The Evolution of a Primordial Galactic Magnetic Field
  We consider the hypothesis that galactic magnetic fields are primordial. We also discuss the various objections to this hypothesis. We assume that there was a magnetic field present in the galactic plasma before the galaxy formed. After the galactic disk formed, the lines of force thread through it and remain connected to the external cosmic medium. They enter through one side of the disk, proceed horizontally a distance $ l $ in the disk, and then leave through the other side. We find that the lines of force are stretched rotation of the galactic disk, which amplifies the toroidal component of the field and increases$l $. When the magnetic field is strong enough, it produces ambipolar velocities that try to lift the line out of the galactic disk but in opposite directions ondifferent parts of the line. The result is, instead of the line being expelled from the disk, its horizontal length $l $ is shortened, both in the radial, and in the toroidal direction. This leads to a reduction of the rate of horizontal stretching, and, finally, a reduction in the magnetic field strength. After a sufficient time, the magnetic field at all points goes through this stretching and reduction, and the field strength approaches a universal function of time. This function is slowly decreasing, and only depends on the ambipolar propertiesof the interstellar medium. At any given time the magnetic field is toroidal, and has the same strength almost everywhere. On the other hand, it turns out that its direction varies rapidly with radius, changing sign every one hundred parsecs field dominate over that of the other. The resulting field has a net Faraday rotation. If such a field were observed with low resolution in an external galaxy then the field would appear toroidal in between the spiral arms. The spiral density wave would turn it so that the lines appear to trace out the spiral arm, 
Armando M. Howard and Russell M. Kulsrud