> how can you have a current in a single wire without a loop?
There are ions always wandering around in the ionosphere - the ionosphere is partly-ionized plasma. Low-density, but there. When you have a generator that produces an electric potential bias across the top/bottom of the craft, you end up with electrons being emitted into space from and positive ions being attracted to the side biased negative, and electrons in the ionosphere being attracted to the side biased positive. Effectively: the plasma completes the circuit. There are bunches of additional optimizations (electron guns, etc) but that's the basic idea.
There's a surprising amount of atmosphere up where we would consider it to be at orbital heights. People think of the atmosphere as suddenly ending, but it doesn't.
For example, one of the major considerations for how the ISS orients its solar panels is minimizing drag.
And that's what an electrical generator does. It produces an electric potential difference between its two terminals.
> how can you have a current in a single wire without a loop?
There are ions always wandering around in the ionosphere - the ionosphere is partly-ionized plasma. Low-density, but there. When you have a generator that produces an electric potential bias across the top/bottom of the craft, you end up with electrons being emitted into space from and positive ions being attracted to the side biased negative, and electrons in the ionosphere being attracted to the side biased positive. Effectively: the plasma completes the circuit. There are bunches of additional optimizations (electron guns, etc) but that's the basic idea.