The α ω Dynamo
We briefly describe how the α ω dynamo works as originally
envisaged by Parker1. We use as an example the dynamo we predict
forms in the accretion disk leading to the massive, central black hole
of presumably every galaxy. The peculiar circumstance of this
astrophysical dynamo avoids the uncertainties of the formation of
plumes by convection in stellar atmospheres. Instead, in this dynamo
the plumes are driven by star collisions with the disk. These stars
are a small faction of the accreting mass that creates the black hole.
These stars periodically collide with or plunge through the low mass
(thickness) disk many times. These plumes are driven with great force
and pressure and so the disk material, with embedded magnetic flux, is
carried to great heights above the disk and also with sufficient heat
and pressure from the collision to greatly expand or diverge in
radius. This divergence in radius causes the differential rotation
observed in the plume experiment [LINK TO PRX]. Thus these star-disk
collisions and the plumes they form create the helicity necessary for
positive dynamo gain. The combination of the Keplerian flow of the
disk and the robust, expanding plumes make the simplest astrophysical
dynamo to visualize, and also the largest dynamos in the universe.
The resulting dynamo mechanism is shown in Fig. 1.
Figure 1: The α ω dynamo in a galactic black hole accretion disk (ANIMATE  ). The initial poloidal quadrupole field within the disk (Panel A) is sheared by the differential rotation within the
disk, developing a strong toroidal component (Panel B). As a star
passes through the disk it heats by shock and by radiation a fraction
of the matter of the disk, which expands vertically and lifts a
fraction of the toroidal flux within an expanding plume (Panel C).
Due to the conservation of angular momentum, the expanding plume and
embedded flux rotate ~ π/2 radians before the plume
falls back to the disk (Panel D). (The Pulsed Jet Rotation
Experiment explains the relative counter-rotation of an expanding
plume in a rotating frame due to conserved angular momentum.)
Reconnection allows the new poloidal flux to merge with and augment
the original poloidal flux (Panel D).
An initial, seed, quadrupole field, Fig. 1(A) establishes a radial
field within the conducting disk. It is then wrapped up
differentially the "Ω" flow, into a much stronger toroidal
field, Fig. 1(B) within the accretion disk by the differential
Keplerian rotation around the central massive black hole. (The black
hole itself is formed by the mass inflow through this accretion
disk. Toroidal flux has just an azimuthal component; poloidal flux has
both radial and axial components.) A plume driven by a star-disk
collision carries a fraction of this now multiplied toroidal flux,
embedded in the conducting matter of the disk as a loop above the
surface of the disk, Fig. 1(C). Expansion of the plume in the near
vacuum above (and below) the disk causes differential rotation of the
plume matter which carries and twists this loop of toroidal flux,
~ π/2 radians, into the orthogonal, poloidal plane, Fig. 1(C).
Reconnection allows this loop of flux to merge with the original
quadrupole flux, Fig. 1(D), thereby augmenting the initial quadrupole
field. For positive dynamo gain, the rate of adding these increments
of poloidal flux must exceed the negative quadrupole resistive decay
rate. The Ω flow of the dynamo is the differential rotation of
this experiment. The α effect is derived from the plumes and
their rotation.
A robust dynamo has long been sought in both theory and experiment,
but has eluded very many attempts of proof (e.g. Roberts and
Soward2). Recently Rädler3 and Gailitis4 have
announced positive gain in laboratory sodium dynamos. These dynamos
are of the pure helicity, or α2 type where the helical flow is
driven by multiple shaped vanes. It is recognized that an
astrophysical dynamo must be much less constrained, resulting from
flows occurring naturally without ridged materials. In addition,
Forest5 and collaborators are testing a liquid sodium model of a
dynamo of the Dudley and James6 type.
1E.N. Parker, Cosmical Magnetic Fields: Their
Origin and Their Activity (Claredon Press, New York, 1978).
2P.H. Roberts and A.M. Soward, "Dynamo Theory,"
Ann. Rev. Fluid Mech. 24 459 (1992).
3K.-H. Rädler, E. Apstein, M. Rheinhardt, and M.
Schüler, "The Karlsruhe Dynamo Experiment; a Mean Field Approach"
Studis geoph. et geod. (Prague) 42 1-9 (1988). http://www.aip.de/~preprint/preprints/1998/1998_tres5.5.html
4 A. Gailitis, O. Lielausis, S. Dement'ev, E. Platacis,
A. Cifersons, et al. "Detection of a Flow Induced Magnetic Field
Eigenmode in the Riga Dynamo Facility" Phys. Rev. Let. 84
4365-4368 (2000).
5 C. Forest, Madison Wisconsin Dynamo Experiment,
http://aida.physics.wisc.edu/
6 Dudley and James, Proc. of the Roy. Soc. London A,
Vol. 425 pp. 407-429 (1989).
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