Dielectric strength of vacuum is 20kv/inch. Thus your megavolt needs 50 inches of separation at an absolute minimum. And you're operating this in space where you have ionizing radiation. Free electrons with a big voltage differential? You're describing a vacuum tube.
Breakdown voltage is pressure dependent, not a constant.
Your figure is for (eyeballing a graph) approximately 2e-2 torr and 150 torr, less between, rapidly increasing with harder vacuum. The extreme limit even in a perfect vacuum is ~1.32e18 volts per meter due to pair production.
For a sense of "perfect" vacuum: if I used Wolfram Alpha right just now, the mean free path of particles at the Kármán line is about 15 cm, becomes hundreds of meters at 200km.
> And you're operating this in space where you have ionizing radiation. Free electrons with a big voltage differential?
Mm.
Possibly. But see previous about mean free paths, not much actual stuff up there. From an (admittedly quick) perusal of the literature, the particle density of the Van Allen belts is order-of 1e4-1e5 per cubic meter, so the entire mass of the structure is only order-of a kilogram: https://www.wolframalpha.com/input?i=%284%2F3%29π%282%5E3-1%...
If this is an important constraint, this would actually be a good use for a some-mega-amps current, regardless of voltage drop between supply and return paths due to load. Or, same effect, coil the wires. And they'd already necessarily be coiled to do anything useful: Use the current itself to magnetically shield everything from the Van Allen belts.
Superconductors would only need a few square centimetres cross section to carry mega-amps, given their critical current limit at liquid nitrogen temperatures can be kilo-amps per mm^2.
But once you're talking about a 36,000 km long superconducting wire with a mega-amp current, you could also do a whole bunch of other fun stuff; lying them in concentric circular rings in the Sahara would give you a very silly, but effective, magnetic catapult. (This will upset a lot of people, and likely a lot of animals, so don't do that on Earth).
No, I wasn't eyeballing, but perhaps someone else was. I went looking for the dielectric strength of vacuum and I found a chart with values for a bunch of different things including vacuum.
And I don't understand the connection to the Van Allen belts--I'm talking about sunlight knocking electrons off your conductors.
> I went looking for the dielectric strength of vacuum and I found a chart with values for a bunch of different things including vacuum.
That's even more wrong than looking up the value of acceleration due to gravity and applying "9.8m/s/s" to the full length of a structure several times Earth's radius (which was also being done in these comments).
Think critically: when you're reducing pressure, at what point does it become "a vacuum"? Answer: there is no hard cut-off point.
> And I don't understand the connection to the Van Allen belts
You mentioned free electrons. The thing Van Allen belts are, is fast-moving charged particles captured by Earth's magnetic field.
> I'm talking about sunlight knocking electrons off your conductors.
Very easy to defend against photoelectric emission.
Just to re-iterate, if you're lifting something up with a magnetic field, it's non-contact. You can hide the conductors behind any thin non-magnetic barrier you want and it still works.
Say, Selenium, with a work function of 5.9 eV. Tiny percentage of the solar flux is above that.
Even just shading them from the sunlight would work. Like, a sun-shade held off to one side.
Also, you could just have the return line inside the tether: If the supply is on the outside, return on the inside, you can even use the structure of the tether itself as shielding — coaxial voltage differential, so the voltage difference between supply and return lines due to load creates negligible external electrical field.
Honestly, this feels like you've just decided it won't work and are deliberately choosing the worst possible design to fit that conclusion. Extra weird as "but we can't actually build carbon nanotubes longer than 55 cm yet" is a great deal more important than all the stuff I've listed that we can do.
