Geoscience Reference
In-Depth Information
Now we estimate the solar wind pressure. Equation of state of an ideal gas can be
applied to the solar wind particles to relate the number density n
j
and the pressure
P
j
of each species
P
j
D
n
j
k
B
T
j
;
(1.45)
where the subscript “j” stands for the j-th ionized species, i.e., ions or electrons.
In this text we use k
B
to represent Boltzmann's constant. The mass density
j
relates to the number density n
j
through
j
D
n
j
m
j
where m
j
is the particle
mass of each species. Now we will estimate the ratio between the pressure P due
to the thermal motion and the dynamic pressure V
2
resulted from the solar wind
motion. Taking the numerical values of the solar wind parameters T
D
10-40 eV,
and V
D
300-800 km/s we get P=V
2
k
B
T=m
P
V
2
0.04-0.004, where m
P
is
the proton/neutron mass. This means that the dynamic pressure dominates over the
thermal one in the solar wind.
To estimate scale size of the magnetosphere on its upstream/sunlit side, we
consider the bow shock at the ecliptic plane and the point A (Fig.
1.8
), which is
nearest to the Sun. Since the magnetic field is perpendicular to this plane, Eq. (
1.42
)
is reduced to
V
n
C
P
C
B
2
2
0
D
0:
(1.46)
We set B
D
0 in the solar wind because the interplanetary magnetic field is
neglected. In the magnetosphere the dynamic pressure of plasma can be dropped
since the flow is slowed across the shock. Additionally P is everywhere negligible
compared with V
2
. In this notation, the pressure balance at the boundary between
the solar wind and the magnetosphere yields V
2
B
2
=.2
0
/. Below we slightly
specify this rough estimate.
The magnetosphere thus serves as an obstacle in such a way that the solar plasma
flows around the magnetosphere. Assuming a perfect/mirror reflection of the solar
wind from the boundary, then the dynamic pressure of the solar wind is estimated
as 2V
2
that is twice as great as that under inelastic reflection. Since the Earth'
magnetic field (
1.32
) is approximately doubled inside the magnetosphere, we get
the assessment
M
e
4r
0
2
B
2
2
0
D
0
2
2V
2
;
(1.47)
where M
e
is the dipole moment of the Earth magnetic field, and r
0
is geocentric dis-
tance of the magnetopause on the sunward side of the magnetosphere. Substituting
the numerical parameters into Eq. (
1.47
) gives the value r
0
10R
e
. This estimate
is compatible with observations, which show that the bow shock forms at about 13
Earth radii on the sunlit side of our planet.
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