Environmental Engineering Reference
In-Depth Information
Let us make simple estimations for capture of fast protons by the Earth's mag-
netic field when protons are moving as shown in Figure 4.29. For definiteness, we
take a beam of protons of energy 100 keV that crosses magnetic lines of force at lat-
itudes corresponding to the equator. This beam is captured by the magnetic field at
distances
R
from the Earth where the Larmor radius
r
L
for protons is comparable
to this distance. Because the proton velocity is
10
8
cm/s at this energy, we
D
4
v
p
obtain from the above criterion
s
0
R
3
˚
ω
R
70
R
˚
,
v
p
10
3
Hz is the Larmor frequency at the equator near the Earth's
surface and
R
˚
is the Earth's radius. Being captured, protons are moving along an
appropriate magnetic line of force and approach the Earth near its poles, where the
Larmor radius of protons is
r
L
where
ω
D
3
0
1 km. The protons may be reflected in regions of
high magnetic field strength, as shown in Figure 4.29 or may penetrate the Earth's
atmosphere depending on the angle with the magnetic line of force when they are
captured by the Earth's magnetic field. If protons penetrate the Earth's atmosphere
in the polar region, they their energy is partially used in excitation of atmospher-
ic atoms and molecules and causes glowing of the atmosphere. In this manner
auroras occur that are observed at latitudes near the Earth poles.
Along with the character of motion of charged particles in the Earth's atmosphere
shown in Figure 4.28, when charged particles move along a helical trajectory, par-
ticle motion along an elliptic trajectory is possible if the particle energy is high
enough. There are so-called radiation belts where fast electrons and protons are
captured by the Earth's magnetic field. These regions are located at a distance of
several Earth radii from the Earth's surface, and captured fast electrons and pro-
tons may have an energy of several million electronvolts. Although along with the
Earth's magnetic field other factors provide the stability of the radiation belts, we
now estimate the depth of the potential well for a captured electron. Using (4.148),
we have for the maximum depth of the magnetic potential well
U
max
for an electron
U
0
R
R
4
R
2
10
10
MeV .
U
max
D
μ
H
D
do
,
U
0
D
e
ω
π
˚
D
1.7
0
Here
R
is the distance from the Earth's surface,
do
is the solid angle related to
the electron trajectory, so that the area
S
R
2
do
is located inside the electron
D
π
10
6
s
1
is the Larmor frequency for an electron located
near the equator and the Earth's surface. As is seen, the depth of the magnetic
well in this case is large enough to trap electrons. Because of their larger mass,
protons have a longer lifetime in the Earth's magnetic trap than do electrons, and
hence the number of captured protons is greater than that for electrons if this
lifetime is determined by collisions with atmospheric atoms. In addition, owing to
the influence of the solar wind, this magnetic trap acts more effectively on the side
of the Earth opposite the Sun.
trajectory, and
ω
D
5.5
0
