Keeha:
Take a look at this page:
(Chapter VI. On Possible Electric Phenomena in Solar Systems and Nebulae; from Norwegian Aurora Polaris Expedition)
http://www.plasma-universe.com/index.ph ... nd_Nebulaehttp://www.archive.org/details/norwegia ... 01chririch (full text)
Specifically the part on page 662 relating to the banding patterns and what causes them to contract equatorward, or expand poleward.
Kristian Birkeland wrote:We will now pass on to experiments that in my opinion have brought about the most important discoveries in the long chain of experimental analogies to terrestrial and cosmic phenomena that I have produced. In the experiments represented in figs. 248 a-e, there are some small white patches on the globe, which are due to a kind of discharge that, under ordinary circumstances, is disruptive, and which radiates from points on the cathode. If the globe has a smooth surface and is not magnetized, the disruptive discharges come rapidly one after another, and are distributed more or less uniformly all over the globe (see a). On the other hand, if the globe is magnetized, even very slightly, the patches from which the disruptive discharges issue, arrange themselves then in two zones parallel with the magnetic equator of the globe; and the more powerfully the globe is magnetized, the nearer do they come to the equator (see b, c, d). With a constant magnetization, the zones of patches will be found near the equator if the discharge-tension is low, but far from the equator if the tension is high. Fig. 248e shows the phenomenon seen from below.
From this we glean:
1) If the globe is non-magnetized, the distribution of arc spots is more or less random about the globe.
2) If the globe is magnetized, then the spots arrange themselves into bands parallel to the equator.
--a) With constant current:
----i) the more powerful the magnetic field, the closer the spot bands come to the equator.
----ii) the weaker the magnetic field the further the spot bands will migrate away from the equator toward the poles.
--b) With constant magnetization:
----i) the more powerful the discharge, the further from the equator and the closer to the poles the spot bands will be.
----ii) the less powerful the discharge, the closer to the equator the spot bands will be.
So, can this be applied to the sun? One would think so, if the process works the same in space as it does in the lab.
Let me try to answer the question, then, according to Birkeland, and possibly with reference to Alfvén's solar circuit diagram as well...
So, here's the solar cycle, more-or-less complete:

We can see the oscillation of any 11-year "hemicycle" (for lack of a better term off the top of my head). Hemicycle is basically a half-circle, which is apt. The typical 11-year cycle is only 1/2 of a "full solar cycle" (I prefer to the term "grand cycle," personally, so I'll probably use that for here forward).
I say that the 11-year cycle is only half the cycle because, although the solar flare and sunspot cycle goes from minimum to maximum to minimum, the polarity of sunspots also flips between 11-year cycles. So to technically get back to "scratch," we have to get back to the same polarity configuration on sunspots too. Hence I refer to the 22-year cycle as the "grand cycle" or "full solar cycle."
So, that said, what happens when? I guess we should define our reference points.
Four points that seem to be obvious, more-or-less would be the minima and maxima of the solar activity over one grand cycle. IE, minimum, maximum, minimum, maximum [and back to the starting minimum for the next grand cycle].
However, different aspects of the sun do different things at those times and in between. At solar minima, the sunspot polarities flip. At solar maximum, the sun's overall field flips. See
another thread I'd made comments on.
Birkeland's stuff may come in handy in figuring out what's going on when. Alfven's stuff may also be equally handy in diagramming the sun, electrically.
(Alfven's solar circuit diagram)

My understanding of Alfven's diagram is that the secondary currents seen in the upper right and lower right quadrants of the schematic are induced when the primary input current is either increasing or decreasing, but disappear when the current is holding steady. Likewise, the secondary current direction is dependent on whether current is rising or falling. IE, it will reverse when the current changes behavior from a rising mode to a falling mode or vice versa. That is, I believe, how sunspot polarity flips are accounted for in understanding the Alfvén schematic.
So, let's go back to Birkeland for a bit... If the sun had no magnetic field, and we're working under Birkeland's model, we'd expect the sun to have randomly distributed spots all over its face. But, that's not the case. The various solar activity is arranged into neat little bands of activity. That accords with our understanding that the sun does in fact have a magnetic field. In fact, it extends throughout the solar system as the
IMF (interplanetary magnetic field). So, that seems to make sense.
We see that the solar cycle oscillates in latitude over the course of the solar cycle. According to Birkeland, that would mean that either the magnetization is constant and the current is fluctuating, or the current is constant and the magnetic field is fluctuating. I think that there might be a third options as well. IE, I think there's a relationship between magnetic field strength, electric current strength and the behavior of the bands. IE, if the current exceeds some ratio of current strength to magnetic field strength, you get one kind of behavior (or migration of the banding spots), if it falls below the ratio, you get the opposite behavior (migration the other way). Since the sun's probably not a permanent magnet, it may be that both aspect vary over the course of the cycle and it's the relationship between them that determines the behavior?
But, let's take a look at the cycle again via Alfvén... So, okay, we know that sunspots flip polarity at solar minimum and the sun's magnetic field flips polarity at solar maximum. According to Alfvén, if I've understood correctly, the sunspot minimum and flip flip is predicated on the behavior of the secondary currents in Alfvén's diagram. Those are predicated on the behavior of the primary currents. When the primary currents are rising, the secondary currents will flow a specific way and the sunspots will have a specific polarity. When the primary currents are falling, the secondary currents go into reverse and the sunspot polarity flips with them. When the primary currents reach a local maximum or minimum, the secondary currents falter and the sunspots go away. This could be very roughly modeled via sine or cosine curves. Figuring out the secondary current direction would be something like taking the tangent of the primary current's graph at any point and figuring out whether the slope is rising, falling or 0. The 0-slope bits are where the secondary currents collapse, as do the sunspots. I'm trying to remember, I think that's not unlike the 1st derivative of the primary current graph? IE, graphing the change in the first graph...
So, the sunspot minimum is actually at the local maximum or minimum of the graph of the input current (where the tangent would be zero, thus the secondary current more-or-less zero as well). So, sunspot minimums correspond to either a peak in current flow or a trough in current flow. Essentially constant current flow at that point, before the graph gets back to "sloping" one way or the other.
Solar maximum and/or sunspot maximum would be the point at which the
secondary currents are strongest and the primary currents are undergoing the most change (gaining or losing strength the most rapidly). If secondary currents are strongest here, might we expect sunspot magnetic fields to be at their most prominent as well?
Regards,
~Michael Gmirkin