Here's a kind of brainstorming session, which will combine a few concepts into a plausible way to harvest gases at the edge of space. This is called Loxleo ( liquid oxygen at low earth orbit --- don't you love these acronyms?).
I've done this before, and as before this will include a speculation alert.
The elements include the use of Parkins concept in his doctoral thesis in order to get a high ISP propulsion with a lot of delta-v, saving a lot of fuel. The energy will be supplied by the use of solar panels posted at GEO. There would have to be an array of these panels, which would include all of the necessary hardware to beam the microwave energy down to an orbiting aeroshell that is on the edge of space, in very low orbit. The solar panels at the edge of space comes from a concept in the book Mining The Sky. The author, John S. Lewis suggested that this was a way to get the space program on a paying basis. You could manufacture the solar panels on the moon, and send them back to GEO in order to make some money for the lunar base.
As could be seen on those spectacular videos of Starship's re-entries, there's plenty of atmosphere that could be gathered up. It is also creating a lot of friction on the Starship, which causes it to lose velocity. If you add a gas harvester, it will create even more drag. In order to keep the Starship up in space, you need to fire up some sort of engine that will keep up the delta-v at orbital levels. So the microwave energy is beamed down from GEO, and it heats up an aeroshell. From there, cold gases are injected to cool down the aeroshell, as the Parkins concept showed. The gases would be ejected out a nozzle, thus creating thrust. The ISP that might be achievable could be comparable to a nuclear thermal rocket. More than twice that of the best chemical engines.
The Loxleo concept itself was an idea that orginated back in the sixties. ( or possibly sooner) That concept included nuclear thermal engines to keep the vehicle up to orbital speed. The concept's weakness was in how to get energy to the thruster. A nuclear reactor in orbit tended to make people nervous.
Perhaps the harvested gases themselves could supply some, or perhaps all of the reaction mass that will provide the thrust. The trick would be to harvest it faster than it would be used up! It just won't do to end up with less mass than what you started with. The atmosphere consists of oxygen, nitrogen, and argon. The argon is only about 1% of the atmosphere, so you may have to mix some nitrogen in there with it. The most valuable resource could well be the oxygen. Hence the name, "loxleo". You'd want to keep all of that you could gather. Argon, by the way, is a noble gas--which means it doesn't react with other elements very easily or at all.
The advantage of loxleo is to reduce the number of launches from the deep gravity well of Earth. Oxygen would provide as much as 80% of the reaction mass to run the Raptor engines. In order to refill the Starship, it will be necessary to launch multiple times from the ground. The advantage should be obvious if you could make loxleo work. It is in situ resourcing, which is better than bringing everything you need from home.
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