Geoscience Reference
In-Depth Information
V
A
L
z
V
SW
B
SW
E
SW
B
SW
J
II
J
SW
L
x
L
y
J
II
V
B
PC
Dawn
E
PC
Dusk
Figure 8.1a
Schematic representation of the magnetic connection between the solar wind
dynamo and the ionospheric load. Note that
J
×
B
in the solar wind is toward the sun.
Our goal here is to make a simplified but interesting estimate of the percentage
change of the solar wind velocity as it streams by the earth. We argue that what
controls this slowdown in part is the conductivity of the polar cap ionospheres.
This is characterized by the magnetic field line-integrated Pedersen conductivity,
P
, which is the electrical load on the MHD generator.
The total current enclosed in the polar cap is
I
pc
=
P
L
pc
E
pc
, where
L
pc
is the
size of the polar cap and
E
pc
is the dawn-to-dusk component of the polar cap
electric field. Since
P
can be very different in the two hemispheres at solstice,
we treat each polar cap separately.
I
pc
must be closed in the solar wind. Its value
is given by the expression
I
sw
=
J
sw
L
T
L
z
, where
L
T
is the distance the field line
moves before it reconnects in the magnetotail and
L
z
is the distance along the
IMF in which an Alfvén wave travels in this time. For a “square” polar cap we
have
L
z
=
V
A
δ
t
, where
δ
t
=
(
L
pc
B
pc
)/
E
pc
, since the polar cap velocity is
E
pc
/
B
pc
.
Likewise,
L
T
=
t
.
By Kirchoff's current law,
I
pc
=
V
sw
δ
I
sw
and thus,
J
sw
=
P
L
pc
E
pc
L
T
L
z
.
(8.8)
The current density can also be expressed as
dV
sw
dt
J
sw
=
(ρ/
B
sw
)
.
(8.9)
Search WWH ::
Custom Search