Neumann thrusters work very differently from existing ion thrusters, though. At a high enough level, the concept is the same - ionize some stuff, accelerate it using an electric field - but the details matter a ton. Or, indeed, several tons. The existing ion thrusters mostly use gases - xenon is popular - as reaction mass. That means your reaction mass is already conveniently in tiny individual particles (single atoms, since it's a noble gas) suitable for extreme acceleration, but it also means you need to have a bunch of tankage, valves, and so on... and once the xenon runs out, you're done. Xenon thrusters - especially the most efficient ones, which use grids that the particles fly through - have a limited lifetime, too; they wear out pretty fast if you use them with a lot of power.
Neumann thrusters use solid fuels, usually metals (though they also tested with pure carbon, and it worked reasonably well). There's no tankage, no moving parts such as valves (although the fuel rods may occasionally need replacement), and no risk of your fuel leaking off into space. What's more, in theory you can simply use metal that is *already in orbit* (such as discarded rocket upper stages, end-of-life satellites, or even outright junk if you can catch it safely) and that means you can easily "refuel" while in orbit. The performance you get varies depending on the reaction mass, with some metals producing absurdly high specific impulses (11000 seconds?!? That's far better than existing ion thrusters) and some producing more moderate efficiency but permitting quite high thrust (well, relative to other ion thrusters; it's still measured in m/s of delta-V per month) if you have the power (without eroding any part of the thruster except the fuel rod, unlike a conventional ion thruster running at such power levels).
Some of it, like the in-space "fueling", is more than a little difficult, but the basic idea seems sound. It's also a pretty new technology, and they've already come up with some improvements (such as a magnetized "nozzle" that gives better thrust, presumably meaning it improves electrical-power-to-thrust efficiency) so I'm sure the technology will mature still further as research on it continues.