The magnetic field of Earth was the first known example of
an astronomical magnetic field. Its form was mapped out by
Gilbert (1600) and its origin was attributed to magnetic
iron oxide. With the work of Pierre Curie at the end of the
19th century, this explanation became untenable and various
atomic effects, e.g. thermoelectricity, were considered. In
1908 Hale showed observationally that a sunspot contains a
magnetic field of a few kilogauss. Larmor (1919) suggested
that the sunspot is a rapidly rotating cyclonic structure
whose circular motion somehow produces the observed magnetic
field. This idea motivated Cowling (1934) to explore the
inductive effects of a conducting fluid flowing in a
magnetic field with axial symmetry, demonstrating his
theorem that such a magnetic field cannot be maintained by
fluid motions alone. Then in 1945 Walter Elsasser pointed
out that none of the known atomic effects are adequate,
leaving only the inductive effects of fluid motions as a
theoretical possibility for the origin of the magnetic field
of Earth. He went on to show that the nonuniform rotation of
the core interacts with the dipole field to produce a strong
azimuthal (toroidal) magnetic field in the core. The
problem, then, was to get around Cowling's dictum that
axisymmetric fields cannot be sustained by fluid motions.
Note, then, that the 24 hour rotation of Earth implies that
the convection in the liquid metal core is cyclonic. It is
obvious that a rotating rising volume of fluid raises a
bulge in the azimuthal field and rotates that upward bulge
into the meridional plane (see the motif on the upper left
hand corner of the home page for this meeting), thereby
producing a net circulation of magnetic field in the
meridional plane. There are many such cyclonic cells at any
given time and resistive dissipation merges them all into an
overall poloidal circulation of magnetic field in the
meridional planes This "alpha effect" amplifies the dipole
field, whose continual shearing by the nonuniform rotation
regenerates the toroidal field (Parker, 1955), providing an
ongoing dynamo. The intermittent contribution of the
individual cyclonic cells was first treated in the "short
sudden approximation", in which the large cyclonic
displacement was introduced as a high speed motion over such
a short period of time that resistive diffusion can be
neglected. Then the cyclonic moltion is switched off while
the resistive diffusion destroys the small-scale field
components, leaving only the overall average dipole magnetic
field. The nonuniform rotation is considered to be steady in
time. The dynamo field equations are naturally formulated in
terms of the azimuthal magnetic field and the azimuthal
vector potential, representing the poloidal magnetic field.
It is immediately obvious from these equations that the
basic mode is a migratory dynamo wave, as observed in the
magnetic field of the Sun (Parker, 1956). When the
propagation of the dynamo wave is blocked by the geometry of
the convecting fluid region, the magnetic field may be
steady in time, as in Earth. Steenbeck, Krause, and Radler
(1966) formulated the physics of the dynamo using the
quasilinear approximation, providing a systematic approach
to the higher order dynamo effects. The "short sudden"
formulation was expanded to all orders (Parker, 1979),
providing such things as the flux expulsion dynamo. The
essential point is that the basic combination of the
nonuniform rotation and the alpha effect, providing a
poloidal field (dipole, quadrupole, etc.)or a simple dynamo
wave, represents the most efficient field generation and may
be presumed to be the origin of the magnetic fields of most
astrophysical bodies. It should be noted that an effective
turbulent diffusion is an essential part of the generation
of the magnetic field in the Sun and other stars, and in the
Galaxy. But there is no theory for how this comes about in
the strong magnetic fields observed. It should also be
appreciated that the intergalactic fields, with scales of a
megaparsec or more, cannot be explained by a dynamo effect,
nor is the origin of the initial "seed field" known.