No, I think normally the solar wind is not considered to be a current, because the the number of positive and negative ions are thought to be equal. So there's no net charge.

I think the question is whether that is really true. How would we know whether the number of protons and electrons in the solar wind is equivalent? It should be testable, and I presume that the reason people conclude it isn't charged it because this has been tested. But it might just be an assumption.

The thing, though, is that one would presume that if only electrons are given out, for example, then eventually the charge would get positive and the electrons would be pulled back in. Unless there is some process that keeps producing a charge, i.e. electrons are coming in from another dimension or something like that. But they you get into unknown physics.

But if you can show that the solar wind is charged, I'd like to hear about it.

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