The magnetic field would not even exist in the interplanetary plasma were it not for the "current flow" that sustains it!
And I get the feeling that you keep coming back to "current flow" because you want to justify putting large electrostatic fields in space. Let's just head that off at the pass, shall we?
We've agreed (repeatedly) that magnetic fields are generated by currents. Not very surprising; it's all B = del cross J as usual. Tell me J and I'll tell you B, and vice versa, modulo a constant of integration. Where are those Js coming from? You want them to come from J = sigma E, Ohm's law, or F = qE. And you want those Es to come from charge separation. Is that a fair statement?
You've got Maxwell's equations in front of you: grad E = rho (charge separation) and curl E = -dB/dt. Standard astrophysics isn't "there's no E in space", standard astrophysics is "there's usually no grad E in space". Space charge separations are small, rare, and generally transient. You get currents in plasma because of changing, usually turbulent, magnetic fields; those currents generate their own changing fields, which generate more currents, and this generates complex plasma dynamics and waves in the absence of charge separation. That's standard astrophysical plasmas: Grad E ~= 0. Curl E != 0. Curl B != 0. Not "J=0", not "there's no plasma", not "plasma is unimportant", not "the current is bunched into discrete ropes or lines". Is that clear?
If you've got a coherent objection to mainstream astrophysics at all, that objection is "I think that grad E != 0 configurations are an important/dominant source of currents" Is that a fair statement? "You ignore currents" is a false premise. "Maxwell's Equations don't apply" is ... well, let me just say wrong.
Since dB/dt implies some sort of B to begin with, we need a "primary" source of currents. You want to put big charge separations on or near the Sun to push a "primary" Ohm's Law (nor Coulomb's Law) current around. This would be sort of a reasonable wacky hypothesis ...
if you, MM, had shown us that you were *generally quite good* with Maxwell's Equations, and that *your best effort* at getting non-Ohms-law currents had failed and that this idea worked better. Instead, you've shown us that someone who doesn't understand Freshman E&M also doesn't understand where solar currents come from. Anyway, there's a perfectly good mainstream explanation for where solar surface fields come from. Why don't you read up on it, with your newfound understanding of E&M, and explain it to us? Give us the Devil's Advocate version before you launch into what you think are its flaws.
As an other exercise---there's one very common piece of lab equipment (ubiquitous in teaching labs, found in specialized research labs) in which an electric current is created, but *not* driven by an electric field (though such a field happens to be present) or a changing magnetic field. Can you name it? It's tangentially relevant to the mainstream heliomagnetic and geomagnetic models.