The Earth’s Magnetic Field - Ultra and Extremely Low Frequency Electromagnetic Fields - page 16

Fig. 1.6 A mechanism of
hydromagnetic dynamo due
to the mean helicity of a
conducting medium. Taken
from the site http://www.
astronet.ru/db/msg/1191490

The turbulence can create and twist the loops of toroidal/azimuthal field ǝ B ' Ǜ .
One of such loops is highlighted in Fig. 1.5 with the dotted circle. The same loop is
shown in Fig. 1.6 in a large scale. If the motion of conducting medium has the mean
helicity, there is a predominant direction of twisting of the loops. We recall that the
helicity is described by the term r Ǜ h B i on the right-hand side of Eq. ( 1.25 ). The
implication of this term is that there are not only the conduction current h E i and
the fluid-driven current . h V ih B i / but also the current proportional to Ǜ h B i that
results from the turbulence and helicity of the flow. This means that the azimuthal

component ǝ B ' Ǜ of the mean magnetic field gives rise to the generation of azimuthal

component of mean current since ǝ j ' Ǜ / Ǜ ǝ B ' Ǜ . If the left-handed .Ǜ>0/ helicity

prevails over the right-handed one, the azimuthal current and magnetic field ǝ B ' Ǜ
have the same sign as shown in Fig. 1.6 and vice versa in the inverse case of the
right-handed helicity .Ǜ<0/.
As is seen from Fig. 1.6 , the azimuthal current in turn originates a new component
poloidal/meridional field B p . Notice that the generation of the poloidal field from the
toroidal one follows from Eq. ( 1.25 ). It is clear that substituting the toroidal field B t
into r Ǜ h B i gives the term r Ǜ h B t i which plays a role of source of the poloidal
field B p . To summarize, the poloidal magnetic field in a rotating conductive medium
with nonzero mean helicity induces the toroidal field, which in turn generates the
poloidal field and so on.
The combined action of the mechanisms treated here, that are the inhomogeneous
rotation and the mean helicity, can result in self-excitation of the magnetic field.
Moreover the dynamo-effect may arise at proper conditions even though only the
latter mechanism is operative.

1.1.8 Magnetic Field Structure on the Earth Surface

To first order the Earth magnetic field in the atmosphere and ionosphere can be
approximated by a dipole field. At present the Earth dipole magnetic moment is
about M e 8:3 10 22 A m 2 (Stacey 1969 ; Yanovsky 1978 ). The dipole is slightly