Alpha

Magnetic flux tubes are formed in the convection zone.  As the flux tubes rise through the convection zone they may be twisted by turbulence or they might be created along with some twist. After emergence flux tubes, within active regions, may be further twisted by footpoint motions.

Alpha is a parameter describing the amount of twist in a magnetic field.

From Ampere's Law we have

                                                        (1)

If we assume that active regions are in equilibrium then we have a balance among
Pressure, Gravity, and Magnetic Forces.

                                            (2)

But Fp and Fg are small compared to the magnetic forces so we can say

                                                                        (3)

which implies that J and B are parallel, and also we can combine (1) and (3) to
get.

                (4)

But this implies that curl(B) is parallel to B so it follows that we can write

                                                                  (5)

If alpha is constant we say that there is a linear force free field and if alpha is some function of space
then we say that alpha is a non-linear force free field.

    For a given value of alpha,  the minimum energy state of a closed flux system is known to be a linear force free field. Therefore we might expect magnetic fields to converge to a single value of alpha and in the process release energy somehow, such as in the form of solar flares.