I think it's more complex than that, and doesn't need to be an ion trap to do it. Electrons go right on through wires, while the protons can't leave the tank in a sealed off system. They can hit the grid and become neutrals, of course, and then leave and be ionized again. If you model the power supply as a pump -- there's a source of infinite electrons, but only so much gas (nuclei).
I know from experience that I can put so much current in there that it has to be mostly electrons that carry it. Easy if you forget to have a ballast on there and dump a charged capacitor into it by accident (of course, after that you have metal ions too).
I think the mechanism is that when a very fast ion hits the grid, it ejects many electrons from the negatively charged conductor....so there can actually be more of them, but the only thing I really care about is that there are a lot and they waste energy like crazy.
You are right, a faraday cup only tells you so much, and this isn't proof exactly, just an indication. In this case, one that is pretty far from the "action" - about a foot away and off any of the axes.
Another indication is that scope trace from the thread here on non isotropic neutron production. You can see the electrons being swept out of the space by the second grid, and how long that takes when it tries to go positive on that trace.
There are ions in valves to be sure, just not many. Nothing is perfect. Otherwise you'd not need grid resistors...but you do, it's a measurable current in there in most valves (we call them tubes here, but I know the other nomenclature). But then I started out in electronics when tubes were all there was, and got pretty familiar with them, including electrometer tubes especially designed to limit that problem, and it's enough to be a problem.
I dunno if you're the first to show possibility of net gain that way, but I never argued that myself -- it's what made me think you were onto something, actually. I'd not seen anything else that made my brain happy before myself on that topic. But hey, lets take this to some thread on theories, we're polluting Jon's Hello thread here -- and we know we can both talk this endlessly.
Why not start it with an upload of that paper you turned me onto about "why fusors can't work"? It's good and still very relevant, and we shouldn't keep that to ourselves alone here. I've forgotten who the author was or I'd do it. Brian something?