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Comment by archermarks | Hacker News Reader

Oh I'm well aware, I work on this stuff, but I'm still curious about their system, and any on-orbit data they might have. We're working on krypton Hall thrusters right now in our lab and trying to characterize the differences in operation. There's some non-obvious scaling factors we're working to understand in order to try and better optimize thrusters for krypton operation. We have a recent paper (free pdf) about this at pepl.engin.umich.edu/pdf/2021_JoAP_Su.pdf.

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Assuming a spherical cow, would there be any advantage to building ion thrusters to accelerate the particles to speeds where relativistic effects become meaningful?

No, because thrust per unit power drops as exhaust velocity increases. You’ll be increasing your power supply and thruster mass far more than any propellant you save. It’s also energy inefficient to use too high of an exhaust velocity.

The mass-optimal exhaust velocity is approximately equal to the square root of (twice the thrusting time times overall power-and-propulsion system specific power times electrical efficiency).

Assuming no dry mass (spherical cow!), energy optimal Exhaust velocity is equal to the total elapsed mission velocity at any point. If you can’t adjust exhaust velocity, it’s proportional to approximately to 60-65% of the total mission delta-v (off the top of my head). More discussion of where this energy-optimal exhaust velocity comes from: https://www.youtube.com/watch?v=ogKKjpQvfuM

Indeed, one of the memorable stories from https://www.amazon.com/Ignition-Informal-History-Liquid-Prop... was when the author wrote a joke paper analyzing the optimal amount of mercury (!) to mix into rocket fuel for maximal thrust. It takes away from the power, but since mercury is heavy it slows the exhaust, and therefore can increase thrust.

To the author's surprise, the general evaluating the crazy ideas that the lab came up with failed to recognize that it was meant as a joke, and ordered that it actually be tested. So some unfortunate test site had to actually set up the test, and verify the theory.

Luckily the military came to their senses about then and never actually built real rockets using the principle.

(For those who are confused, mercury may be heavy, but is a nasty contaminant. Organic compounds including mercury have a disturbing tendency to be neural toxins. See https://en.wikipedia.org/wiki/Karen_Wetterhahn for a famous example of how little is needed to be lethal. You really don't want to be spewing it over the countryside in a flaming ball.)

Stories like this make Charlie Stross' "A Tall Tale" seem that much more believable: https://www.tor.com/2012/07/20/a-tall-tail/

Thank you so much for those links, I’ve casually been following space travel for some time and this is the first time I’ve heard about optimal exhaust velocity. I’m about 20 minutes into that presentation and it’s great!

Not really.

As the ion energy approaches relativistic, the engine also starts approaching the behaviour of a photon thruster. If your ion drive is solar powered, the system as a whole then starts to behave like a solar sail made from grey paper rather than shiny mirrors.

It would be hugely energy inefficient. Generally, you want the exhaust velocity of your rockets to be close to the total mission delta-V (or, better, the total delta-V up to that point in the mission.)

> the total delta-V up to that point in the mission.

Doesn't this give ION drives a big advantage... they can have variable exhaust velocity...

The space charge limit on the ion current increases with voltage, as does the momentum per particle. The result is that thrust/area of a given ion engine will scale as the square of the voltage. So, one doesn't want to reduce the voltage too much.

Electromagnetic rockets, like Hall thrusters, do not have the same space charge limit, and are typically operated at lower exhaust velocity.

> would there be any advantage to building ion thrusters to accelerate the particles to speeds where relativistic effects become meaningful?

Probably not; why wouldn't you just shine a light in one direction? It's effectively the same thing.

Don't photons have zero mass?

Photons have mass equal to their energy equivalent. And relativistic ions have most of their mass in the same form. So propulsion-wise, the two are almost equal...except that a light emitting diode is much simpler than a particle accelerator. Both would have very poor thrust, of course, and with existing energy sources, the waste mass from the energy production would be disproportional so neither would really be used for anything practical.

Photons have zero rest mass. That sounds like hair-splitting but it is not.

Interesting! Thanks for the paper link.

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