Can a Ionic engine work in a vacum?

Ionic air cleaners move air without fans.
Can a engine based on ionic principle move in a vacum?

Sure. In fact, several unmanned spacecraft and satellites in the European and Russian space programs have used ion engines successfully. They don't have much oomph as far as thrust, but pound for pound they're the most efficient type of engine for use in space.
to add to the above.
Ion engines will gain momentum over time. It gets faster the further it travels. potentially as long as the fuel source holds up.

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