Why isn't current carried through a vacuum? The empty vacuum of space shouldn't offer any resistance to a travelling electron, and so a large collection of electrons should similarly travel through a vacuum without resistance.
As a result, the bottom line is that an empty vacuum should be an excellent conductor of electricity, since it offers no resistance. 
And in fact, this is exactly what a Free-electron laser does:
Here is a Wikipedia article on the subject.
Now, I understand this is expensive gear, but presumably someone could come up with a cheaper version that could offer charges pumped through a difference in potential.
There's another post here, the answers to which, frankly, don't seem to be very useful and claim that empty space isn't a good conductor - that's just not correct, since a free electron laser is a real thing that exists, and does exactly what they said it couldn't, which is pump high voltage.
I found a similar SE post here.
Does anyone know if there's a cheap consumer version that pumps charge through a vacuum?
 A: As you noted, particle accelerators are examples of electric currents flowing though a vacuum. In order to answer why a vacuum is considered an insulator, you have to consider where the charged particles come from. Consider the space between the plates of a capacitor that is connected to a battery. Even though there is a voltage difference between the plates, the electrons cannot cross the gap because they are too tightly bonded to the atoms in the plates. It takes a very high voltage for the electrons to be torn away from the atoms in the plates. Once this happens (or the electrons are helped by incoming photons), then the electrons can be accelerated through the vacuum by the electric field between the plates.
A vacuum is an insulator because of the work you have to do to put mobile electric charges into it. A conductor like a copper wire already has mobile electrons, so it takes very little work to get them moving in a current.
A: It is perfectly possible for current to flow through vacuum: it is just not a conduction current but instead a convection current.  Quoting this page:

... any stream of charged objects (ions, for example) may constitute an electric current.

For instance ions travelling in an accelerator (usually under vacuum or near vacuum) create a current which experimentalists measure in Amps (or fractions thereof).
