Thread by @lougrims

As promised here is a thread on SpaceX announcement about their new Hall thruster for Starlink V2 mini. Trying to go over the figures they published and why it's kind of a unique thruster. Please excuse in advance typos, I had a long day of meetings.

https://twitter.com/SpaceX/status/1629898794874687489?s=20

SpaceX has been using Hall thrusters since the beginning of the Starlink project. Hall thrusters are a type of electric/plasma/ion propulsion that was developed in the USSR in the 70s. I go a little bit in more details on how they work in the thread below

https://twitter.com/lougrims/status/1516013489722216450

After the fall of the Soviet block this was one of the key space technology that was happily copied by the western world as they tested the Soviet thrusters and were happy to welcome emigrating scientists and engineers. The point is, it's not a new technology.

Hall Thruster are neat because they fall into a sweet spot for performances. They have good efficiency, good thrust to power ratio and a good middle ground specific impulse. Let's explain what each of those mean.

First the efficiency: In EP you have 3 important values.
- The thrust (T) self explanatory.
- The input power (P) or how much electricity you feed the thruster
- The specific impulse (Isp) which is how efficient you use your propellant (and is proportional to the exhaust speed)

The useful power coming out of the thruster is the kinetic energy of the beam: 1/2*m_dot*v^2. m_dot being the mass flow and v the velocity along the thrust vector. Since T=m_dot*v and Isp=v/g your beam power is T*Isp/g
So the efficiency of the system is:

n= 1/2*T*Isp/(g*P)

You can verify it with Starlink's numbers and we indeed get 49.7%. This is always a good thing to check with EP systems as you find people who advertise thrusters with more than 100% efficiency 🙃. It also confirms that the input power is indeed 4.2kW.

https://twitter.com/SpaceX/status/1629948869239873538

This number is important because it means 50% of the energy (~2kW) is wasted. A small part is spend ionizing the propellant into plasma, some in divergence , a larger part is lost to the walls of the thruster (heat!) and the rest in the electronics (more heat!).

You can expect classic xenon HT in that power range to be around 60% efficient. But 50% with argon is a really really good number. Just substituting the xenon for argon in a normal thruster can drop the efficiency by more than half! They clearly worked a lot to get there.

Details will have to be left to another time but thrust to power is proportional to the square root of the molar mass of the propellant. With xenon at 131 AMU and argon at 40 AMU you expect it to be around 55% of a xenon thruster for their argon propellant in similar conditions.

For xenon you would typically expect around 60 to 65 mN/kW for nominal ~300V, 1500s Isp operation point. Starlink's V2 thruster gets 40mN/kW (>60% of the xenon value), which is higher than what I would have expected. That's an indication that they are pulling some tricks.

Lastly Isp. Them using a lighter propellant should increase it the same ratio as it decreases the thrust. Typical Hall thruster operate around 1500 to 1800s Isp so an argon one should be landing in the 2700 to 3200s range. But Starlink V2 "only" gets 2500s?

That's more indication that they are doing something strange. Remember the tweet below from further up thread? Well the final equation says that for a fixed efficiency (which is usually what you get) you can trade thrust to power ratio with Isp.

https://twitter.com/lougrims/status/1630302098964267008?s=20

To do that you decrease the acceleration voltage and increase the discharge current. This let's you get a slower exhaust that consumes less power (at the cost of more propellant). But you have to be careful because too low and the discharge can become unstable.

However it can be worth pursuing because the spacecraft will accelerate faster. Remember that in EP maneuvers takes days or weeks. A typical performance figure is that you can do 0 to 100 km/h (60 mph) in about 3 days! And each day spent accelerating is a day of lost revenue.

So why did SpaceX switch from the heavy established xenon giving you great thrust to power to lighter krypton and now even lighter argon? Most of it is cost and availability. Xenon is a really rare gas with only a few tens of tons produced per year. As a result it's very costly.

The supply could not have easily kept up with a megaconstellation in the scale of Starlink and the cost would be been astronomical. Krypton is much more available and very roughly 10x cheaper. So it made sense to take the performance hit.

However a lot of both xenon and krypton production was done in Ukraine (about 40% IIRC). Since last year violent invasion by Russia of Ukrainian territories, especially its eastern industrial areas the prices have skyrocketed. Rumors are that xenon shot up to $30k/kg at one point

And while I don't have the price krypton was doing something similar. Argon however is extracted from the air in most air liquefaction plant (like the ones used to make liquide O2 for rockets) and costs next to nothing as a common industrial gas.

So SpaceX basically solved their supply chain headache at the cost of spending a bit more time (~40% more) doing orbit raising at the beginning of the mission. They also probably save 30 to 50k$ per spacecraft in propellant cost.

Another drawback of argon is while the Isp is bigger the density is much lower so your tankage fraction (mass of propellant over that of the tank) is really bad and you tanks are bigger. You need to store is at around 150 bars so those are not easy tanks either.

Anyway that's pretty much all I have for tonight. I also wrote a thread some time ago about project Kuiper thruster (see below). But it's much less detailed as there is not a lot of public info.

/fin

https://twitter.com/lougrims/status/1454508950544687104?s=20

Actually, I still need to do a thread explaining why too much Isp is bad and why 1500 to 2000s has been the gold standard commercially.