Modelling The Sun’s Magnetic Field

[JvanDyne]

I’m currently constructing a solar wind outflow model, incrementally relaxing a series of initial assumptions in a stage-by-stage process. I’ve now arrived at the stage where I want to consider magnetism – and the MHD equations. My plan is, in what seems the simplest starting point, to approximate the sun’s magnetic field as a north-south magnetic dipole. My question is, therefore, given I am (as a maths student) an EM newbie, are there any recommend books, etc, w/r/t/ my particular interests, and secondly, more mathematically, how would I, assuming a 2D solar model and obvious spherical polars, calculate the magnetic field at any point?

Thanks. And thanks again if you understood that.

EDIT: This - http://seismo.berkeley.edu/~rallen/eps122/lectures/L05.pdf (pages 3,4,5,6) - seems, for the earth, to exactly calculate what I'm talkling about, but I don't quite follow the absent steps(?).

 

[Ken G]

Any book on winds that includes the Weber-Davis model would be the starting point. Just go to a library and scan the books on stars for one that has those words in its appendix or table of contents, or google for class lecture notes on that. W-D is 1D, for a journal article on 2D, try http://adsabs.harvard.edu/full/1985A&A...152..121S. The first key thing you will find is that your outflow model must change the situation significantly from a 2D dipole, but that does not necessarily mean more complexity. What's hard is to merge the dipole lower down where the field is strong with the outflow-type field farther out (and then way far out, the solar rotation gives you a "Parker spiral."). That first transition is of significant importance to how the wind carries off angular momentum, and is a subject of current research! Weber-Davis will show you that the transition happens gradually, but can be treated for some purposes as if it occurred rapidly at the Alfven radius. So perhaps your study should begin with the concept of an "Alfven radius"-- you can google that too (but beware, some people treat it like a sudden transition, and it's not-- that's just an as if.)

 

[JvanDyne]

Any book on winds that includes the Weber-Davis model would be the starting point. Just go to a library and scan the books on stars for one that has those words in its appendix or table of contents, or google for class lecture notes on that. W-D is 1D, for a journal article on 2D, try http://adsabs.harvard.edu/full/1985A&A...152..121S. The first key thing you will find is that your outflow model must change the situation significantly from a 2D dipole, but that does not necessarily mean more complexity. What's hard is to merge the dipole lower down where the field is strong with the outflow-type field farther out (and then way far out, the solar rotation gives you a "Parker spiral."). That first transition is of significant importance to how the wind carries off angular momentum, and is a subject of current research! Weber-Davis will show you that the transition happens gradually, but can be treated for some purposes as if it occurred rapidly at the Alfven radius. So perhaps your study should begin with the concept of an "Alfven radius"-- you can google that too (but beware, some people treat it like a sudden transition, and it's not-- that's just an as if.)

Thanks, I'll check it out.

I should have been clearer with where I'm currently at: I have been, up to this point, largely shadowing some of the very early work by, in fact, Eugene Parker. My current model neglects rotation, presuming outwardly radial emission and velocity, with dependences of temperature, pressure and density. It is in an embryonic early form, and I have been tasked with continuing to improve it. -- i.e. with the introduction of magnetism and the MHD equations (my choice).