Environmental Engineering Reference
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From this it follows that the wave has circular polarization. This wave propagating
along the magnetic field therefore has a helical structure. The direction of rotation
of wave polarization is the same as the direction of electron rotation. The develop-
ment of such a wave can be described as follows. Suppose electrons in a certain
region possess a velocity perpendicular to the magnetic field. This electron motion
gives rise to an electric field and compels electrons to circulate in the plane perpen-
dicular to the magnetic field. This perturbation is transferred to the neighboring
regions with a phase delay. Such a wave is known as a helicon wave.
5.3
Plasma Instabilities
5.3.1
Damping of Plasma Oscillations in Ionized Gases
Interaction of electrons and atoms leads to damping of plasma oscillations because
electron-atom collisions shift the phase of the electron vibration and change the
character of collective interaction of electrons in plasma oscillations. We shall take
this fact into account below, and include it in the dispersion relation for the plasma
oscillations. To obtain this relation, we use (4.9) instead of (4.6) as the equation
for the average electron momentum. Then the second equation in set (5.56) is
transformed into
kp 0
m e N 0 C
eE 0
m e D
w 0
τ
w 0 C
i
ω
i
,
(5.82)
and the remaining equations of this set are unchanged. Here
τ
is the characteristic
time for elastic electron-atom collisions.
Replacing the first equation in system (5.56) by (5.82), we obtain the dispersion
relation in the form
q
C γ ˝ v
x ˛ k 2
i
τ
ω D
ω
2
p
(5.83)
instead of (5.57). This dispersion relation requires the condition
ωτ
1 .
(5.84)
Substituting dispersion relation (5.83) into (5.48), we find that the wave ampli-
tude decreases with time as exp(
), where this decrease is due to the scattering
of electrons by atoms of the gas. The condition for existence of plasma oscillations
is such that the characteristic time of the wave damping must be considerably high-
er than the oscillation period; namely, inequality (5.84) must hold. The frequency of
collisions between electrons and atoms is 1/
t /
τ
τ
N
σ v ,where N is the atom num-
ber density, v
is the cross section for
electron-atom collisions. Assuming this cross section to be of the order of a gas-
kinetic cross section, the mean electron energy to be approximately 1 eV, and the
is a typical velocity of the electrons, and
σ
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