Geology Reference
In-Depth Information
A small portion of solar wind plasma enters the
magnetosphere along the dayside region near the
polar cusps
, two funnel-shaped areas between
the dayside and the magnetotail. Here, the solar
plasma particles follow the magnetic field lines
towards the Earth's atmosphere (Fig.
4.13
).
Three major regions can be distinguished in
the space around the Earth. In the outer space,
the
interplanetary magnetic field
(IMF) has sub
parallel field lines, and the solar wind stream-
lines are straight lines toward the Earth. The
bow shock
is the shock surface where the solar
wind is suddenly slowed from supersonic to sonic
velocities. It marks the transition to turbulent flow
in the
magnetosheath
, the intermediate region
where IMF geometry and solar wind stream-
lines are affected by the presence of the Earth's
magnetic field. The
magnetopause
is the inner
boundary that separates the magnetosphere from
the outer region. Along the magnetopause, the
inward
dynamic pressure
of the advancing solar
wind plasma is balanced by the outward
magnetic
pressure
of the magnetosphere. To understand
this important concept, let us consider again the
magnetic field inside a long solenoid (Fig.
4.4
),
and let us assume that the coil is infinitely thin
with square cross-section of dimension
h
.Inthis
instance, the current through the solenoid is re-
lated to the current density by:
I
D
jh
2
.If
n
is
the number of turns per unit length, then
h
D
1/
n
.
Therefore, the magnitude of the current density in
the solenoid is given by:
uct in (
4.20
) we take into account that the cur-
rent density vector is always tangent to the coil.
Therefore, the Lorentz force per unit volume,
f
,is
directed radially outwards and has magnitude:
2
n
0
D
B
2
n
2
0
2
h
B
i
f
D
I
h
B
i
n
2
D
(4.54)
wherewehaveused(
4.53
). If
L
and
r
are respec-
tively length and radius of the solenoid, then the
volume of a small slice is
dV
D
rLhd
',where
d
'
is an arc element of the coil circumference. The
area of its internal surface will be
dA
D
rLd
'.
Therefore, the force on the volume element is:
B
2
rLd'
2
0
dF
D
fdV
D
(4.55)
This force determines an outward
pressure
on
the internal surface of the solenoid, which will be
given by the force per unit area:
B
2
2
0
dF
dA
D
P
m
D
(4.56)
The quantity
P
m
is called
magnetic pressure
and can be quite effective. For example, for
B
D
1T,wehave
P
m
Š
4.0
10
5
Pa
D
4bar.Nowlet
us consider the
dynamic pressure
,whichforany
fluid is defined as the
density
of kinetic energy:
1
2
¡
m
u
2
P
d
D
(4.57)
j
D
In
2
(4.52)
where ¡
m
is the mass density and
u
is the fluid
velocity. This quantity contributes to the total
fluid pressure just like the usual hydrostatic pres-
sure. The solar wind is a neutral fluid formed by
positive ions and electrons. For a flow dominated
by protons and electrons, with a typical density
of five protons per cm
3
and an average velocity
u
500 km s
1
, it results:
We know that the magnetic field
B
is zero
outside the solenoid and assumes the uniform
value (
4.34
) in the internal region. The region
occupied by the coil is a transition zone where
the average field is given by:
1
2
B
Š
1
2
0
nI
h
B
iD
(4.53)
2
5cm
3
1:67
10
27
kg
500kms
1
2
1
P
d
D
The presence of a magnetic field within the
coil generates a Lorentz force that can be cal-
culated using (
4.20
). To evaluate the cross prod-
Š
1:04
10
9
Pa
(4.58)
