I made a satellite ion thruster [video]
youtube.com
youtube.com
Momentum is mass times velocity. Energy is m v^2 / 2. Both with adjustments in the relativistic realm, which this barely gets to.
The maximum thrust per atom lost is going to be at insanely high velocity. The maximum thrust per unit energy is going to be at low velocity. Which makes ion thrusters great for slow changes of velocity when powered by unlimited solar power. But terrible for launch with a finite energy budget.
Useless trivia. A traditional rocket becomes more efficient if you mix some mercury into the fuel. The loss of energy is made up for by the extra mass. The collateral damage from the mercury is an environmental disaster though.
For a lot more, including the source of that trivia, I highly recommend reading https://library.sciencemadness.org/library/books/ignition.pd....
It gets worse. The reasoning process actually started not with mercury, but with dimethyl mercury. My ex knew https://en.wikipedia.org/wiki/Karen_Wetterhahn while she was dying. And so that story brought particular horror for me, and made it particularly memorable.
I calculated the performance of Cavea A with various proportions of mercury —up to six times the mass of the primary propellant. (It was easy to fit mercury into the NQD calculation method.) As expected, the specific impulse dropped outrageously as mercury was added to the system, but the density impulse (specific impulse X propellant density) rose spectacularly, to peak at 50 percent above that of the neat mono-propellant with a mercury/propellant ratio of about 4.8.
Specific impulse is overwhelmingly the metric that matters for rocket performance in all but a small number of applications, so I feel justified in saying that your original claim that:
A traditional rocket becomes more efficient if you mix some mercury into the fuel. The loss of energy is made up for by the extra mass.
is simply not correct!
1. The problems you end up having won't be the ones you expect to have.
2. It's easy to shy away from burning time on better diagnostics, but the amount of time you'll waste by not doing so is often greater.
3. Sometimes you need to step out of the room and talk it over with a colleague who's not working on the same project.
The fact that this same problem plagued every iteration and it wasn't until it was fixed that the project turned from "banging head against wall" to "how cool is that" just adds so much to the video.
I love this and I am so pleased he got it working.
Hope I can one day explore my passion and curiosity on these issues like I see so many doing.