 Quote by Nukedropout
How fast does an air molecules velocity through an electrostatic field have to be to induce ionization? Stated simply, how much friction is needed to cause ionization. Is it possible to factor in velocity, temperature(at room temperature), and strength of the static field, using a math equation to figure out how fast air's speed must be to ionize?
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If by this you are referring to the ionization of air in front of a re-entry vehicle entering the atmosphere, then it isn't friction that causes this, it is the temperatures associated with compression across the shock wave. In those cases, the temperatures can be similar to the surface of the sun, so naturally air will ionize and become a plasma at that temperature.
If instead you were talking about the kind of stuff shown in the video, that has nothing to do with speed. That was, as someone mentioned earlier, from subjecting the air to a strong electric field to ionize and accelerate the air molecules.
 Quote by Nukedropout
Is it possible to cause ionization of air and induce acceleration? Is that what air ionizers (electric air filters) do?
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You absolutely can, and there is a pretty large body of work doing exactly this. In fact, in the video you posted, there were a couple shots of the separated flow over an airfoil being reattached. Those make use of this principle by injecting momentum into the boundary layer just before it separates to help keep it attached. They have also looked into similar idea for creating plasma-based flaps and slats for wings and rudders for the vertical stabilizer on a plane, though these kinds of technologies are nowhere near ready to be fielded.