  A magnetic field dynamo in the inner regions of the accretion disk
surrounding the supermassive black holes in AGNs may be the mechanism for the
generation of magnetic fields in galaxies and in extragalactic space. We argue
that the two coherent motions produced by 1) the Keplerian motion and 2)
star-disk collisions, numerous in the inner region of AGN accretion disks, are
both basic to the formation of a robust, coherent dynamo and consequently the
generation of large scale magnetic fields. They are frequent enough to account
for an integrated dynamo gain, e^{10^{9}} at 100 gravitational radii of a
central black hole, many orders of magnitude greater than required to amplify
any seed field no matter how small. The existence of extra-galactic, coherent,
large scale magnetic fields whose energies greatly exceed all but massive black
hole energies is recognized. In paper II (Pariev, Colgate, and Finn 2006) we
argue that in order to produce a dynamo that can access the free energy of
black hole formation and produce all the magnetic flux in a coherent fashion
the existence of these two coherent motions in a conducting fluid is required.
The differential winding of Keplerian motion is obvious, but the disk structure
depends upon the model of "alpha", the transport coefficient of angular
momentum chosen. The counter rotation of driven plumes in a rotating frame is
less well known, but fortunately the magnetic effect is independent of the disk
model. Both motions are discussed in this paper, paper I. The description of
the two motions are preliminary to two theoretical derivations and one
numerical simulation of the alpha-omega dynamo in paper II. (Abridged)
