Thus far people seem to have been making cathodes like in vacuum tubes, using heat or high voltage to drive electrons out of emitters like you see in ion-generator room-air cleaners.
That might be a dead end, from a complexity, cost, and power waste standpoint. On the other hand, maybe maintaining a second grid at high voltage relative to an emitter array could be simple enough, with just one charge pump for the whole system that need not burn much power.
But a purely passive, air-friction driven system ought to be more foolproof.
Probably either would work, so it just comes down to cost and extraction efficiency. A single active grid that can capture a high fraction of the available power (up to theoretical maximum around 30%) might end up better that a whole bunch of stacked, cheap, passive grids.
The materials science needed to make the somewhat-conductive, hydrophobic, passive-grid streamers that readily give up electrons to colliding air molecules seems within reach, but that is not a thing I know enough about.