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At the moment the ions reach the central area, we reverse the charges on the plates. The ions decellerate, reverse course, and again accelerate toward the center. Again reaching the center, we reverse the charges on the plates. And so on.
I have in mind the fact that "ordinary" power-plant "step-up" transformers are able to reverse 750KiloVolts 60 times a second, for high-tension power-transmission lines. I think that is plenty more voltage than needed here (the larger the cube the lower the voltage needed), and probably a higher operation frequency, too, which means this ought to be build-able. As to how well it might work...I imagine the ions might eventually curve toward the charged corners. There might be a solution to that (extra plates turned on at need?). Feel free to reply!