Environmental Engineering Reference
In-Depth Information
From the above results it follows that the Faraday effect is strong in the region
of the cyclotron resonance
H . Then a strong interaction occurs between
the plasma and the electromagnetic wave with left-handed polarization. In partic-
ular, it is possible for the electromagnetic wave with left-handed polarization to be
absorbed, but for the wave with right-handed circular polarization to pass freely
through the plasma. Then the Faraday effect can be detected at small distances.
ω ω
5.2.7
Whistlers
Insertion of a magnetic field into a plasma leads to a large variety of new types
of oscillations in it. We considered above magnetohydrodynamic waves and mag-
netic sound, both of which are governed by elastic magnetic properties of a cold
plasma. In addition to these phenomena, a magnetic field can produce electron
and ion cyclotron waves that correspond to rotation of electrons and ions in the
magnetic field. Mixing of these oscillations with plasma oscillations, ion sound,
and electromagnetic waves creates many types of hybrid waves in a plasma. As an
example of this, we now consider waves that are a mixture of electron cyclotron
and electromagnetic waves. These waves are called whistlers and are observed
as atmospheric electromagnetic waves of low frequency (in the frequency inter-
val 300-30 000 Hz). These waves are a consequence of lightning in the upper at-
mosphere and propagate along magnetic lines of force. They can approach the
magnetosphere boundary and then reflect from it. Therefore, whistlers are used
for exploration of the Earth's magnetosphere up to distances of 5-10 Earth radii.
The whistler frequency is low compared with the electron cyclotron frequency
ω
D
eH /( m e c )
10 7 Hz, and it is high compared with the ion cyclotron fre-
H
10 3 Hz ( M is the ion mass). Below we consider
whistlers as electromagnetic waves of frequency
10 2
quency
ω
D
eH /( Mc )
i H
ω ω
H that propagate in a plas-
ma in the presence of a constant magnetic field.
We employ relation (5.48) to give the oscillatory parameters of a monochromatic
electromagnetic wave. Then (5.68) gives
4
πω
c 2
k 2
E k ( k E )
i j
D
0
(5.75)
where
eN e w ,
where N e is the electron number density. The electron drift velocity follows from
the electron equation of motion (4.157), which, when
ω
kc . We state the current density of electrons in the form j D
ν ω ω
H ,hastheform
e E / m e
H ( w h ), where h is the unit vector directed along the magnetic field.
Substituting this into equation (5.75), we obtain the dispersion relation
D ω
2
p
i j ωω
k 2 ( j h )
k [ k
( j h )]
D
0 ,
(5.76)
H c 2
ω
D p 4
where
N 0 e 2 / m e is the plasma frequency in accordance with (1.13).
We introduce a coordinate system such that the z -axis is parallel to the external
ω
π
p
 
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