omega effect: turning poloidal magnetic field into toroidal field

Aziza

Could someone please explain exactly how the omega effect works? It is supposed to explain how a poloidal magnetic field (of the sun for example, or a black hole accretion disk) becomes toroidal. This is supposed to be due to differential rotation and the inertia of mass. But I just don't see how this can cause field lines to twist into helix...if anyone knows a good reference regarding this subject I would appreciate it, I can't find anything detailed!

justsomeguy

Do you have an example of where you heard of this? The terms don't even make sense to me in this context, though I'm no expert on the subject.

Aziza

I have attached a picture as it applies to AGN. Also link to solar dynamo:
http://solarscience.msfc.nasa.gov/dynamo.shtml

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ImaLooser

I've never heard this name. I do know that in (most? all?) heavenly bodies both purely poloidal and purely toroidal orbits are unstable. Either will decay into a mixed field, and eventually the energy will be divided evenly between the two. It was discovered in 1970 or so. The argument is simple but I never tried to understand it. There is a professor in Bonn named Jonathan Braithwaite who has some presentations about this, with all the detail you might care for.

justsomeguy

I think he's asking the "how" or "why" the magnetic field becomes "wrapped" around the sun. The terminology seemed a bit strange to me, for sure, but if I can reword it, I think this is what he was getting at:

Imagine the sun is a stationary bar magnet. The magnetic field lines are arranged the normal way. As you start to spin the bar magnet, at first the lines rotate with it, but as the pace picks up, the lines start to bend and 'wrap around' the magnet (the sun) until, eventually, any particular field line leaves the pole, wraps around the northern hemisphere a bunch of times in one direction, reverses at the equator, and then unwraps the same number of times before diving into the south pole.

Why/how this happens is a mystery to me as well. I've read the explanation, but I lack the background to really grasp what's happening.

Of course I could be completely wrong in describing the OPs question.

ImaLooser

Aha. Well, when you have a magnetic field in a highly conductive environment then the flux tends to get "frozen" to the conductive medium. That is, they move together as one and wherever one goes the other goes too. So if you have a differentially rotating sun, then the flux tends to get twisted like a barber pole.

Aziza

ohh so it is sufficient to just prove that flux is frozen into plasma in order to see why field lines can get twisted, right?

ImaLooser

I guess. My understanding is superficial.