Antimatter Generation With The Help Of A Plasma Globe

I know this sounds absurd, but after doing a little research I found that it may be possible (not entirely, but that is why I am asking about this here). I have been reading up on antimatter and quantum mechanics and I stumbled across this article on the subject of "creating antimatter with lightning". All lightning is is a stream of electrons travelling through a channel of ionised air. This is true of any electrical "arc". This brings me to my question. There is a trick which you can do with plasma globes (you can probably pick one up at a toy store quite easily), where you place a piece of aluminium foil on the top of the globe which attracts a stream of electrons via parasitic capacitance the the environment. However, I have put together a specialised spark-gap chamber which consists of two metal rods with sharp points ~0.2mm apart so that an arc jumps the gap. I attached a wire from the aluminium foil on the plasma globe to one of the electrodes, and I connected the other to ground. When I switched on the plasma globe, as expected, a small arc jumped the gap.

This experiment, while much less powerful (about 900,000 times less powerful) than lightning, does simulate it to some degree (with a constant flow of electrons with AC current instead of a small pulse of electrons with pulse current).

So if lightning can emit antiprotons and positrons, can my setup do the same?