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becomes very large, then the parallel electric field component vanishes. For many
applications, MHD theory applies on the high-altitude portions of the field lines
that contact the ionosphere. This theory is discussed in the next section in the
context of the “frozen-in” condition.
The implication of these calculations is that large-scale electrical features per-
pendicular to
B
map for long distances along the earth's magnetic field lines. This
has been verified experimentally via the simultaneous measurements shown in
Fig. 2.8. In this experiment the zonal electric field component was measured
in the Northern Hemispheric ionosphere with the Millstone Hill Radar (see
Appendix A) and in the inner magnetosphere at a point very close to where
the same magnetic field line crossed the equatorial plane. The latter measure-
ment was accomplished using the whistler technique (Carpenter et al., 1972).
The two measurements clearly have the same temporal form, but the magneto-
spheric component is 10 times smaller. This difference may be explained as a
geometric effect arising from the spreading of the magnetic field lines as follows.
First we take
σ
0
to be infinite so that the field lines act like perfect conductors.
This implies that there is no potential difference along them and in turn that
the voltage difference between two lines is conserved. The magnetic flux density
(measured in tesla) decreases along the field line as a function of distance from the
mid- or high-latitude ionosphere to the equatorial plane in the magnetosphere.
Since the voltage between adjacent field lines is constant, the perpendicular
9 - 10 July, 1978
E
E
2.5
0.0
0.25
E
E
0.0
Whistlers
(
L
>
3.5
2
4.7)
00
04
08
12
U T
Figure 2.8
Electric field components perpendicular to the magnetic field. The top panel
is a measurement of the zonal electric field in the ionosphere. The lower panel is a mea-
surement of the zonal electric field at the equatorial plane on the same magnetic field line.
[After Gonzales et al. (1980). Reproduced with permission of the American Geophysical
Union.]
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