Whatever the relevant science/technobabble is, the effects of the Baryon sweep are stated in the episode. My projection for the numbers of arrays comes out of the size of the Federation rather than the capacity of the arrays. The E-D's sweep took a couple of hours, tops; with time to clear the ship out and re-occupy it afterwards, I'd guess you could sweep at least one ship per day - actually many more if you have a queue of ships offloading and reloading outside the array itself, but let's take one per day as a conservative figure. Given that the E-D got its sweep in the sixth season, then I would assume that ships need a sweep on average every six years. One a day for six years lets an array handle some 2,190 ships - over half of Starfleet, according to the 4,000+ numbers I settled on! You'd never need more than two of the things.
However, given that it can take many years to cross the Federation at
normal (rather than maximum) warp speeds, you would need several arrays
if you were to avoid having to spend years travelling to and from your
arrays. I would assume that there is at least a couple of dozen smaller
arrays out there for the likes of the Saber and Oberth classes, and possibly
hundreds for stuff like warp-capable shuttles and Runabouts.
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