full of gas with electrons. The electron stream knocks other electrons off the neutrally charged gas, producing a flow of positive ions that can be accelerated outward with an electrode, as well as more electrons that can continue the reaction. But while Ignition taught me everything I know about conventional rocket fuel and the pros and cons of various choices like kerosene, liquid hydrogen, and hypergolic fuels (learn more here), I realized I had no idea why we use the propellants we do for ion engines! Most ion drives use xenon - why is that the case, and have we considered anything else?

 Looks complicated, but it's actually easy to picture with a simple animation - click this video!

In theory, we could use any gas that can be ionized, but noble gases like xenon are particularly appealing because they don't react with anything else (if you recall your AP Chemistry, it's because their outermost electron orbital is full!). But xenon isn't the only noble gas; if you check out the periodic table below, you'll see we've got a whole host of other options to pick from. What else makes xenon ideal?

 Back when I was in high school chemistry, oganesson (Og) hadn't even been named yet!

Remember that our goal is to ionize the propellant, which means we need to knock an electron off each atom. As you go down the periodic table, the elements have more and more electrons, so they get farther and farther away from the nucleus and require less energy to displace, making heavier noble gases more suitable for ion drives. Additionally, heavier ions carry more momentum, producing more thrust for the spacecraft. But then why stop at xenon; why not use radon (Rn) or oganesson (Og) in our spacecraft? Unfortunately radon is radioactive, even the most stable isotope only has a half life of a couple of days. And oganesson? Well, that's just a downright wacky element, completely manmade, ridiculously unstable, and entirely impractical. So xenon it is!
 Simplified electron diagrams of the first 5 noble gases. It takes about twice as much energy to ionize helium versus xenon (source)

#### A little more detail...

For those of you who want to go one step further, I thought it'd be cool to quantify the thrust advantage produced by xenon versus argon. This video by Scott Manley from his absolutely fantastic YouTube series Things Kerbal Space Program Doesn't Teach lays it out perfectly, so I'll summarize it here

The first ionization energy (energy needed to remove the first electron) of argon is 15.75 electron volts versus 12.13 eV for xenon, about a 25% energy saving per atom. But factor in the atomic mass of argon at 39.95 daltons versus 131.29 daltons for xenon (daltons are a handier unit of mass at the atomic scale than kilograms), and this tells us that the ionization energy per unit mass of xenon is about 1/4 that of argon

$\frac{12.13}{131.29} \div \frac{15.75}{39.95} = 23.4\%$

But this alone isn't enough, we need to know momentum generated to determine thrust advantage. Regardless of the propellant chosen, both ions will emerge from the engine with the same energy, as that depends on the design of the engine itself. For our purposes, we'll assume our engine has a 2,500 electron volt potential, which is equivalent to $3.20 \cdot 10^{-16}$ Joules. Here are the other numbers we'll need:

Mass of an argon atom: $\quad m_{argon} = 6.6 \cdot 10^{-26} kg$
Mass of a xenon atom: $\quad m_{xenon} = 2.2 \cdot 10^{-25} kg$
Kinetic energy formula: $\quad KE = \frac{1}{2}mv^2$

Using this, we can solve for velocity for both atoms

Argon exhaust velocity: $\quad v_{argon} = 95,664 \thinspace m/s$
Xenon exhaust velocity: $\quad v_{xenon} = 52,397 \thinspace m/s$

So actually, the argon ion comes out of the engine faster, which works in argon's favor. But when calculating momentum, the heavier mass of the xenon ion outweighs the higher exhaust velocity of argon, so in the end xenon produces about double the thrust per atom compared to argon! Pretty neat!

Momentum formula: $\quad p = mv$
Argon momentum: $\quad p_{argon} = 6.31 \cdot 10^{-21} \thinspace kg \cdot m/s$
Xenon momentum: $\quad p_{xenon} = 1.15 \cdot 10^{-20} \thinspace kg \cdot m/s$

82.5% higher thrust per atom for xenon versus argon

Here's the last point I'll make: xenon is the best performing ion propellant, but are there any drawbacks? In fact, there is one very important one, particularly to a finance guy like me: cost. Xenon is significantly more expensive than the next best option, krypton (whose performance is between xenon and argon, from our example), which explains why although NASA uses xenon on all its ion thrusters, SpaceX opted to go with krypton for its Starlink satellites. Unfortunately since I'm a SpaceX employee I can't comment further, but to learn more, there's a great public Reddit thread here

But hey, as I like to say, the best rocket fuel is cash!